{ "nbformat": 4, "nbformat_minor": 0, "metadata": { "colab": { "provenance": [], "include_colab_link": true }, "kernelspec": { "name": "python3", "display_name": "Python 3" } }, "cells": [ { "cell_type": "markdown", "metadata": { "id": "view-in-github", "colab_type": "text" }, "source": [ "\"Open" ] }, { "cell_type": "markdown", "metadata": { "id": "_k5tMB9V9yTc" }, "source": [ "# [복원추출하여 만든 표본의 표본평균의 표본분포 예제(Sege Math 이용)(Example of the Sampling Distribution of the Sample Mean of a Random Sample with Replacement )](https://min7014.github.io/math20230327001.html)\n" ] }, { "cell_type": "markdown", "source": [ "((Example of the Sampling Distribution of the Sample Mean of a Random Sample with Replacement))\n", "\n", "심볼릭 계산을 이용해서인지 근사값으로 계산되지 않아 정확히 값이 딱 떨어진다.\n" ], "metadata": { "id": "hvLEyFDYdE7d" } }, { "cell_type": "markdown", "source": [ "\n", "\n", "```\n", "number_of_sample:=1\n", "size_of_product_of_population:= 5\n", "size_of_sample_space_of_product_of_population:= 5\n", "size_of_range_of_sample_mean_as_duplicates:=5\n", "range_of_sample_mean:=[1, 3, 5, 7, 9]\n", "size_of_range_of_sample_mean:=5\n", "distribution_of_sample_mean:=[[1, 1/5], [3, 1/5], [5, 1/5], [7, 1/5],[9, 1/5]]\n", "mean_of_sample_mean:=5\n", "variance_of_sample_mean:=8\n", "[-1, 1, 3, 5, 7, 9, 11]\n", "[0, 1/5, 1/5, 1/5, 1/5, 1/5, 0]\n", "```\n", "\n" ], "metadata": { "id": "163GiNEsgJFg" } }, { "cell_type": "markdown", "source": [ "![image.png](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAxAAAAJICAIAAAB+MZWEAAAgAElEQVR4Ae2dD6ydd13/zy1lvSWga5cN1nXrLS4OlmyBmNlu/m2yaI54pGZBQClroy4sJA2orVaBadBKa9QsrE5HNOnAs7ZBtOCEiBI349K0HlbGxpybTQuhwU4ilUZCDff8cnd/nlzvec7tc1+f53k+9/S+ThZyzvc8n+/3nNfnfs77tdNy1+p7k4AEJCABCUhAAhJYkEBrwWd9UgISkIAEJCABCUigrzD5QyABCUhAAhKQgAQuQUBhugQgn5aABCQgAQlIQAIKkz8DEpCABCQgAQlI4BIEFKZLAPJpCUhAAhKQgAQkoDD5MyABCUhAAhKQgAQuQUBhugQgn5aABCQgAQlIQAIKkz8DEpCABCQgAQlI4BIElrswTU9Pnz9/fnp6+hKcfFoCEpCABCQggWVMYLkL0/nz51ut1vnz55fxz4BvXQISkIAEJCCBSxBQmBSmS/yI+LQEJCABCUhAAgqTwuQUSEACEpCABCRwCQIKk8J0iR8Rn5aABCQgAQlIQGFSmJwCCUhAAhKQgAQuQWBchemBBx6YmpqanJzctGnT8ePHh9/lRz7ykR/6oR9a89LtzjvvLLym3+/7l76H0bkiAQlIQAISkMA8AmMpTIcOHVq1atXBgwefffbZe+65Z82aNS+++OK8N/aOd7zjwQcf/MIXvvDcc8/t2LHjyiuvPHv27LxrFKZhIK5IQAISkIAEJDBMYCyFadOmTTt37px9M9PT09ddd92+ffuG39tg5Tvf+c53fdd3ffSjHx2sDO74DdMAhXckIAEJSEACEhhFYPyE6eLFiytXrjx69OjgLd19991bt24dPBy+81//9V+rV69+9NFHh59SmIaZuCIBCUhAAhKQwDwC4ydMZ8+enZiYOHbs2OCd7N69e/PmzYOHw3fuvffeG2+88dvf/vbwUwrTMBNXJCABCUhAAhKYR+ByEKZdu3bdfvvt897Y4OHv/u7vXnXVVU8//fRgZe6dJSJMZ86c6XlDBJ544glUZ1FPdOyHQG6MW6/njxwm1ztz5szc5PJ+CoHxE6ZF/ZHc7/3e761Zs+bzn//8KLizwtRutztzbt1ud9T1dayfOXNmcvIVLW+QwMtgnWUt0bEfArkxbq2WP3KU3OTkK3SmOvJ3UXuOnzD1+/15f+l7/fr1+/fvH37b+/fvv/LKK0f9QoHZ65fCN0y9Xu+lIfpYq9Xzn0US+KDoFkls8DMmugGKRd2R26Jwzb1YdHNpLOr+x1qtVq/XG445V5okMJbCdPjw4cnJycGvFVi7du25c+f6/f62bdv27Nkzi2/fvn2rVq36xCc+8bX/vV24cGGY7FISpl6r1fefRRKY+Rx5yRhEt1gColsssdnr5ca49Vst0WF0M/9SrTANJ3jDK2MpTP1+/8CBAxs2bJicnNy8efOJEydmqW3ZsmXHjh2z96emplb839tv/dZvDcNVmBYpKHjgayr0IxiDFR1DJzfGTWHC3Pov/TuhwjQc4E2vjKswVcVJYVKYxpwA/hQ2+Bk6uTFuChPmpjBVFfjRfRSm/P+W3P/+HSb/SA58oJheANpsiegYOrkxbgoT5qYwRUWnqnqFSWGKjHF6remFWyA6hk5ujJvChLkpTFUJT3QfhUlhioxxeq3phVsgOoZOboybwoS5KUxR0amqXmFSmCJjnF5reuEWiI6hkxvjpjBhbgpTVcIT3UdhUpgiY5xea3rhFoiOoZMb46YwYW4KU1R0qqpXmBSmyBin15peuAWiY+jkxrgpTJibwlSV8ET3UZgUpsgYp9eaXrgFomPo5Ma4KUyYm8IUFZ2q6hUmhSkyxum1phdugegYOrkxbgoT5qYwVSU80X0UJoUpMsbptaYXboHoGDq5MW4KE+amMEVFp6p6hUlhioxxeq3phVsgOoZOboybwoS5KUxVCU90H4VJYYqMcXqt6YVbIDqGTm6Mm8KEuSlMUdGpql5hUpgiY5xea3rhFoiOoZMb46YwYW4KU1XCE91HYVKYImOcXmt64RaIjqGTG+OmMGFuClNUdKqqV5gUpsgYp9eaXrgFomPo5Ma4KUyYm8JUlfBE91GYFKbIGKfXml64BaJj6OTGuClMmJvCFBWdquoVJoUpMsbptaYXboHoGDq5MW4KE+amMFUlPNF9FCaFKTLG6bWmF26B6Bg6uTFuChPmpjBFRaeqeoVJYYqMcXqt6YVbIDqGTm6Mm8KEuSlMVQlPdB+FSWGKjHF6remFWyA6hk5ujJvChLkpTFHRqapeYVKYImOcXmt64RaIjqGTG+OmMGFuClNVwhPdR2FSmCJjnF5reuEWiI6hkxvjpjBhbgpTVHSqqleYZoSp3W53Op1ut1sV1kXt0+v1WjO3XqsVmajlWWt64b6LjqGTG+OmMGFuCtOiErXGixUmv2GKjHF6remFWyA6hk5ujJvChLkpTDU60KK2VpgUpsgYp9eaXrgFomPo5Ma4KUyYm8K0KKup8WKFSWGKjHF6remFWyA6hk5ujJvChLkpTDU60KK2VpgUpsgYp9eaXrgFomPo5Ma4KUyYm8K0KKup8WKFSWGKjHF6remFWyA6hk5ujJvChLkpTDU60KK2VpgUpsgYp9eaXrgFomPo5Ma4KUyYm8K0KKup8WKFSWGKjHF6remFWyA6hk5ujJvChLkpTDU60KK2VpgUpsgYp9eaXrgFomPo5Ma4KUyYm8K0KKup8WKFSWGKjHF6remFWyA6hk5ujJvChLkpTDU60KK2VpgUpsgYp9eaXrgFomPo5Ma4KUyYm8K0KKup8WKFSWGKjHF6remFWyA6hk5ujJvChLkpTDU60KK2VpgUpsgYp9eaXrgFomPo5Ma4KUyYm8K0KKup8WKFSWGKjHF6remFWyA6hk5ujJvChLkpTDU60KK2VpgUpsgYp9eaXrgFomPo5Ma4KUyYm8K0KKup8WKFSWGKjHF6remFWyA6hk5ujJvChLkpTDU60KK2VpgUpsgYp9eaXrgFomPo5Ma4KUyYm8K0KKup8WKFSWGKjHF6remFWyA6hk5ujJvChLkpTDU60KK2VpgUpsgYp9eaXrgFomPo5Ma4KUyYm8K0KKup8WKFSWGKjHF6remFWyA6hk5ujJvChLkpTDU60KK2VpgUpsgYp9eaXrgFomPo5Ma4KUyYm8K0KKup8WKFSWGKjHF6remFWyA6hk5ujJvChLkpTDU60KK2VpgUpsgYp9eaXrgFomPo5Ma4KUyYm8K0KKup8WKFSWGKjHF6remFWyA6hk5ujJvChLkpTDU60KK2VpgUpsgYp9eaXrgFomPo5Ma4KUyYm8K0KKup8WKFSWGKjHF6remFWyA6hk5ujJvChLkpTDU60KK2VpgUpsgYp9eaXrgFomPo5Ma4KUyYm8K0KKup8WKFaUaY2u12p9Ppdrs1kh69da/Xa83ceq1WZKKWZ63phfsuOoZOboybwoS5KUyj47PZZxQmv2GKjHF6remFWyA6hk5ujJvChLkpTM1q0ejTFCaFKTLG6bWmF26B6Bg6uTFuChPmpjCNVphmn1GYFKbIGKfXml64BaJj6OTGuClMmJvC1KwWjT5NYVKYImOcXmt64RaIjqGTG+OmMGFuCtNohWn2GYVJYYqMcXqt6YVbIDqGTm6Mm8KEuSlMzWrR6NMUJoUpMsbptaYXboHoGDq5MW4KE+amMI1WmGafUZgUpsgYp9eaXrgFomPo5Ma4KUyYm8LUrBaNPk1hUpgiY5xea3rhFoiOoZMb46YwYW4K02iFafYZhUlhioxxeq3phVsgOoZOboybwoS5KUzNatHo0xQmhSkyxum1phdugegYOrkxbgoT5qYwjVaYZp9RmBSmyBin15peuAWiY+jkxrgpTJibwtSsFo0+TWFSmCJjnF5reuEWiI6hkxvjpjBhbgrTaIVp9hmFSWGKjHF6remFWyA6hk5ujJvChLkpTM1q0ejTFCaFKTLG6bWmF26B6Bg6uTFuChPmpjCNVphmn1GYFKbIGKfXml64BaJj6OTGuClMmJvC1KwWjT5NYVKYImOcXmt64RaIjqGTG+OmMGFuCtNohWn2GYVJYYqMcXqt6YVbIDqGTm6Mm8KEuSlMzWrR6NMUJoUpMsbptaYXboHoGDq5MW4KE+amMI1WmGafUZgUpsgYp9eaXrgFomPo5Ma4KUyYm8LUrBaNPk1hUpgiY5xea3rhFoiOoZMb46YwYW4K02iFafYZhUlhioxxeq3phVsgOoZOboybwoS5KUzNatHo0xQmhSkyxum1phdugegYOrkxbgoT5qYwjVaYZp9RmBSmyBin15peuAWiY+jkxrgpTJibwtSsFo0+TWFSmCJjnF5reuEWiI6hkxvjpjBhbgrTaIVp9hmFSWGKjHF6remFWyA6hk5ujJvChLkpTM1q0ejTFCaFKTLG6bWmF26B6Bg6uTFuChPmpjCNVphmn1GYZoSp3W53Op1ut9ss/P9/Wq/Xa83ceq1WZKKWZ63phfsuOoZOboybwoS5KUwpyVxwqMLkN0yRMU6vNb1wC0TH0MmNcVOYMDeFqcBdUpYUJoUpMsbptaYXboHoGDq5MW4KE+amMKXYUcGhCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5gK3CVlSWFSmCJjnF5reuEWiI6hkxvjpjBhbgpTih0VHKowKUyRMU6vNb1wC0TH0MmNcVOYMDeFqcBdUpYUJoUpMsbptaYXboHoGDq5MW4KE+amMKXYUcGhCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5gK3CVlSWFSmCJjnF5reuEWiI6hkxvjpjBhbgpTih0VHKowKUyRMU6vNb1wC0TH0MmNcVOYMDeFqcBdUpYUJoUpMsbptaYXboHoGDq5MW4KE+amMKXYUcGhCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5gK3CVlSWFSmCJjnF5reuEWiI6hkxvjpjBhbgpTih0VHKowKUyRMU6vNb1wC0TH0MmNcVOYMDeFqcBdUpYUJoUpMsbptaYXboHoGDq5MW4KE+amMKXYUcGhCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5gK3CVlSWFSmCJjnF5reuEWiI6hkxvjpjBhbgpTih0VHKowKUyRMU6vNb1wC0TH0MmNcVOYMDeFqcBdUpYUJoUpMsbptaYXboHoGDq5MW4KE+amMKXYUcGhCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5gK3CVlSWFSmCJjnF5reuEWiI6hkxvjpjBhbgpTih0VHKowKUyRMU6vNb1wC0TH0MmNcVOYMDeFqcBdUpYUJoUpMsbptaYXboHoGDq5MW4KE+amMKXYUcGhCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5gK3CVlSWFSmCJjnF5reuEWiI6hkxvjpjBhbgpTih0VHKowKUyRMU6vNb1wC0TH0MmNcVOYMDeFqcBdUpYUphlharfbnU6n2+2m9KDX67Vmbr1WKzJRy7PW9MJ9Fx1DJzfGTWHC3BSmlGQuOFRh8humyBin15peuAWiY+jkxrgpTJibwlTgLilLCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5hS7KjgUIVJYYqMcXqt6YVbIDqGTm6Mm8KEuSlMBe6SsqQwKUyRMU6vNb1wC0TH0MmNcVOYMDeFKcWOCg5VmBSmyBin15peuAWiY+jkxrgpTJibwlTgLilLCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5hS7KjgUIVJYYqMcXqt6YVbIDqGTm6Mm8KEuSlMBe6SsqQwKUyRMU6vNb1wC0TH0MmNcVOYMDeFKcWOCg5VmBSmyBin15peuAWiY+jkxrgpTJibwlTgLilLCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5hS7KjgUIVJYYqMcXqt6YVbIDqGTm6Mm8KEuSlMBe6SsqQwKUyRMU6vNb1wC0TH0MmNcVOYMDeFKcWOCg5VmBSmyBin15peuAWiY+jkxrgpTJibwlTgLilLCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5hS7KjgUIVJYYqMcXqt6YVbIDqGTm6Mm8KEuSlMBe6SsqQwKUyRMU6vNb1wC0TH0MmNcVOYMDeFKcWOCg5VmBSmyBin15peuAWiY+jkxrgpTJibwlTgLilLCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5hS7KjgUIVJYYqMcXqt6YVbIDqGTm6Mm8KEuSlMBe6SsqQwKUyRMU6vNb1wC0TH0MmNcVOYMDeFKcWOCg5d0sL0wAMPTE1NTU5Obtq06fjx48Mv/5lnnrnrrrumpqYmJibuv//+uRf85m/+5sSc2+tf//q5zw7unz+vMEXGOL3W9MItEB1DJzfGTWHC3BSmQWIn31m6wnTo0KFVq1YdPHjw2Wefveeee9asWfPiiy/Oo3XixIndu3cfPnx43bp1w8J0yy23nDt37t9fun3961+fVzv7UGFqtSJjnF5reuEWiI6hkxvjpjBhbgpTYXonLC5dYdq0adPOnTtnkUxPT1933XX79u0bRWhqampYmN74xjeOun6wrjApTGNOAH8KG/wMndwYN4UJc1OYBomdfGeJCtPFixdXrlx59OjRAZ67775769atg4fz7hQK0ytf+cp169a99rWv/bmf+7kvf/nL80pmHypMY64Lphf+FBYdQyc3xk1hwtwUpsL0TlhcosJ09uzZiYmJY8eODZDs3r178+bNg4fz7gwL02c+85mPf/zjX/ziF//2b//2jjvumJqaunDhwryqfr+vMClMY04Afwob/Ayd3Bg3hQlzU5iGoztnZWyEadeuXbfffvsoSMPCNPfKb3zjG9/93d/9Z3/2Z3MXZ+8rTGOuC6YX/hQWHUMnN8ZNYcLcFKbh6M5ZWaLCFP8juXk4b7vttl//9V+ftzj4hqndbnfm3Lrd7vCV9a30er3WzK035u4S+TjAtaaX6DABVuiPHOOmMGFuClN98bu4nZeoMPX7/Xl/6Xv9+vX79+8f9eYW/obpm9/85tq1az/84Q8Pl/sN05hbmumFP4VFx9DJjXFTmDA3hWk4unNWlq4wHT58eHJycvBrBdauXXvu3Ll+v79t27Y9e/bM0rp48eLJkyeffPLJdevW7d69++TJky+88MLsU7/yK7/y2GOPnT59+p/+6Z/uvPPOa6655j/+4z+GGStMCtOYE8CfwgY/Qyc3xk1hwtwUpuHozllZusLU7/cPHDiwYcOGycnJzZs3nzhxYpbQli1bduzYMXv/9OnTExMTK+bctmzZMvvU2972tuuuu25ycvL6669/+9vffurUqULACtOY64LphT+FRcfQyY1xU5gwN4WpML0TFpe0MDXAQ2FSmMacAP4UNvgZOrkxbgoT5qYwNeACpY5QmPxPo0TGOL3W9MItEB1DJzfGTWHC3BSmUjbTwEUKk8IUGeP0WtMLt0B0DJ3cGDeFCXNTmBpwoVJHKEwKU2SM02tNL9wC0TF0cmPcFCbMTWEqZTMNXKQwKUyRMU6vNb1wC0TH0MmNcVOYMDeFqQEXKnWEwqQwRcY4vdb0wi0QHUMnN8ZNYcLcFKZSNtPARQqTwhQZ4/Ra0wu3QHQMndwYN4UJc1OYGnChUkcoTApTZIzTa00v3ALRMXRyY9wUJsxNYSplMw1cpDApTJExTq81vXALRMfQyY1xU5gwN4WpARcqdYTCpDBFxji91vTCLRAdQyc3xk1hwtwUplI208BFCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5gacKFSRyhMClNkjNNrTS/cAtExdHJj3BQmzE1hKmUzDVykMClMkTFOrzW9cAtEx9DJjXFTmDA3hakBFyp1hMKkMEXGOL3W9MItEB1DJzfGTWHC3BSmUjbTwEUKk8IUGeP0WtMLt0B0DJ3cGDeFCXNTmBpwoVJHKEwKU2SM02tNL9wC0TF0cmPcFCbMTWEqZTMNXKQwKUyRMU6vNb1wC0TH0MmNcVOYMDeFqQEXKnWEwqQwRcY4vdb0wi0QHUMnN8ZNYcLcFKZSNtPARQqTwhQZ4/Ra0wu3QHQMndwYN4UJc1OYGnChUkcoTApTZIzTa00v3ALRMXRyY9wUJsxNYSplMw1cpDApTJExTq81vXALRMfQyY1xU5gwN4WpARcqdYTCpDBFxji91vTCLRAdQyc3xk1hwtwUplI208BFCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5gacKFSRyhMM8LUbrc7nU632y3FrOqLer1ea+bWa7UiE7U8a00v3HfRMXRyY9wUJsxNYao6dOl+CpPfMEXGOL3W9MItEB1DJzfGTWHC3BQmKjhV1ylMClNkjNNrTS/cAtExdHJj3BQmzE1hqlp86H4Kk8IUGeP0WtMLt0B0DJ3cGDeFCXNTmKjgVF2nMClMkTFOrzW9cAtEx9DJjXFTmDA3halq8aH7KUwKU2SM02tNL9wC0TF0cmPcFCbMTWGiglN1ncKkMEXGOL3W9MItEB1DJzfGTWHC3BSmqsWH7qcwKUyRMU6vNb1wC0TH0MmNcVOYMDeFiQpO1XUKk8IUGeP0WtMLt0B0DJ3cGDeFCXNTmKoWH7qfwqQwRcY4vdb0wi0QHUMnN8ZNYcLcFCYqOFXXKUwKU2SM02tNL9wC0TF0cmPcFCbMTWGqWnzofgqTwhQZ4/Ra0wu3QHQMndwYN4UJc1OYqOBUXacwKUyRMU6vNb1wC0TH0MmNcVOYMDeFqWrxofspTApTZIzTa00v3ALRMXRyY9wUJsxNYaKCU3WdwqQwRcY4vdb0wi0QHUMnN8ZNYcLcFKaqxYfupzApTJExTq81vXALRMfQyY1xU5gwN4WJCk7VdQqTwhQZ4/Ra0wu3QHQMndwYN4UJc1OYqhYfup/CpDBFxji91vTCLRAdQyc3xk1hwtwUJio4VdcpTApTZIzTa00v3ALRMXRyY9wUJsxNYapafOh+CpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5io4FRdpzApTJExTq81vXALRMfQyY1xU5gwN4WpavGh+ylMClNkjNNrTS/cAtExdHJj3BQmzE1hooJTdZ3CpDBFxji91vTCLRAdQyc3xk1hwtwUpqrFh+6nMClMkTFOrzW9cAtEx9DJjXFTmDA3hYkKTtV1CpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5iqFh+6n8KkMEXGOL3W9MItEB1DJzfGTWHC3BQmKjhV1ylMM8LUbrc7nU63260ab6n9er1ea+bWa7UiE7U8a00v3HfRMXRyY9wUJsxNYSqVpA1cpDD5DVNkjNNrTS/cAtExdHJj3BQmzE1hasCFSh2hMClMkTFOrzW9cAtEx9DJjXFTmDA3hamUzTRwkcKkMEXGOL3W9MItEB1DJzfGTWHC3BSmBlyo1BEKk8IUGeP0WtMLt0B0DJ3cGDeFCXNTmErZTAMXKUwKU2SM02tNL9wC0TF0cmPcFCbMTWFqwIVKHaEwKUyRMU6vNb1wC0TH0MmNcVOYMDeFqZTNNHCRwqQwRcY4vdb0wi0QHUMnN8ZNYcLcFKYGXKjUEQqTwhQZ4/Ra0wu3QHQMndwYN4UJc1OYStlMAxcpTApTZIzTa00v3ALRMXRyY9wUJsxNYWrAhUodoTApTJExTq81vXALRMfQyY1xU5gwN4WplM00cJHCpDBFxji91vTCLRAdQyc3xk1hwtwUpgZcqNQRCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5hK2UwDFylMClNkjNNrTS/cAtExdHJj3BQmzE1hasCFSh2hMClMkTFOrzW9cAtEx9DJjXFTmDA3hamUzTRwkcKkMEXGOL3W9MItEB1DJzfGTWHC3BSmBlyo1BEKk8IUGeP0WtMLt0B0DJ3cGDeFCXNTmErZTAMXKUwKU2SM02tNL9wC0TF0cmPcFCbMTWFqwIVKHaEwKUyRMU6vNb1wC0TH0MmNcVOYMDeFqZTNNHCRwqQwRcY4vdb0wi0QHUMnN8ZNYcLcFKYGXKjUEQqTwhQZ4/Ra0wu3QHQMndwYN4UJc1OYStlMAxcpTApTZIzTa00v3ALRMXRyY9wUJsxNYWrAhUodoTApTJExTq81vXALRMfQyY1xU5gwN4WplM00cJHCpDBFxji91vTCLRAdQyc3xk1hwtwUpgZcqNQRCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5hK2UwDFylMClNkjNNrTS/cAtExdHJj3BQmzE1hasCFSh2hMClMkTFOrzW9cAtEx9DJjXFTmDA3hamUzTRwkcI0I0ztdrvT6XS73QaIDx/R6/VaM7deqxWZqOVZa3rhvouOoZMb46YwYW4K03Bs5qwoTH7DFBnj9FrTC7dAdAyd3Bg3hQlzU5hy9Gj4VIVJYYqMcXqt6YVbIDqGTm6Mm8KEuSlMw+qSs6IwKUyRMU6vNb1wC0TH0MmNcVOYMDeFKUePhk9VmBSmyBin15peuAWiY+jkxrgpTJibwjSsLjkrCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5hy9Gj4VIVJYYqMcXqt6YVbIDqGTm6Mm8KEuSlMw+qSs6IwKUyRMU6vNb1wC0TH0MmNcVOYMDeFKUePhk9VmBSmyBin15peuAWiY+jkxrgpTJibwjSsLjkrCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5hy9Gj4VIVJYYqMcXqt6YVbIDqGTm6Mm8KEuSlMw+qSs6IwKUyRMU6vNb1wC0TH0MmNcVOYMDeFKUePhk9VmBSmyBin15peuAWiY+jkxrgpTJibwjSsLjkrCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5hy9Gj4VIVJYYqMcXqt6YVbIDqGTm6Mm8KEuSlMw+qSs6IwKUyRMU6vNb1wC0TH0MmNcVOYMDeFKUePhk9VmBSmyBin15peuAWiY+jkxrgpTJibwjSsLjkrCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5hy9Gj4VIVJYYqMcXqt6YVbIDqGTt+36EgAACAASURBVG6Mm8KEuSlMw+qSs6IwKUyRMU6vNb1wC0TH0MmNcVOYMDeFKUePhk9VmBSmyBin15peuAWiY+jkxrgpTJibwjSsLjkrCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5hy9Gj4VIVJYYqMcXqt6YVbIDqGTm6Mm8KEuSlMw+qSs6IwKUyRMU6vNb1wC0TH0MmNcVOYMDeFKUePhk9VmBSmyBin15peuAWiY+jkxrgpTJibwjSsLjkrCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5hy9Gj4VIVJYYqMcXqt6YVbIDqGTm6Mm8KEuSlMw+qSs6IwzQhTu93udDrdbjelCb1erzVz67VakYlanrWmF+676Bg6uTFuChPmpjClJHPBoQqT3zBFxji91vTCLRAdQyc3xk1hwtwUpgJ3SVlSmBSmyBin15peuAWiY+jkxrgpTJibwpRiRwWHKkwKU2SM02tNL9wC0TF0cmPcFCbMTWEqcJeUJYVJYYqMcXqt6YVbIDqGTm6Mm8KEuSlMKXZUcKjCpDBFxji91vTCLRAdQyc3xk1hwtwUpgJ3SVlSmBSmyBin15peuAWiY+jkxrgpTJibwpRiRwWHKkwKU2SM02tNL9wC0TF0cmPcFCbMTWEqcJeUJYVJYYqMcXqt6YVbIDqGTm6Mm8KEuSlMKXZUcKjCpDBFxji91vTCLRAdQyc3xk1hwtwUpgJ3SVlSmBSmyBin15peuAWiY+jkxrgpTJibwpRiRwWHKkwKU2SM02tNL9wC0TF0cmPcFCbMTWEqcJeUJYVJYYqMcXqt6YVbIDqGTm6Mm8KEuSlMKXZUcKjCpDBFxji91vTCLRAdQyc3xk1hwtwUpgJ3SVlSmBSmyBin15peuAWiY+jkxrgpTJibwpRiRwWHKkwKU2SM02tNL9wC0TF0cmPcFCbMTWEqcJeUJYVJYYqMcXqt6YVbIDqGTm6Mm8KEuSlMKXZUcKjCpDBFxji91vTCLRAdQyc3xk1hwtwUpgJ3SVlSmBSmyBin15peuAWiY+jkxrgpTJibwpRiRwWHKkwKU2SM02tNL9wC0TF0cmPcFCbMTWEqcJeUJYVJYYqMcXqt6YVbIDqGTm6Mm8KEuSlMKXZUcOi4CtMDDzwwNTU1OTm5adOm48ePD7+zZ5555q677pqampqYmLj//vuHL5hdOX9eYYqMcXqt6YVbIDqGTm6Mm8KEuSlMowK86fWxFKZDhw6tWrXq4MGDzz777D333LNmzZoXX3xxHrkTJ07s3r378OHD69atU5harcisLuVa0wt3R3QMndwYN4UJc1OY5sV72sOxFKZNmzbt3Llzltn09PR11123b9++UQinpqYUJoXp8iWAP4UNfoZOboybwoS5KUyj4r3p9fETposXL65cufLo0aMDVHfffffWrVsHD+fdUZgua1cwvfCnsOgYOrkxbgoT5qYwzUv1tIfjJ0xnz56dmJg4duzYgNnu3bs3b948eDjvjsKkMF3WBPCnsMHP0MmNcVOYMDeFaV6qpz28HIRp165dt99++yiECtNlrQumF/4UFh1DJzfGTWHC3BSmUfHe9Pr4CVMdfyTXbrc7c27dbrfJPvR6vdbMrXdZm03kw2KBWtNrATgLPyW6hfmMelZuo8hccl10l0Q06oKZjOj1ek0Gk2cNExg/Yer3+/P+0vf69ev3798//N5mV/yG6bL2MD+CR33CXnJddJdEVHiB3AqxlFkUXRlKhdcoTKMSvtH1sRSmw4cPT05ODn6twNq1a8+dO9fv97dt27Znz55ZfhcvXjx58uSTTz65bt263bt3nzx58oUXXhhG6+9hGnOd8iO48OO1zKLoylAavkZuw0xKroiuJKjhyxSm4fROWBlLYer3+wcOHNiwYcPk5OTmzZtPnDgxS27Lli07duyYvX/69OmJiYkVc25btmwZBqwwKUxjTmD4s7XkiulVEtS8y+Q2D0j5h6Irz2relQrTcHonrIyrMFWFSmEac13wI3jeB2v5h6Irz2rulXKbS2NR90W3KFxzL1aYqsr80D4Kk/9plLljOXb3/QjGLRMdQyc3xs3/lxzm5v9LLmQ5FRYrTApTZIzTa00v3ALRMXRyY9wUJsxNYarQeUJbKUwKU2SM02tNL9wC0TF0cmPcFCbMTWEKWU6FxQqTwhQZ4/Ra0wu3QHQMndwYN4UJc1OYKnSe0FYKk8IUGeP0WtMLt0B0DJ3cGDeFCXNTmEKWU2GxwqQwRcY4vdb0wi0QHUMnN8ZNYcLcFKYKnSe0lcKkMEXGOL3W9MItEB1DJzfGTWHC3BSmkOVUWKwwKUyRMU6vNb1wC0TH0MmNcVOYMDeFqULnCW2lMClMkTFOrzW9cAtEx9DJjXFTmDA3hSlkORUWK0wKU2SM02tNL9wC0TF0cmPcFCbMTWGq0HlCWylMClNkjNNrTS/cAtExdHJj3BQmzE1hCllOhcUKk8IUGeP0WtMLt0B0DJ3cGDeFCXNTmCp0ntBWCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5hCllNhscKkMEXGOL3W9MItEB1DJzfGTWHC3BSmCp0ntJXCpDBFxji91vTCLRAdQyc3xk1hwtwUppDlVFisMClMkTFOrzW9cAtEx9DJjXFTmDA3halC5wltpTApTJExTq81vXALRMfQyY1xU5gwN4UpZDkVFitMClNkjNNrTS/cAtExdHJj3BQmzE1hqtB5QlspTApTZIzTa00v3ALRMXRyY9wUJsxNYQpZToXFCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5gqdJ7QVgqTwhQZ4/Ra0wu3QHQMndwYN4UJc1OYQpZTYbHCNCNM7Xa70+l0u90KyZbfqtfrtWZuvVYrMlHLs9b0wn0XHUMnN8ZNYcLcFKbycVrvlQqT3zBFxji91vTCLRAdQyc3xk1hwtwUpno1qPzuCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5jKK029VypMClNkjNNrTS/cAtExdHJj3BQmzE1hqleDyu+uMClMkTFOrzW9cAtEx9DJjXFTmDA3ham80tR7pcKkMEXGOL3W9MItEB1DJzfGTWHC3BSmejWo/O4Kk8IUGeP0WtMLt0B0DJ3cGDeFCXNTmMorTb1XKkwKU2SM02tNL9wC0TF0cmPcFCbMTWGqV4PK764wKUyRMU6vNb1wC0TH0MmNcVOYMDeFqbzS1HulwqQwRcY4vdb0wi0QHUMnN8ZNYcLcFKZ6Naj87gqTwhQZ4/Ra0wu3QHQMndwYN4UJc1OYyitNvVcqTApTZIzTa00v3ALRMXRyY9wUJsxNYapXg8rvrjApTJExTq81vXALRMfQyY1xU5gwN4WpvNLUe6XCpDBFxji91vTCLRAdQyc3xk1hwtwUpno1qPzuCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5jKK029VypMClNkjNNrTS/cAtExdHJj3BQmzE1hqleDyu+uMClMkTFOrzW9cAtEx9DJjXFTmDA3ham80tR7pcKkMEXGOL3W9MItEB1DJzfGTWHC3BSmejWo/O4Kk8IUGeP0WtMLt0B0DJ3cGDeFCXNTmMorTb1XKkwKU2SM02tNL9wC0TF0cmPcFCbMTWGqV4PK764wKUyRMU6vNb1wC0TH0MmNcVOYMDeFqbzS1HulwqQwRcY4vdb0wi0QHUMnN8ZNYcLcFKZ6Naj87gqTwhQZ4/Ra0wu3QHQMndwYN4UJc1OYyitNvVcqTApTZIzTa00v3ALRMXRyY9wUJsxNYapXg8rvrjApTJExTq81vXALRMfQyY1xU5gwN4WpvNLUe6XCpDBFxji91vTCLRAdQyc3xk1hwtwUpno1qPzuCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5jKK029VypMM8LUbrc7nU63260X9ojde71ea+bWa7UiE7U8a00v3HfRMXRyY9wUJsxNYRqRnY0vK0x+wxQZ4/Ra0wu3QHQMndwYN4UJc1OYGjejEQcqTApTZIzTa00v3ALRMXRyY9wUJsxNYRrhL40vK0wKU2SM02tNL9wC0TF0cmPcFCbMTWFq3IxGHKgwKUyRMU6vNb1wC0TH0MmNcVOYMDeFaYS/NL6sMClMkTFOrzW9cAtEx9DJjXFTmDA3halxMxpxoMKkMEXGOL3W9MItEB1DJzfGTWHC3BSmEf7S+LLCpDBFxji91vTCLRAdQyc3xk1hwtwUpsbNaMSBCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5hG+EvjywqTwhQZ4/Ra0wu3QHQMndwYN4UJc1OYGjejEQcqTApTZIzTa00v3ALRMXRyY9wUJsxNYRrhL40vK0wKU2SM02tNL9wC0TF0cmPcFCbMTWFq3IxGHKgwKUyRMU6vNb1wC0TH0MmNcVOYMDeFaYS/NL6sMClMkTFOrzW9cAtEx9DJjXFTmDA3halxMxpxoMKkMEXGOL3W9MItEB1DJzfGTWHC3BSmEf7S+LLCpDBFxji91vTCLRAdQyc3xk1hwtwUpsbNaMSBCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5hG+EvjywqTwhQZ4/Ra0wu3QHQMndwYN4UJc1OYGjejEQcqTApTZIzTa00v3ALRMXRyY9wUJsxNYRrhL40vK0wKU2SM02tNL9wC0TF0cmPcFCbMTWFq3IxGHKgwKUyRMU6vNb1wC0TH0MmNcVOYMDeFaYS/NL6sMClMkTFOrzW9cAtEx9DJjXFTmDA3halxMxpxoMKkMEXGOL3W9MItEB1DJzfGTWHC3BSmEf7S+LLCpDBFxji91vTCLRAdQyc3xk1hwtwUpsbNaMSBCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5hG+EvjywqTwhQZ4/Ra0wu3QHQMndwYN4UJc1OYGjejEQcqTApTZIzTa00v3ALRMXRyY9wUJsxNYRrhL40vK0wzwtRutzudTrfbbZz/zIG9Xq81c+u1WpGJWp61phfuu+gYOrkxbgoT5qYwpSRzwaEKk98wRcY4vdb0wi0QHUMnN8ZNYcLcFKYCd0lZUpgUpsgYp9eaXrgFomPo5Ma4KUyYm8KUYkcFhypMClNkjNNrTS/cAtExdHJj3BQmzE1hKnCXlCWFSWGKjHF6remFWyA6hk5ujJvChLkpTCl2VHCowqQwRcY4vdb0wi0QHUMnN8ZNYcLcFKYCd0lZUpgUpsgYp9eaXrgFomPo5Ma4KUyYm8KUYkcFhypMClNkjNNrTS/cAtExdHJj3BQmzE1hKnCXlCWFSWGKjHF6remFWyA6hk5ujJvChLkpTCl2VHCowqQwRcY4vdb0wi0QHUMnN8ZNYcLcFKYCd0lZUpgUpsgYp9eaXrgFomPo5Ma4KUyYm8KUYkcFhypMClNkjNNrTS/cAtExdHJj3BQmzE1hKnCXlCWFSWGKjHF6remFWyA6hk5ujJvChLkpTCl2VHCowqQwRcY4vdb0wi0QHUMnN8ZNYcLcFKYCd0lZUpgUpsgYp9eaXrgFomPo5Ma4KUyYm8KUYkcFhypMClNkjNNrTS/cAtExdHJj3BQmzE1hKnCXlCWFSWGKjHF6remFWyA6hk5ujJvChLkpTCl2VHCowqQwRcY4vdb0wi0QHUMnN8ZNYcLcFKYCd0lZUpgUpsgYp9eaXrgFomPo5Ma4KUyYm8KUYkcFhypMClNkjNNrTS/cAtExdHJj3BQmzE1hKnCXlCWFSWGKjHF6remFWyA6hk5ujJvChLkpTCl2VHCowqQwRcY4vdb0wi0QHUMnN8ZNYcLcFKYCd0lZUpgUpsgYp9eaXrgFomPo5Ma4KUyYm8KUYkcFhypMClNkjNNrTS/cAtExdHJj3BQmzE1hKnCXlCWFSWGKjHF6remFWyA6hk5ujJvChLkpTCl2VHCowqQwRcY4vdb0wi0QHUMnN8ZNYcLcFKYCd0lZUphmhKndbnc6nW63m9KDXq/Xmrn1Wq3IRC3PWtML9110DJ3cGDeFCXNTmFKSueBQhclvmCJjnF5reuEWiI6hkxvjpjBhbgpTgbukLClMClNkjNNrTS/cAtExdHJj3BQmzE1hSrGjgkMVJoUpMsbptaYXboHoGDq5MW4KE+amMBW4S8qSwqQwRcY4vdb0wi0QHUMnN8ZNYcLcFKYUOyo4VGFSmCJjnF5reuEWiI6hkxvjpjBhbgpTgbukLClMClNkjNNrTS/cAtExdHJj3BQmzE1hSrGjgkMVJoUpMsbptaYXboHoGDq5MW4KE+amMBW4S8qSwqQwRcY4vdb0wi0QHUMnN8ZNYcLcFKYUOyo4VGFSmCJjnF5reuEWiI6hkxvjpjBhbgpTgbukLClMClNkjNNrTS/cAtExdHJj3BQmzE1hSrGjgkMVJoUpMsbptaYXboHoGDq5MW4KE+amMBW4S8qSwqQwRcY4vdb0wi0QHUMnN8ZNYcLcFKYUOyo4VGFSmCJjnF5reuEWiI6hkxvjpjBhbgpTgbukLClMClNkjNNrTS/cAtExdHJj3BQmzE1hSrGjgkMVJoUpMsbptaYXboHoGDq5MW4KE+amMBW4S8qSwqQwRcY4vdb0wi0QHUMnN8ZNYcLcFKYUOyo4VGFSmCJjnF5reuEWiI6hkxvjpjBhbgpTgbukLClMClNkjNNrTS/cAtExdHJj3BQmzE1hSrGjgkMVJoUpMsbptaYXboHoGDq5MW4KE+amMBW4S8qSwqQwRcY4vdb0wi0QHUMnN8ZNYcLcFKYUOyo4dKkL0wMPPDA1NTU5Oblp06bjx48XvIN+/8iRI6973esmJydvvfXWv/mbvxlcs3379ok5t3a7PXhqcOf8eYUpMsbptaYXboHoGDq5MW4KE+amMA0SO/nOkhamQ4cOrVq16uDBg88+++w999yzZs2aF198cR6wJ554YuXKlb//+7//L//yLx/4wAeuuOKKZ555Zvaa7du3/8RP/MS5c+f+/aXbN77xjXm1/X5fYWq1ImOcXmt64RaIjqGTG+OmMGFuCtNwdOesLGlh2rRp086dO2fBTE9PX3fddfv27ZvH6a1vfWun0xksbt68+d577519uH379p/+6Z8ePFV4R2FSmMacAP4UNvgZOrkxbgoT5qYwFaZ3wuLSFaaLFy+uXLny6NGjAyp333331q1bBw9n79xwww3333//YPG+++57wxveMPtw+/bta9asueaaa2666aZ7773361//+uCywR2Facx1wfTCn8KiY+jkxrgpTJibwjRI7OQ7S1eYzp49OzExcezYsQGh3bt3b968efBw9s4VV1xx6NChweIf/dEfveY1r5l9ePjw4U996lNPP/300aNHb7755k2bNk1PTw+unL2jMClMY04Afwob/Ayd3Bg3hQlzU5jm5Xbaw3ESpl27dt1+++3zUM0TpgMHDlx77bXzrun3+6dOnZqYmPjc5z437ymFacx1wfTCn8KiY+jkxrgpTJibwjQvt9MeLl1hiv+R3DyoV1999UMPPTRvcVaY2u12Z86t2+3Ou6zWh71erzVz6425u0Q+DnCt6SU6TIAV+iPHuClMmJvCVGsCL2LzpStM/X5/3l/6Xr9+/f79++e9ube+9a0/9VM/NVi84447Bn/pe7DY7/e/8pWvrFix4lOf+tTcRf9fcuOvaKYX/hQWHUMnN8ZNYcLcFKZ5uZ32cEkL0+HDhycnJwe/VmDt2rXnzp3r9/vbtm3bs2fPLLMnnnji5S9/+eyvFbjvvvtWrVo1+2sFLly4sGvXrmPHjp0+ffrv/u7vvu/7vu91r3vdxYsX55H2j+TG3JlML/wpLDqGTm6Mm8KEuSlM83I77eGSFqZ+v3/gwIENGzZMTk5u3rz5xIkTs5y2bNmyY8eOAbOPf/zjN9100+Tk5C233PKZz3xmdv1b3/rWj//4j7/61a9etWrVxo0b3/Wud83K1qBq9o7CpDCNOQH8KWzwM3RyY9wUJsxNYZqX22kPl7ow1Q1GYRpzXTC98Kew6Bg6uTFuChPmpjDVLQJl91eY/E+jRMY4vdb0wi0QHUMnN8ZNYcLcFKayQlP3dQqTwhQZ4/Ra0wu3QHQMndwYN4UJc1OY6hahsvsrTApTZIzTa00v3ALRMXRyY9wUJsxNYSorNHVfpzApTJExTq81vXALRMfQyY1xU5gwN4WpbhEqu7/CpDBFxji91vTCLRAdQyc3xk1hwtwUprJCU/d1CpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5jqFqGy+ytMClNkjNNrTS/cAtExdHJj3BQmzE1hKis0dV+nMClMkTFOrzW9cAtEx9DJjXFTmDA3haluESq7v8KkMEXGOL3W9MItEB1DJzfGTWHC3BSmskJT93UKk8IUGeP0WtMLt0B0DJ3cGDeFCXNTmOoWobL7K0wKU2SM02tNL9wC0TF0cmPcFCbMTWEqKzR1X6cwKUyRMU6vNb1wC0TH0MmNcVOYMDeFqW4RKru/wqQwRcY4vdb0wi0QHUMnN8ZNYcLcFKayQlP3dQqTwhQZ4/Ra0wu3QHQMndwYN4UJc1OY6hahsvsrTApTZIzTa00v3ALRMXRyY9wUJsxNYSorNHVfpzApTJExTq81vXALRMfQyY1xU5gwN4WpbhEqu7/CpDBFxji91vTCLRAdQyc3xk1hwtwUprJCU/d1CpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5jqFqGy+ytMClNkjNNrTS/cAtExdHJj3BQmzE1hKis0dV+nMClMkTFOrzW9cAtEx9DJjXFTmDA3haluESq7v8KkMEXGOL3W9MItEB1DJzfGTWHC3BSmskJT93UKk8IUGeP0WtMLt0B0DJ3cGDeFCXNTmOoWobL7K0wzwtRutzudTrfbLYut0ut6vV5r5tZrtSITtTxrTS/cd9ExdHJj3BQmzE1hqjRxA5spTH7DFBnj9FrTC7dAdAyd3Bg3hQlzU5gCjlNpqcKkMEXGOL3W9MItEB1DJzfGTWHC3BSmSq0nsJnCpDBFxji91vTCLRAdQyc3xk1hwtwUpoDjVFqqMClMkTFOrzW9cAtEx9DJjXFTmDA3halS6wlspjApTJExTq81vXALRMfQyY1xU5gwN4Up4DiVlipMClNkjNNrTS/cAtExdHJj3BQmzE1hqtR6ApspTApTZIzTa00v3ALRMXRyY9wUJsxNYQo4TqWlCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5gqtZ7AZgqTwhQZ4/Ra0wu3QHQMndwYN4UJc1OYAo5TaanCpDBFxji91vTCLRAdQyc3xk1hwtwUpkqtJ7CZwqQwRcY4vdb0wi0QHUMnN8ZNYcLcFKaA41RaqjApTJExTq81vXALRMfQyY1xU5gwN4WpUusJbKYwKUyRMU6vNb1wC0TH0MmNcVOYMDeFKeA4lZYqTApTZIzTa00v3ALRMXRyY9wUJsxNYarUegKbKUwKU2SM02tNL9wC0TF0cmPcFCbMTWEKOE6lpQqTwhQZ4/Ra0wu3QHQMndwYN4UJc1OYKrWewGYKk8IUGeP0WtMLt0B0DJ3cGDeFCXNTmAKOU2mpwqQwRcY4vdb0wi0QHUMnN8ZNYcLcFKZKrSewmcKkMEXGOL3W9MItEB1DJzfGTWHC3BSmgONUWqowKUyRMU6vNb1wC0TH0MmNcVOYMDeFqVLrCWymMClMkTFOrzW9cAtEx9DJjXFTmDA3hSngOJWWKkwKU2SM02tNL9wC0TF0cmPcFCbMTWGq1HoCmylMClNkjNNrTS/cAtExdHJj3BQmzE1hCjhOpaUKk8IUGeP0WtMLt0B0DJ3cGDeFCXNTmCq1nsBmCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5gCjlNpqcI0I0ztdrvT6XS73UrZlt2s1+u1Zm69VisyUcuz1vTCfRcdQyc3xk1hwtwUprJhWvd1CpPfMEXGOL3W9MItEB1DJzfGTWHC3BSmukWo7P4Kk8IUGeP0WtMLt0B0DJ3cGDeFCXNTmMoKTd3XKUwKU2SM02tNL9wC0TF0cmPcFCbMTWGqW4TK7q8wKUyRMU6vNb1wC0TH0MmNcVOYMDeFqazQ1H2dwqQwRcY4vdb0wi0QHUMnN8ZNYcLcFKa6Rajs/gqTwhQZ4/Ra0wu3QHQMndwYN4UJc1OYygpN3dcpTApTZIzTa00v3ALRMXRyY9wUJsxNYapbhMrurzApTJExTq81vXALRMfQyY1xU5gwN4WprNDUfZ3CpDBFxji91vTCLRAdQyc3xk1hwtwUprpFqOz+CpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5jKCk3d1ylMClNkjNNrTS/cAtExdHJj3BQmzE1hqluEyu6vMClMkTFOrzW9cAtEx9DJjXFTmDA3hams0NR9ncKkMEXGOL3W9MItEB1DJzfGTWHC3BSmukWo7P4Kk8IUGeP0WtMLt0B0DJ3cGDeFCXNTmMoKTd3XKUwKU2SM02tNL9wC0TF0cmPcFCbMTWGqW4TK7q8wKUyRMU6vNb1wC0TH0MmNcVOYMDeFqazQ1H2dwqQwRcY4vdb0wi0QHUMnN8ZNYcLcFKa6Rajs/gqTwhQZ4/Ra0wu3QHQMndwYN4UJc1OYygpN3dcpTApTZIzTa00v3ALRMXRyY9wUJsxNYapbhMrurzApTJExTq81vXALRMfQyY1xU5gwN4WprNDUfZ3CpDBFxji91vTCLRAdQyc3xk1hwtwUprpFqOz+CpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5jKCk3d1ylMClNkjNNrTS/cAtExdHJj3BQmzE1hqluEyu6vMClMkTFOrzW9cAtEx9DJjXFTmDA3hams0NR9ncKkMEXGOL3W9MItEB1DJzfGTWHC3BSmukWo7P4Kk8IUGeP0WtMLt0B0DJ3cGDeFCXNTmMoKTd3XKUwzwtRutzudTrfbrRt34f69Xq81c+u1WpGJWp61phfuu+gYOrkxbgoT5qYwFSZnwqLC5DdMkTFOrzW9cAtE5NNwlQAADfpJREFUx9DJjXFTmDA3hSnBjQqPVJgUpsgYp9eaXrgFomPo5Ma4KUyYm8JUaC8JiwqTwhQZ4/Ra0wu3QHQMndwYN4UJc1OYEtyo8EiFSWGKjHF6remFWyA6hk5ujJvChLkpTIX2krCoMClMkTFOrzW9cAtEx9DJjXFTmDA3hSnBjQqPVJgUpsgYp9eaXrgFomPo5Ma4KUyYm8JUaC8JiwqTwhQZ4/Ra0wu3QHQMndwYN4UJc1OYEtyo8EiFSWGKjHF6remFWyA6hk5ujJvChLkpTIX2krCoMClMkTFOrzW9cAtEx9DJjXFTmDA3hSnBjQqPVJgUpsgYp9eaXrgFomPo5Ma4KUyYm8JUaC8JiwqTwhQZ4/Ra0wu3QHQMndwYN4UJc1OYEtyo8EiFSWGKjHF6remFWyA6hk5ujJvChLkpTIX2krCoMClMkTFOrzW9cAtEx9DJjXFTmDA3hSnBjQqPVJgUpsgYp9eaXrgFomPo5Ma4KUyYm8JUaC8JiwqTwhQZ4/Ra0wu3QHQMndwYN4UJc1OYEtyo8EiFSWGKjHF6remFWyA6hk5ujJvChLkpTIX2krCoMClMkTFOrzW9cAtEx9DJjXFTmDA3hSnBjQqPVJgUpsgYp9eaXrgFomPo5Ma4KUyYm8JUaC8JiwqTwhQZ4/Ra0wu3QHQMndwYN4UJc1OYEtyo8EiFSWGKjHF6remFWyA6hk5ujJvChLkpTIX2krCoMClMkTFOrzW9cAtEx9DJjXFTmDA3hSnBjQqPVJgUpsgYp9eaXrgFomPo5Ma4KUyYm8JUaC8JiwqTwhQZ4/Ra0wu3QHQMndwYN4UJc1OYEtyo8EiFSWGKjHF6remFWyA6hk5ujJvChLkpTIX2krCoMClMkTFOrzW9cAtEx9DJjXFTmDA3hSnBjQqPVJgUpsgYp9eaXrgFomPo5Ma4KUyYm8JUaC8JiwrTjDC12+1Op9PtdhM60O/3er3WzK3XakUmannWml6476Jj6OTGuClMmJvClJLMBYcqTH7DFBnj9FrTC7dAdAyd3Bg3hQlzU5gK3CVlSWFSmCJjnF5reuEWiI6hkxvjpjBhbgpTih0VHKowKUyRMU6vNb1wC0TH0MmNcVOYMDeFqcBdUpYUJoUpMsbptaYXboHoGDq5MW4KE+amMKXYUcGhCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5gK3CVlSWFSmCJjnF5reuEWiI6hkxvjpjBhbgpTih0VHKowKUyRMU6vNb1wC0TH0MmNcVOYMDeFqcBdUpYUJoUpMsbptaYXboHoGDq5MW4KE+amMKXYUcGhCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5gK3CVlSWFSmCJjnF5reuEWiI6hkxvjpjBhbgpTih0VHKowKUyRMU6vNb1wC0TH0MmNcVOYMDeFqcBdUpYUJoUpMsbptaYXboHoGDq5MW4KE+amMKXYUcGhCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5gK3CVlSWFSmCJjnF5reuEWiI6hkxvjpjBhbgpTih0VHKowKUyRMU6vNb1wC0TH0MmNcVOYMDeFqcBdUpYUJoUpMsbptaYXboHoGDq5MW4KE+amMKXYUcGhCpPCFBnj9FrTC7dAdAyd3Bg3hQlzU5gK3CVlSWFSmCJjnF5reuEWiI6hkxvjpjBhbgpTih0VHKowKUyRMU6vNb1wC0TH0MmNcVOYMDeFqcBdUpYUJoUpMsagtttqgapRJabXKDKD9VHARTdAtKg7C3MbRXtRR1yuFy+Mjr3rZQK812q1er1eiiUMDu12u4P7y/OOwqQwsc8pXNVRmColcMlGjAJeR3pd8sVcBhcszG0U7cvgjcffwsLo2P7LBPiSEKZOp7M8PWnwrhUmhYl9TuGqaj/g6vgIxm9taRaOAi461q+FuY2izc66zKoWRsfe7DIBrjANpCXzTpXCVN/3dfXtfP58vcJU5pX3ejPD0Gr1FvnFQ63fRde3ebUfcPM+gut72f1Wq77N69u532qNAj4PHYirWl/2kt18YW6jaAO8wyX1Malv57mDszC64fdbZqU+4M0wKfMeF/F3mMokDjaOWr9hqu+VV7hzlcJUH836dq5bmMq8cipM9X1SLJCyJcd7gcuqfdnzPoKr3Xzeu6hv8/p2XqCV89DNe7NlHqa87DIv7JLXRF75wtwiO9f6shfevJmXvTC6hV/hqGfre+X17bzAVI56m2W/YSqTOEtTmOp75RXuvJAwTU9Pny99O3Xq1Pd///f/dT23+nY+cuRIq9U6cuRIPS/8r8u88ocffvilb5gearUeW8w/dyzm4kXt/FirVd/m1e78G/8XXbWbz4NW3+b17bxAK+ehm/dmyzxMedllXtglr4m88oW5RXau9WUvvHkzL3thdAu/wlHP1vfK69t5gakc9TYfarVaDz300GOXut1xxx2XuoQ/P6abb9mypbTIzFw4PT09yikXEqbZb19eCiT/RwISkIAEJCABCVzmBM6fP0+EaVHfMH31q1/9/BjeHn/88Var9fjjjye+9ueff/7pp5/m2r+8Kz/72c8ubwD83YuOsZMb4/bYY4+JDqP73Oc+h2uXeeFzzz3XxDdMoyTrclqv++8wXU6sfC8SkIAEJCCBZUtgoT+SWw5QFKbl0GXfowQkIAEJSCBIQGGq99cKBNtjuQQkIAEJSEACS4GAwqQwLYWfQ1+DBCQgAQlIYEkTUJgUpiX9A+qLk4AEJCABCSwFAgqTwtTEz+HevXtvu+22V73qVddcc83WrVufe+65Jk71jH5/7969ExMT733ve4VRK4GvfvWr73jHO6666qrVq1ffeuut6f+d1FrfbO7m3/nOd973vvdt3Lhx9erV3/M93/PBD34w9/Vclqc//vjjnU5n3bp1ExMTR48enfse3//+91977bWrV6++8847n3/++blPXfb3FSaFqYkf8na7/fDDD3/pS1966qmn3vSmN23YsOG///u/mzh4eZ9x/PjxjRs3vuENb1CYav1B+M///M+pqamf//mf/+d//ufTp09/9rOfPXXqVK0nLufNf+d3fufqq6/+9Kc/febMmb/4i7941ate9eEPf3g5A6njvX/6059+//vf/5d/+ZcrVqyYK0wf+tCH1qxZ88lPfvKLX/zim9/85te+9rXf/va363gBS3NPhUlhavon88UXX5yYmPjHf/zHpg9eZud985vf/N7v/d6///u//9Ef/VGFqdbm/+qv/uoP//AP13qEmw8I/ORP/uQv/MIvDB7edddd27ZtGzz0TrUE5n3DdO211/7BH/zB7BHnz5+fnJw8fPhwtScu5d0UJoWp6Z/P559/fsWKFc8880zTBy+z8975znf+8i//cr/fV5jq7vzNN9/8S7/0S295y1uuueaaN77xjR/5yEfqPnE57793796NGzf+67/+a7/fP3ny5Gte85pHHnlkOQOp9b3PFaZTp05NTEx84QtfGJz4Iz/yI+95z3sGDy/7OwqTwtToD/n09PSb3vQm/3W8buiPPPLIrbfeevHiRYWpbtT9fn9ycnL16tXve9/7Tp48+Sd/8ierV6/+6Ec/2sC5y/OI6enpX/u1X1uxYsXLX/7yl73sZR/60IeWJ4dm3vVcYXriiSdWrFjxta99bXD0z/zMz7ztbW8bPLzs7yx3YZr9z78s8B/bu+x/Ahp+g+9617s2btx49uzZhs9dVsd95StfefWrX/3UU0/Nvmu/Yaq7+1dcccUP/uAPDk7ZuXPnHXfcMXjonWoJPPLIIzfccMORI0eefvrpj33sY1ddddXDDz9c7RHuNiCwsDC95S1vefvb3z64+LK/s9yF6bJv8JJ6g+9+97tvuOGGM2fOLKlXdfm9mL/6q7+a/ffvlS/dJiYmZh/6LwY19XrDhg2/+Iu/ONj8wQcfXL9+/eChd6olcP311z/44IODPX/7t3/79a9//eChd6olMFeY/CM5hanany53G0ng3e9+9/r16//t3/5t5BU+URGBCxcuPDPndtttt73zne/80pe+VNH2bjOfwM/+7M/O/VPm97znPT/wAz8w/yIfV0Tgqquu+uM//uPBZnv37r3pppsGD71TLYG5wtTv94f/0veRI0eqPXEp76YwLeXuXD6v7d57773yyisff/zxr/3v7Vvf+tbl8/aW9jvxj+Tq7s+JEyeuuOKKvXv3vvDCC3/+53/+yle+0r+GXB/z7du3X3/99Y8++ujp06c/8YlPXH311Xv27KnvuOW584ULF06ePPnkk09OTEz84R/+4cmTJ7/85S/3+/19+/atXbv2k5/85FNPPfXmN7/5xhtv9NcKLM+fEN91jQRm/1RoxZzbwYMHazzPrecQ2LJli79WYA6PWu4++uijt9xyy+rVq2+++eY//dM/reUMN32JwIULF9773vdOTU294hWvuPHGGz/wgQ/8z//8j2yqJfAP//AP8z60d+zYMXvEfffdN/uLK3/sx37MX1xZLXZ3k4AEJCABCUhAAmNPwD+SG/sW+gYkIAEJSEACEqibgMJUN2H3l4AEJCABCUhg7AkoTGPfQt+ABCQgAQlIQAJ1E1CY6ibs/hKQgAQkIAEJjD0BhWnsW+gbkIAEJCABCUigbgIKU92E3V8CEpCABCQggbEnoDCNfQt9AxKQgAQkIAEJ1E1AYaqbsPtLQAISkIAEJDD2BBSmsW+hb0ACEpCABCQggboJKEx1E3Z/CUhAAhKQgATGnoDCNPYt9A1IQAISkIAEJFA3AYWpbsLuLwEJSEACEpDA2BP4f/qxhJ4jl6gAAAAAAElFTkSuQmCC)" ], "metadata": { "id": "a1G_EJ1tgOgD" } }, { "cell_type": "markdown", "source": [ "\n", "\n", "```\n", "number_of_sample:=2\n", "size_of_product_of_population:= 25\n", "size_of_sample_space_of_product_of_population:= 25\n", "size_of_range_of_sample_mean_as_duplicates:=25\n", "range_of_sample_mean:=[1, 2, 3, 4, 5, 6, 7, 8, 9]\n", "size_of_range_of_sample_mean:=9\n", "distribution_of_sample_mean:=[[1, 1/25], [2, 2/25], [3, 3/25], [4,4/25], [5, 1/5], [6, 4/25], [7, 3/25], [8, 2/25], [9, 1/25]]\n", "mean_of_sample_mean:=5\n", "variance_of_sample_mean:=4\n", "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n", "[0, 1/25, 2/25, 3/25, 4/25, 1/5, 4/25, 3/25, 2/25, 1/25, 0]\n", "\n", "\n", "```\n", "\n" ], "metadata": { "id": "heSw-D2SgVAw" } }, { "cell_type": "markdown", "source": [ "![image.png](data:image/png;base64,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)" ], "metadata": { "id": "3Wq9UemNgfQ8" } }, { "cell_type": "markdown", "source": [ "\n", "\n", "```\n", "number_of_sample:=3\n", "size_of_product_of_population:= 125\n", "size_of_sample_space_of_product_of_population:= 125\n", "size_of_range_of_sample_mean_as_duplicates:=125\n", "range_of_sample_mean:=[1, 5/3, 7/3, 3, 11/3, 13/3, 5, 17/3, 19/3, 7,23/3, 25/3, 9]\n", "size_of_range_of_sample_mean:=13\n", "distribution_of_sample_mean:=[[1, 1/125], [5/3, 3/125], [7/3, 6/125],[3, 2/25], [11/3, 3/25], [13/3, 18/125], [5, 19/125], [17/3, 18/125],[19/3, 3/25], [7, 2/25], [23/3, 6/125], [25/3, 3/125], [9, 1/125]]\n", "mean_of_sample_mean:=5\n", "variance_of_sample_mean:=8/3\n", "[1/3, 1, 5/3, 7/3, 3, 11/3, 13/3, 5, 17/3, 19/3, 7, 23/3, 25/3, 9, 29/3]\n", "[0, 1/125, 3/125, 6/125, 2/25, 3/25, 18/125, 19/125, 18/125, 3/25, 2/25,6/125, 3/125, 1/125, 0]\n", "```\n", "\n" ], "metadata": { "id": "e46OYUNfgiXT" } }, { "cell_type": "markdown", "source": [ "\n", "\n", "```\n", "number_of_sample:=4\n", "size_of_product_of_population:= 625\n", "size_of_sample_space_of_product_of_population:= 625\n", "size_of_range_of_sample_mean_as_duplicates:=625\n", "range_of_sample_mean:=[1, 3/2, 2, 5/2, 3, 7/2, 4, 9/2, 5, 11/2, 6, 13/2,7, 15/2, 8, 17/2, 9]\n", "size_of_range_of_sample_mean:=17\n", "distribution_of_sample_mean:=[[1, 1/625], [3/2, 4/625], [2, 2/125],[5/2, 4/125], [3, 7/125], [7/2, 52/625], [4, 68/625], [9/2, 16/125], [5,17/125], [11/2, 16/125], [6, 68/625], [13/2, 52/625], [7, 7/125], [15/2,4/125], [8, 2/125], [17/2, 4/625], [9, 1/625]]\n", "mean_of_sample_mean:=5\n", "variance_of_sample_mean:=2\n", "[1/2, 1, 3/2, 2, 5/2, 3, 7/2, 4, 9/2, 5, 11/2, 6, 13/2, 7, 15/2, 8,17/2, 9, 19/2]\n", "[0, 1/625, 4/625, 2/125, 4/125, 7/125, 52/625, 68/625, 16/125, 17/125,16/125, 68/625, 52/625, 7/125, 4/125, 2/125, 4/625, 1/625, 0]\n", "```\n", "\n" ], "metadata": { "id": "B-6Tk4rfgpfo" } }, { "cell_type": "markdown", "source": [ "![image.png](data:image/png;base64,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)" ], "metadata": { "id": "pDWugP-agx1-" } }, { "cell_type": "markdown", "source": [ "\n", "\n", "```\n", "number_of_sample:=5\n", "size_of_product_of_population:= 3125\n", "size_of_sample_space_of_product_of_population:= 3125\n", "size_of_range_of_sample_mean_as_duplicates:=3125\n", "range_of_sample_mean:=[1, 7/5, 9/5, 11/5, 13/5, 3, 17/5, 19/5, 21/5,23/5, 5, 27/5, 29/5, 31/5, 33/5, 7, 37/5, 39/5, 41/5, 43/5, 9]\n", "size_of_range_of_sample_mean:=21\n", "distribution_of_sample_mean:=[[1, 1/3125], [7/5, 1/625], [9/5, 3/625],[11/5, 7/625], [13/5, 14/625], [3, 121/3125], [17/5, 37/625], [19/5,51/625], [21/5, 64/625], [23/5, 73/625], [5, 381/3125], [27/5, 73/625],[29/5, 64/625], [31/5, 51/625], [33/5, 37/625], [7, 121/3125], [37/5,14/625], [39/5, 7/625], [41/5, 3/625], [43/5, 1/625], [9, 1/3125]]\n", "mean_of_sample_mean:=5\n", "variance_of_sample_mean:=8/5\n", "[3/5, 1, 7/5, 9/5, 11/5, 13/5, 3, 17/5, 19/5, 21/5, 23/5, 5, 27/5, 29/5,31/5, 33/5, 7, 37/5, 39/5, 41/5, 43/5, 9, 47/5]\n", "[0, 1/3125, 1/625, 3/625, 7/625, 14/625, 121/3125, 37/625, 51/625,64/625, 73/625, 381/3125, 73/625, 64/625, 51/625, 37/625, 121/3125,14/625, 7/625, 3/625, 1/625, 1/3125, 0]\n", "```\n", "\n" ], "metadata": { "id": "7Se3q4JTg0Nk" } }, { "cell_type": "markdown", "source": [ "![image.png](data:image/png;base64,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)" ], "metadata": { "id": "cf-kevJdg5QE" } }, { "cell_type": "markdown", "source": [ "\n", "\n", "```\n", "number_of_sample:=6\n", "size_of_product_of_population:= 15625\n", "size_of_sample_space_of_product_of_population:= 15625\n", "size_of_range_of_sample_mean_as_duplicates:=15625\n", "range_of_sample_mean:=[1, 4/3, 5/3, 2, 7/3, 8/3, 3, 10/3, 11/3, 4, 13/3,14/3, 5, 16/3, 17/3, 6, 19/3, 20/3, 7, 22/3, 23/3, 8, 25/3, 26/3, 9]\n", "size_of_range_of_sample_mean:=25\n", "distribution_of_sample_mean:=[[1, 1/15625], [4/3, 6/15625], [5/3,21/15625], [2, 56/15625], [7/3, 126/15625], [8/3, 246/15625], [3,426/15625], [10/3, 666/15625], [11/3, 951/15625], [4, 1246/15625],[13/3, 1506/15625], [14/3, 1686/15625], [5, 1751/15625], [16/3,\n", "1686/15625], [17/3, 1506/15625], [6, 1246/15625], [19/3, 951/15625],[20/3, 666/15625], [7, 426/15625], [22/3, 246/15625], [23/3, 126/15625],[8, 56/15625], [25/3, 21/15625], [26/3, 6/15625], [9, 1/15625]]\n", "mean_of_sample_mean:=5\n", "variance_of_sample_mean:=4/3\n", "[2/3, 1, 4/3, 5/3, 2, 7/3, 8/3, 3, 10/3, 11/3, 4, 13/3, 14/3, 5, 16/3,17/3, 6, 19/3, 20/3, 7, 22/3, 23/3, 8, 25/3, 26/3, 9, 28/3]\n", "[0, 1/15625, 6/15625, 21/15625, 56/15625, 126/15625, 246/15625,426/15625, 666/15625, 951/15625, 1246/15625, 1506/15625, 1686/15625,1751/15625, 1686/15625, 1506/15625, 1246/15625, 951/15625, 666/15625,426/15625, 246/15625, 126/15625, 56/15625, 21/15625, 6/15625, 1/15625,0]\n", "```\n", "\n" ], "metadata": { "id": "gAG9R8k-g9Hk" } }, { "cell_type": "markdown", "source": [ "![image.png](data:image/png;base64,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)" ], "metadata": { "id": "IjU4aILWhBdf" } }, { "cell_type": "markdown", "source": [ "\n", "\n", "```\n", "number_of_sample:=7\n", "size_of_product_of_population:= 78125\n", "size_of_sample_space_of_product_of_population:= 78125\n", "size_of_range_of_sample_mean_as_duplicates:=78125\n", "range_of_sample_mean:=[1, 9/7, 11/7, 13/7, 15/7, 17/7, 19/7, 3, 23/7,25/7, 27/7, 29/7, 31/7, 33/7, 5, 37/7, 39/7, 41/7, 43/7, 45/7, 47/7, 7,51/7, 53/7, 55/7, 57/7, 59/7, 61/7, 9]\n", "size_of_range_of_sample_mean:=29\n", "distribution_of_sample_mean:=[[1, 1/78125], [9/7, 7/78125], [11/7,28/78125], [13/7, 84/78125], [15/7, 42/15625], [17/7, 91/15625], [19/7,7/625], [3, 304/15625], [23/7, 483/15625], [25/7, 707/15625], [27/7,959/15625], [29/7, 1211/15625], [31/7, 1428/15625], [33/7, 63/625], [5,1627/15625], [37/7, 63/625], [39/7, 1428/15625], [41/7, 1211/15625],[43/7, 959/15625], [45/7, 707/15625], [47/7, 483/15625], [7, 304/15625],[51/7, 7/625], [53/7, 91/15625], [55/7, 42/15625], [57/7, 84/78125],[59/7, 28/78125], [61/7, 7/78125], [9, 1/78125]]\n", "mean_of_sample_mean:=5\n", "variance_of_sample_mean:=8/7\n", "[5/7, 1, 9/7, 11/7, 13/7, 15/7, 17/7, 19/7, 3, 23/7, 25/7, 27/7, 29/7,31/7, 33/7, 5, 37/7, 39/7, 41/7, 43/7, 45/7, 47/7, 7, 51/7, 53/7, 55/7,57/7, 59/7, 61/7, 9, 65/7]\n", "[0, 1/78125, 7/78125, 28/78125, 84/78125, 42/15625, 91/15625, 7/625,304/15625, 483/15625, 707/15625, 959/15625, 1211/15625, 1428/15625,63/625, 1627/15625, 63/625, 1428/15625, 1211/15625, 959/15625,707/15625, 483/15625, 304/15625, 7/625, 91/15625, 42/15625, 84/78125,28/78125, 7/78125, 1/78125, 0]\n", "```\n", "\n" ], "metadata": { "id": "yQkuNsWMhD-G" } }, { "cell_type": "markdown", "source": [ "![image.png](data:image/png;base64,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)" ], "metadata": { "id": "0pRh6SaBhKcp" } }, { "cell_type": "markdown", "source": [ "\n", "\n", "```\n", "number_of_sample:=8\n", "size_of_product_of_population:= 390625\n", "size_of_sample_space_of_product_of_population:= 390625\n", "size_of_range_of_sample_mean_as_duplicates:=390625\n", "range_of_sample_mean:=[1, 5/4, 3/2, 7/4, 2, 9/4, 5/2, 11/4, 3, 13/4,7/2, 15/4, 4, 17/4, 9/2, 19/4, 5, 21/4, 11/2, 23/4, 6, 25/4, 13/2, 27/4,7, 29/4, 15/2, 31/4, 8, 33/4, 17/2, 35/4, 9]\n", "size_of_range_of_sample_mean:=33\n", "distribution_of_sample_mean:=[[1, 1/390625], [5/4, 8/390625], [3/2,36/390625], [7/4, 24/78125], [2, 66/78125], [9/4, 784/390625], [5/2,1652/390625], [11/4, 3144/390625], [3, 219/15625], [13/4, 352/15625],[7/2, 2628/78125], [15/4, 3664/78125], [4, 4788/78125], [17/4,1176/15625], [9/2, 272/3125], [19/4, 7416/78125], [5, 7633/78125],[21/4, 7416/78125], [11/2, 272/3125], [23/4, 1176/15625], [6,4788/78125], [25/4, 3664/78125], [13/2, 2628/78125], [27/4, 352/15625],[7, 219/15625], [29/4, 3144/390625], [15/2, 1652/390625], [31/4,784/390625], [8, 66/78125], [33/4, 24/78125], [17/2, 36/390625], [35/4,8/390625], [9, 1/390625]]\n", "mean_of_sample_mean:=5\n", "variance_of_sample_mean:=1\n", "[3/4, 1, 5/4, 3/2, 7/4, 2, 9/4, 5/2, 11/4, 3, 13/4, 7/2, 15/4, 4, 17/4,9/2, 19/4, 5, 21/4, 11/2, 23/4, 6, 25/4, 13/2, 27/4, 7, 29/4, 15/2,31/4, 8, 33/4, 17/2, 35/4, 9, 37/4]\n", "[0, 1/390625, 8/390625, 36/390625, 24/78125, 66/78125, 784/390625,1652/390625, 3144/390625, 219/15625, 352/15625, 2628/78125, 3664/78125,4788/78125, 1176/15625, 272/3125, 7416/78125, 7633/78125, 7416/78125,272/3125, 1176/15625, 4788/78125, 3664/78125, 2628/78125, 352/15625,219/15625, 3144/390625, 1652/390625, 784/390625, 66/78125, 24/78125,36/390625, 8/390625, 1/390625, 0]\n", "```\n", "\n" ], "metadata": { "id": "rD3caHsVhN4E" } }, { "cell_type": "markdown", "source": [ "![image.png](data:image/png;base64,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)" ], "metadata": { "id": "shiiMxnqhRY-" } }, { "cell_type": "markdown", "source": [ "\n", "\n", "```\n", "number_of_sample:=9\n", "size_of_product_of_population:= 1953125\n", "size_of_sample_space_of_product_of_population:= 1953125\n", "size_of_range_of_sample_mean_as_duplicates:=1953125\n", "range_of_sample_mean:=[1, 11/9, 13/9, 5/3, 17/9, 19/9, 7/3, 23/9, 25/9,3, 29/9, 31/9, 11/3, 35/9, 37/9, 13/3, 41/9, 43/9, 5, 47/9, 49/9, 17/3,53/9, 55/9, 19/3, 59/9, 61/9, 7, 65/9, 67/9, 23/3, 71/9, 73/9, 25/3,77/9, 79/9, 9]\n", "size_of_range_of_sample_mean:=37\n", "distribution_of_sample_mean:=[[1, 1/1953125], [11/9, 9/1953125], [13/9,\n", "9/390625], [5/3, 33/390625], [17/9, 99/390625], [19/9, 1278/1953125],[7/3, 2922/1953125], [23/9, 1206/390625], [25/9, 2277/390625], [3,3971/390625], [29/9, 32211/1953125], [31/9, 48879/1953125], [11/3,2787/78125], [35/9, 3744/78125], [37/9, 4752/78125], [13/3,28548/390625], [41/9, 32517/390625], [43/9, 7029/78125], [5,7213/78125], [47/9, 7029/78125], [49/9, 32517/390625], [17/3,28548/390625], [53/9, 4752/78125], [55/9, 3744/78125], [19/3,2787/78125], [59/9, 48879/1953125], [61/9, 32211/1953125], [7,\n", "3971/390625], [65/9, 2277/390625], [67/9, 1206/390625], [23/3,2922/1953125], [71/9, 1278/1953125], [73/9, 99/390625], [25/3,33/390625], [77/9, 9/390625], [79/9, 9/1953125], [9, 1/1953125]]\n", "mean_of_sample_mean:=5\n", "variance_of_sample_mean:=8/9\n", "[7/9, 1, 11/9, 13/9, 5/3, 17/9, 19/9, 7/3, 23/9, 25/9, 3, 29/9, 31/9,11/3, 35/9, 37/9, 13/3, 41/9, 43/9, 5, 47/9, 49/9, 17/3, 53/9, 55/9,19/3, 59/9, 61/9, 7, 65/9, 67/9, 23/3, 71/9, 73/9, 25/3, 77/9, 79/9, 9,83/9]\n", "[0, 1/1953125, 9/1953125, 9/390625, 33/390625, 99/390625, 1278/1953125,2922/1953125, 1206/390625, 2277/390625, 3971/390625, 32211/1953125,48879/1953125, 2787/78125, 3744/78125, 4752/78125, 28548/390625,32517/390625, 7029/78125, 7213/78125, 7029/78125, 32517/390625,28548/390625, 4752/78125, 3744/78125, 2787/78125, 48879/1953125,32211/1953125, 3971/390625, 2277/390625, 1206/390625, 2922/1953125,1278/1953125, 99/390625, 33/390625, 9/390625, 9/1953125, 1/1953125, 0]\n", "```\n", "\n" ], "metadata": { "id": "_0Er1LPjhU8k" } }, { "cell_type": "markdown", "source": [ 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b976+IYnt+3Y/ZA4Urf2d7cqeDcSIIFFI0BbWjSUvBAJkICIX/dnar44vjz5yPoXPV8H/l/orwQGWq/6mdDyGrLAMujLMTBQOBO5DGJnSwU5f7ksw/8gg8IKI4wmCwyhdVAYwCAwiNyZBX0JgAsuuKgwsrYciMsMIQES6FMCtKU+rTgWmwRiScD1TH/aEt8Vf+um/cCQjrvOOecnQ9jScgWmgfEBDJ+d3ZXDHuBRA19YgtfFzpawKwNzKR4ALl6W/b6BdQUcXZ7f1zKoIWwBNgL78tiWx78buAmZ5aOjk77sjWWdsVAkQAKnJkBbOjUjHkECJHC6BDwJxDSlMdM4sHbNCPD8HHYDh4CZlmthqeQy/kDmQC57OJuR5UvcpYW/Q7jE60mccYYYsHP4B+CCAQyHD+/C9WDLoICZoTMknxfA1nF4+eAItJUTm6dK5ubTxcjjSIAEYkaAthSzCmFxSKCfCdglCcS3xa56+57avQnGivPObAANZKT1ChOar2WqwCRQ1DVZOvD/QY+dLSETAI0l+W9gKGdov4BmDp1T1pevbx1URjC4GYM7oe0Gdg0OrEZmYPevZkRq/Vy3LDsJpJoAbSnV1c/gSWCRCbgSDu8OL1rcvmMYegaYCB+36UHrtXAMmpcfCgbOdjAgzdHc/xBHW8qGHUWF7E3ILAN+BdSQa5a2XVxwtZxkBmSgIGcNHUA2Mza+uVGdXGTavBwJkEC3CNCWukWa9yGBFBAIfNu0qg1TxHO3jY4B2SFj+4rzRddbr0uW1YE6UA77n3QP8PPavYXC2XF7EochX0eQ0W5EHnljq6aJPmABbru4lg1KJmuGQcHMYBh5bNv6lNgpyACGSAIJJUBbSmjFMiwS6A2B6UDM8Ltfjmxf/9RA7lwdY8CUDrflCuzKIlhWkMwSD0YJsA3cirBzKV7jlqAfMCCDhVtRQN7YEBpefiqblZZBNXdaBkpLslKAGFiNPEbWb5RKb6qEdyUBElg4gba25DhONGWcbYf/T+S6z3791XXdIAjUnlrt6Yfxvu8Xi8WoTPV6XUQ8z3Mcx7Is3/fVW7ZtO46j3ooOLhaLuq6XSqVoDzdIgAT6j4BnB+K7Yft2N25YDS2TxXYYbacygu5q8Az44fRI2Xo4wRLuQwxnEMiIASePu5HVc9gMVLWMAMV2UzQVwsmZ6sh40CWLYegYG9nUf7XJEpMACTxDoK0tqQNmZmYiZxIR3/ePHj36zLlSqVQajYaImKZZKpWUA1mWVSqV1FmO40SO5fv+5ORzHtt7XnN4Q/NytKWIKjdIoI8J0Jaa82HSlvo4h1l0EmhFoK0tKcuxLEvJUK1Wm61N0UvVbxRdOepnEpHp6WkRcRzn6NGjBw8ejI5xHEd5Em0pYsINEkgIAdoSbSkhqcwwSOA5BE5hS6rrSHUaiUgQBEePHo0et6l3lVEdO3ZMHSAian/UqxTdUB2pFIpP4iIs3CCB5BCgLdGWkpPNjIQEniXQ1pZs2450R1lO5Dr1er1SCccrHjlyRF1JjUlSwqT2KGGqVquqa8pvLpFOqS4o9i09Ww/cIoFkEKAt0ZaSkcmMggSeS6CtLakeIM/zGo2GkiFlS6pjKRKjer2uxoArParVap7nlctlEVGqpPaLiG3bvu/bth1JUrQRzs3CUd7PrRi+IoG+JEBboi31ZeKy0CRwCgJtbcmyrGq1Gj2D+8IXvnD55Zdns9lLLrnk5z//uYior7xFl69UKj/+8Y9f9apXnXHGGa9//etXrVpVqVQ8zwuCYHp6+jOf+cxLX/pSAJdddtnXv/515Um0pYgeN0ggIQRoS7SlhKQywyCB5xBoa0vRrAGmaf7oRz8qFArf/va3d+3a9Td/8zcA1DO46Nmc7/tr167VNO2WW25Zu3btF77whYGBgYmJCfU1us9+9rNnnnnmyMjI3r17v/a1r73oRS+6//77OW7pOfXAFySQDAK0JdpSMjKZUZDAcwm0tSU1WFtNAfCWt7zlox/9qFKfarX60pe+9Jvf/KZ6JKcGMJmmedVVV1199dUiohTqta997Yc+9CE1aOnlL3/5P/7jP0ajv1/96ld/4QtfiHqtTNNUb0USNruE0YCn2Tu5TQIkEFMCtCXaUkxTk8UigQURaGtLSoOU7gB49NFHo9mSrrvuuiuvvFLdVg1LCoLg/PPPv/HGG9VoJ9M0v/jFL15xxRVqtsnPfe5zK1asOHz4sGVZjz322PLly5944onIltRw8nK5PDAwoAZIqXkvlahFc1ouKEqeTAIk0B0CtCXaUncyjXchge4SaGtLqhjFYnHfvn3hD4Lv2BF181x33XW/93u/p2ZUiiZPGhwc/NGPfhQV/sYbbzzvvPNEpFwuHzly5LOf/ezg4GAmkzEM44477lBTNxWLRdWxJCJTU1MA9u3bp8aGq+vMnuEpujI3SIAE4kuAtkRbim92smQkMH8CJ7Ml13UrlUq1WjUM46GHHlJP4kTk05/+9GWXXRbdUznNwMDA/fff32g01BfibrjhhoGBAfVVuPvvv/+iiy6655579u/ff8MNN6xcufKXv/xl9MxOGdWxY8dWrlwZ3cLzvEqlErmUumZ0R26QAAnElABtibYU09RksUhgQQROZkuRrAB45JFH1E/FTU9Pf/zjH3/Pe96jxicdOnRIfTnu4osv/vrXv67KUiwWv/nNb/7xH//x5ORkqVTKZrP33nuv0qNSqfSXf/mXb33rW6NSR78NB+Cq5vKOd7zjbW9720c/+tH77rtPjY5iJ1OEixskEGsCtCXaUqwTlIUjgXkSOJktqTFJjUbj0ksv/djHPhZNGbBs2bL/+3//r+/70VxKjUbjgx/84Bvf+MboW3KvetWrooHhAH72s59FMzCpYU+zpw9QPzOXz+fVD6R4nletVmdmZqKrcfTSPKuXp5FAlwnQlmhLXU453o4EukKgrS3Nfvh17733nnfeeXfcccfatWs/8YlPLF++XHUIXXnllV/96ldnZmZEZMeOHQBuu+220dHRz3/+80NDQ0899ZSas/vSSy993ete99hjj+3fv/+73/2uOkzN2BT50MGDBwEEQTD7vqo7KhoP3hUgvAkJkMACCNCWaEsLSB+eSgKxJdDWllSJXddV/To33HDDi1/84sHBwUsuuWTbtm3VatXzvKuuuuqaa65Rg41M03zooYde8YpXDA0NveIVr1i1apWasclxnJmZmfe9730XXHDBwMDAb//2b990002+76uHa0EQKPGyLCuaQUCNlzJNkw/gYps3LBgJtCZAW6Ittc4M7iWB/iZwClvqaHCzH8bxl086ipoXJ4EuEaAt0Za6lGq8DQl0lQBtqau4eTMSSDgB2hJtKeEpzvBSSoC2lNKKZ9gk0BECtCXaUkcSixclgR4ToC31uAJ4exJIFAHaEm0pUQnNYEjgaQK0JaYCCZDA4hGgLdGWFi+beCUSiA8B2lJ86oIlIYH+J0Bboi31fxYzAhI4kQBt6UQm3EMCJDBfArQl2tJ8c4fnkUCcCdCW4lw7LBsJ9BsB2hJtqd9yluUlgdMhQFs6HUo8hgRI4PQI0JZoS6eXKTyKBPqLAG2pv+qLpSWBeBOgLdGW4p2hLB0JzI8AbWl+3HgWCZBAKwK0JdpSq7zgPhLodwK0pX6vQZafBOJEgLZEW4pTPrIsJLBYBGhLi0WS1yEBEhChLdGW2A5IIIkEaEtJrFXGRAK9IkBboi31Kvd4XxLoJAHaUifp8tokkDYCtCXaUtpynvGmgwBtKR31zChJoDsEaEu0pe5kGu9CAt0lQFvqLm/ejQSSTYC2RFtKdoYzurQSoC2lteYZNwl0ggBtibbUibziNUmg1wRoS72uAd6fBJJEgLZEW0pSPjMWEniGAG3pGRL8LwmQwMIJ0JZoSwvPIl6BBOJHgLYUvzphiUigfwnQlmhL/Zu9LDkJtCdAW2rPhu+QAAnMlQBtibY015zh8STQDwRoS/1QSywjCfQLAdoSbalfcpXlJIG5EKAtzYUWjyUBEjg5AdoSbenkGcJ3SaA/CfTSlhqNhoJmWdbMzEyhUDhw4ECEsdFc1Evf96P93CABEogvAdoSbSm+2cmSkcD8CfTSllSpi8Wi2gBw3XXXvelNb7r11lsrlYraWavVLMuaf3w8kwRIoJsEaEu0pW7mG+9FAt0i0DNb8jxPxej7fq1WK5fLuVxu165dswOPupSCIJi9n9skQAIxJUBboi3FNDVZLBJYEIGe2ZKIlMtl13VV8ffv3w+EhWk0GlZzcRwniozdSxEKbpBArAnQlmhLsU5QFo4E5kmgl7YUBIHfXESkUqkA2Lt37+w4TNOMxjbN3s9tEiCBmBKgLdGWYpqaLBYJLIhAz2wpehJXqVQajUalUlm6dKmIuM0lelcFZ5rmgqLkySRAAt0hQFuiLXUn03gXEugugZ7Zkoh4nmeapnriVq1WAUxOTkbhB0Ew+2tx0X5ukAAJxJcAbYm2FN/sZMlIYP4EemZL0SM2NSZpenoagG3bKpTZfUuu67Jvaf41zDNJoJsEaEu0pW7mG+9FAt0i0DNbUn1LUZjFYlHX9VKpFO3hBgmQQAwIWJXqjHgivrgyacmeQGq2VxY/3HPiWrd/7Uu1+R1Wa+OaMR0XDmIGsLSmQ5z4L3RXg2fAB3xk6zoCHfchA2AHMBO+1AQIADdctQDwNaMWbmg+MtWMITocGHfC0LMY1Y0AmqNpkgtP8ZFpe18DvqHdhRyGMK7DQ6YEeCcWL9qDjBhw8rgbWT2HzUBVywhQjA44bkNHPSyAUc4vqy0JCSwbm3gokMaJxNSeQEzHsVxbpPm9l0CmHam5gfi+P/s7LrP/NzIGucEikECKCNCWUlTZDJUE5k6gWjfL4V9xT+o1L/zT7oiEM6A5rdemVwWeSGCvffxhaBkdwxg4cJxMRC+TaksrlthGJmg634EBHIV2/s7tO5om1IablEVM8QMJJ0sxfZn2/LqaOOXEiVQ4o8rc05hnkMBCCdCWFkqQ55NAogk40WRngRs6k1lp9n+4bf71xXZLXjj3/vSG4X/PLoOh/QL5g5EeHbeRVFsCDiNjYUk1s8QcxFNA9vHHfmmW20BzJZQk1VcXhJB9u+miT8+vIkEQeJ4XSVLkT4lOPAZHAvEiQFuKV32wNCQQLwLqT7gUN2x6cMOG9Zu3rlu36Ycbt/90ZGS45bp1fNfo+MiadXvWrN11+/d/nFt6bg5TqXwSF8AQZAVwcngksxQ/uv97T+3e1RLayMjw+uEn1m8YXje6Zt3GX6wdWbNh3Z5NYzt3bH8iegznOI6SpKC5xCtJWBoSSAEB2lIKKpkhksC8CfjSqMj4lp+eeyEGl/wu8CroeeBc5NF6xSBygLEM+XPOOHcIg8jnfqwZ5nFdStHLpPYtZcLhVg5yMlCQs5Y8hAKyuYuAV7eGlgeyQMZAARhECBDP0/LIrsC+fftUl5LrutHGvCuTJ5IACcybAG1p3uh4IgmkgEDgiiN7DqyFoefxHeDBoWX/mss8YmC85TqI7YNLHgOeAB4s6F+Cdu45Q3uyukR6dNxGUm1p+ZBA/zVgA/XB3P0wssuXfjOP/2wJzcB4Hhty2KeH48cfAsYzOJrDj3Tt/xkbG1M/eBD9tkH0xeEUJB9DJIEYEaAtxagyWBQSiBsBu3TYLsrEjkegLR/CliUQIzsDXQy0XjW4hYKED6FgDegPAi/O4XFg5jhJil4m1ZaAaWDHkiViwM8b34dxTh6PDhqtoRmQJZqVM5rcclO6LjmIjv9E/oXDw8Pqe3DRLCq0pbi1EZYnJQRoSympaIZJAvMi4DliyYaJ/4AxZGBLIS/ALmT88Av8LVfYWLIfmhuO18neC+PMMwb+Z5mRur6lZaHu1EIBQlU3bsbgSuAxwGsNTfOBWviu7iF/BDnRdYH2LxjE2NiYqrZKpaI2HMeJhnvPq0Z5EgmQwHwI0JbmQ43nkEBKCHjhnPuVjePD0JZltA3Qy0CQaTN5khbOltSc6AhmQRfgduQLGYxp8KPOpOM2ksfUSnsAACAASURBVNq3NGcOGQvwcwg0TaA5uhFkMQpDHxkZUZmmepjoSSlpdwwzhgRoSzGsFBaJBOJCgLak9G7us1PO0RppS3FJeZaDBFoToC215sK9JEAC4YT77FtqdqTRltgcSCDlBGhLKU8Ahk8CJyNAW2Lf0snyg++RQGoI0JZSU9UMlATmToC2RFuae9bwDBJIIAHaUgIrlSGRwGIRoC3RlhYrl3gdEuhrArSlvq4+Fp4EOkuAtkRb6myG8eok0CcEaEt9UlEsJgn0ggBtibbUi7zjPUkgdgR6ZkuNRkPBUD8bOT09DUBNUxsEgZrsXx3geV50cOz4sUAkkGgCtCXaUqITnMGRwOkS6JkthV9O9jzTNNXvH1WrVQCTk5PR9GtBEDQajegnuE83IB5HAiSweARoS7SlxcsmXokE+phAz2xJTU0rIpVKpdFoVCqVpUuXiojTXKJ3FdroN5L6mDSLTgJ9SIC2RFvqw7RlkUlg8Qn0zJZEJAgCv7koZwKwd+/e2SGapslncLOBcJsEukyAtkRb6nLK8XYkEE8CvbSlcrkcjU/av38/EBZGPX2zLEs9oVPU+DwuntnDUiWeAG2JtpT4JGeAJHA6BHpmS9GzNt/3a7VauVzO5XK7du2aXejZx8zez20SIIHuEKAt0Za6k2m8CwnEnEDPbCniUiwW1TaA66677s1vfvNtt91WrVbVzmq1yodxEStukECXCdCWaEtdTjnejgTiSaCXthRpkGVZMzMzhULhwIEDESbLsqIDok6m6F1ukAAJdIEAbYm21IU04y1IIP4EemlLsx2oWCzqul4qleKPjCUkgfQQoC3RltKT7YyUBE5CgLZ0Ejh8iwTSToC2RFtKextg/CTQJEBbYiKQAAm0JUBboi21TQ6+QQJpIkBbSlNtM1YSmCMB2hJtaY4pw8NJIJkEaEvJrFdGRQKLQoC2RFtalETiRUig3wnQlvq9Bll+EuggAdoSbamD6cVLk0D/EKAt9U9dsaQk0HUCtCXaUteTjjckgTgSoC3FsVZYJhKICQHaEm0pJqnIYpBAbwnQlnrLn3cngVgToC3RlmKdoCwcCXSLAG2pW6R5HxLoQwK0JdpSH6Yti0wCi0+AtrT4THlFEkgMAdoSbSkxycxASGAhBGhLC6HHc0kg4QRoS7SlhKc4wyOB0yNAWzo9TjyKBFJJgLZEW0pl4jNoEjieAG3peCJ8TQIkEBGgLdGWomTgBgmkmQBtKc21z9hJ4BQEaEu0pVOkCN8mgXQQoC2lo54ZJQnMiwBtibY0r8ThSSSQNAK0paTVKOMhgUUkQFuiLS1iOvFSJNC/BGhL/Vt3LDkJdJwAbYm21PEk4w1IoB8I0Jb6oZZYRhLoEQHaEm2pR6nH25JAvAjQluJVHywNCcSKAG2JthSrhGRhSKBXBGhLvSLP+5JAHxCgLdGW+iBNWUQS6DwB2lLnGfMOJNC3BGhLtKW+TV4WnAQWkwBtaTFp8lokkDACtCXaUsJSmuGQwPwI0Jbmx41nkUAqCNCWaEupSHQGSQKnItAzW/J9X0R83y+VSiJi2zaAo0ePep4XBEFUbNu21ZHRHm6QAAl0jQBtibbUtWTjjUggzgR6ZksiUqvVLMtSdA4dOgQ8WxjXdR3HcV03aC4UpjjnEMuWYAK0JdpSgtOboZHA6RN4VlBO/5xFOdJ13eg6pmmWy+V8Pn/o0KGoY0mpkjqm0WhEB3ODBEigawRoS7SlriUbb0QCcSbQM1uKoKgncSIC4KqrrnrXu951zz33OI4jIp7nVSqVyJ+iU7hBAiTQHQK0JdpSdzKNdyGBmBPopS1Fj+HK5fKxY8dWrlypDEn9a5pmxK5Wq0Xb3CABEugaAdoSbalrycYbkUCcCfTSlorFYvSIbWpqCsC+fftmP6ETkSAIPM+LDoszSpaNBJJHgLZEW0peVjMiEpgHgZ7ZUmRFajR3qVQqFAqe50UP4CqVim3b8wiJp5AACSwWAdoSbWmxconXIYG+JtB7W1JP3EzTBDA1NaW+BBcx9X0/8qpoJzdIgAS6Q4C2RFvqTqbxLiQQcwI9s6VoiJICVCwWdV2PRnzHnBqLRwIpIUBboi2lJNUZJgmcnABt6eR8+C4JpJoAbYm2lOoGwOBJ4BkCtKVnSPC/JEACJxCgLdGWTkgK7iCBNBKgLaWx1hkzCZwmAdoSbek0U4WHkUCyCdCWkl2/jI4EFkSAtkRbWlAC8WQSSAoB2lJSapJxkEAHCNCWaEsdSCtekgT6jwBtqf/qjCUmga4RoC3RlrqWbLwRCcSZAG0pzrXDspFAjwnQlmhLPU5B3p4E4kGAthSPemApSCCWBGhLtKVYJiYLRQLdJkBb6jZx3o8E+ogAbYm21EfpyqKSQOcI0JY6x5ZXJoG+J0Bboi31fRIzABJYDAK0pcWgyGuQQEIJ0JZoSwlNbYZFAnMjQFuaGy8eTQKpIkBboi2lKuEZLAm0I0BbakeG+0mABIS2RFtiMyABEhAR2hLTgARIoC0B2hJtqW1y8A0SSBMB2lKaapuxksAcCdCWaEtzTBkeTgLJJHAyW/J9v1qtqrjr9bqIOI7jum65XFY7TdNUG41GwzRN3/dFRP1r27aI1Ot1tRHB8zwvOkZtq7eKxaKu66VSKTqSGyRAAotOoCHVI7W6LeKJU7OmAnEdV4JA3DarGRRF/C0Ta4DlZ2VdwAVsA6Ic4sR/dQSAD5gFXYDbkS9kMKbBP/HIpy1EdzV4RniKj2xdR6DjPmQA7ABmwpeaILxm89ZaeHHNqEELoPnIVDOG6HBg3AlDz2JUNwJojqZJThUjY7W7rwHf0O5CDkMY1+EhUwK8dgdrCJARA04edyOr57AZqGoZAYrtTpkzBzSgec2zXGTMjCEZ/Az64OimjbVG4AXhI1FXAk/80F99cX1xm5X49J5A1DEi4rqu+tSNPp+DIFj0ROIFSSBtBNraUqQytVpN6ZESJgVo7969qilalnXs2LGI2vT0tIh4nmfbdqVSERHVbg8ePCgikWZZlqUOi06kLUUouEECnSMQyCGRqogj4vi2Kb7UZ4LwldRbrpZI4Mua1Y9DzwAb9PzhwlmTAwO0pS7Y0kMwBjZvebJen5ZAPLcRSFnC1ZFAxA+a9VVs1qYf7gn16en/uS0Wi9EHbPRJ3rmk4pVJIA0E2tqSiMzMzET/d/Ld7373Fa94RaFQuPTSS//rv/5LoZndbxQEwZ133vma17wGwMtf/vKf//znIlKr1VQP0+Tk5DXXXHPOOecA+K3f+q0jR45EjVldiraUhmxjjD0n4JXCv7ZrHx3fPLxny9iOsQ1PrF3zX5s2/mJ0ZG3L9dFNv1i1fv0P7vxG4Rzk9OHcgAmYQGXR+lTYt4Qg7LuC/Uzfko1srdm39BPouX9/8PZ1a5/YOLZ53Zr1IyNPbty4Zmx0w9iGLaMbNo6OrBsbe2JsbM3YyPjo8KbRkeGRkcc3bNhwXI5ZlkVhOo4JX5LAPAi0tSX1QE1d8bbbbnvhC19488037969++Mf//j5558/NTUV3czzPNM0V69enc1mb7nllqeeeurzn//8hRdeuGrVKtW3tGPHjuXLl19//fWbNm06fPjwAw880Gg0aEsRQG6QQBcJmPv2rTv/gmXAcuD5YY9RFliiQVvWei1cDPx2Yck5yCGHNRlDAK9QYN/Sovct2ZomzSdxDrJVQ5cM/ht6FkYG+bORfQFwLvTlyK0AVoQVh+dDWwF9KbSzgPOA54XVZ2QuvvjiiYmJIAjM5tLFvOKtSCDhBNrakuOEvfO+78/MzPzhH/7hxz72saifaWBg4Fvf+pY6oNFouK4rIu985zs/8IEPuK5rmqbneW94wxs++MEPKiW69tpr3//+988GSVuaTYPbJNA1ApWSv358A/AK4NtnLz2U13cCW4C9Ota3XLNLfgH8JIu/QOEFQ9kRTa8AxWy+7XigOY/XYd+S6ltqDrcyIICDbNnQxcCD0AH855LCcN7YDIxm9bGcsQFYD2w0sNXAmIF1BkYMbNLDwWH/C+2/AajuJTUcomt5xRuRQOIJtLUlJTQiYlkWgCeeeEJEgiCo1Wof/vCHlf2oB21qXOE555zz5S9/OeL153/+529605vUS8MwvvnNb15++eWapl1++eX33HOP6ria3T/MJ3EROm6QQCcJFDcf+B9kzgRuBqaBo7kBc9lS0bO1lquRNZdCluJfgIs0rDZ0yRbCv+h8ErfIo7w1Tw8NScJHcplS05YegAFo45mBw+HAdlSNXD07UIZRMrKWkfGMXN3IlY1cXc/YWqaK3K9RmDjzzDN/9atfRfnTaDRmjzeN9nODBEhgrgTa2pK6kOM409PTADZu3Bh9Ye1v//ZvL7roouirbZVKxXGcFStWPPjgg0EQqMb5T//0T8973vNqtdru3buXL1+ez+dvuumm7du3f+1rXzMMY926dXwSN9eq4vEksAgEqjK28QnkXlkoPGboAn0a+q6wPwNem/XAGVk5M387sGLAeFKDn8kLUKMtLbIt6f6ztpSd0cOncveHtoSt0ErNCmo0v2zoh6oafk+w+S3Cp//1mt8ZPArsBLB69eqpqSn1v7vq+zSLkDa8BAmknkBbW4qexO3bt2/ZsmWPPvqoYuW67ic/+cnXve51qqtJRNR33wzD+OEPfxg50He+852zzz5bRPbs2VMoFK699tqoI+qP/uiPVNcU+5ZSn34E0HUCpowP3w+cO4BHdbgDhmS0Ug6SQdByhe7mNVmCe2AMnrPiF8Ah6D7y07SlztvSvc2ZFLYP5Kp5TQz4eU2y4VwMYY1k8eyaCaddcDRMQtsGYPv27VFWqbkD6EwREG6QwLwJtLUlv7moMUkAHn74YTVk2/f966+//k//9E/VF+KizqQXv/jFf/d3f6cUqtFofOMb33jZy16mTgFwyy23BEGg9Oiv/uqv/uAP/kA941P/qsYM4Nprr73yyiv/5E/+5K1vfeuHPvShu+66a2ZmRn2rbt4R8kQSIIHZBMZGNkFHFsPQBRkPqBfaz5/U8XmGOG5JjVuaK4dw6ik1/VU4JVVzuNhMc5IqjI+PR9/R4UxLszOf2ySwEAJtbUld9MiRI47jXHXVVR/5yEeihgfgjjvuUAeoZun7/jvf+c7rr79eRNSElpdeeulHP/pRdczv//7vX3PNNWp4k2ma733ve9UA8GhoVLlcnpyczGQye/bsURd0HKdSqShXW0h4PJcESOA4ArQlDUHsZqekLR2XpnxJAjEj0NaW1JRIanDSD3/4w2XLlv3DP/zD+vXrP/GJT7z4xS/evHmziHzkIx/57Gc/KyKNRuOxxx4D8MUvfvHAgQNf+9rXBgYG1q1b5zhOEAQPP/zwsmXLbrzxxlKpdMMNN0Tf2pjdPzw5OZnL5dR04REix3Esy7KbS7STGyRAAgshQFuiLS0kf3guCaSTQFtbUl1BlUpFPXH79re//drXvnb58uWvfvWr169frwYhveENb3jXu94V9QA99NBDl1xyCYBLLrnkwQcfVEDVoO+bb775la98JYBLL7304YcfVoOi1CAnNTGB4zgADhw4oHZG10xnrTBqEugcAdoSbalz2cUrk0BSCZzMltQwoyAI1NOxPXv2zB5CNPuLqY7jqJmZFCbbtlW/URAEkfeoqyk38jwv6lgqlUpq8BMA9dMoQRBYluW6ru/7qnspukhSq4FxkUDXCNCWaEtdSzbeiAQSQ6CtLfm+r5TluFBd11Wio74KV61WZ2ZmlAlF45Cir7+p3+VVA56qzcX3fdVZpU5RPVjqV1YANJpL9FY0ScFxZeBLEiCBeROgLdGW5p08PJEEUkugrS2pJ2LValX1Bqlen6iPR31VLaJm2/axY8eCIFAmpH7T0bbtaGC4OjI6XU3d5DQX9ValUgEwNTUVzRiuRMq2bcdxZvtTdFNukAAJzIMAbYm2NI+04SkkkHICbW0pGloUdfAo9VF9S9E3VE3TjI5UP06kgKrfP1GHNRqNSJtM04we0qkjlTMVi8VCoaBkS91x9o9BRrdIeW0xfBJYOAHaEm1p4VnEK5BA2gi0taUugJjdY8RfPukCcN6CBESEtkRbYkMgARKYKwHa0lyJ8XgS6G8CtCXaUn9nMEtPAr0gQFvqBXXekwR6R4C2RFvqXfbxziTQrwRoS/1acyw3CcyPAG2JtjS/zOFZJJBmArSlNNc+Y08jAdoSbSmNec+YSWBhBGhLC+PHs0mg3wjQlmhL/ZazLC8J9J4Aban3dcASkEA3CdCWaEvdzDfeiwSSQYC2lIx6ZBQkcLoEaEu0pdPNFR5HAiTwDAHa0jMk+F8SSAcB2hJtKR2ZzihJYDEJ0JYWkyavRQLxJ0Bboi3FP0tZQhKIGwHaUtxqhOUhgc4SoC3RljqbYbw6CSSRAG0pibXKmEigPQHaEm2pfXbwHRIggdYEaEutuXAvCSSVAG2JtpTU3GZcJNA5ArSlzrHllUkgjgRoS7SlOOYly0QC8SZAW4p3/bB0JLDYBGhLtKXFzilejwSST4C2lPw6ZoQkMJsAbYm2NDsfuE0CJHA6BHpmS47jqPKZpikijUYDwJEjR4LmEhXd933XdaOX3CABElggAdoSbWmBKcTTSSCFBHpvS7Ztu65bLpcHBgZ83xcRz/MqzcW27RRWCUMmgY4SoC3RljqaYLw4CSSSQM9sSUSKxaLqWBKRqakpAPv27TuuJykIAs/zGo1GIukzKBLoPgHaEm2p+1nHO5JAvxPopS1ZlqXwlcvlY8eOrVy5UnUsqX8jkRKRWq3W76BZfhKICQHaEm0pJqnIYpBAHxHopS0pTKVSSW0AuOqqq971rnfdc889alSTeiQXBEEfAWVRSSDmBGhLtKWYpyiLRwIxJNAzW/I8L8JhmmapVMrn8wcPHozcyHXdaJtP4iJW3CCBBRKgLdGWFphCPJ0EUkigZ7YkIvV6PXoYd/DgQQCRHrmu6ziOEqYgCNTo7xRWD0MmgUUnQFuiLS16UvGCJJB4Aj2zJSVGQRCoJ3GWZakZBDzPi5xJRGzbpiolPgsZYDcJ0JZoS93MN96LBJJBoGe2FA3oVhyLxaKu69EYpmTAZRQkEEMCtCXaUgzTkkUigZgToC3FvIJYPBJYZAK0JdrSIqcUL0cCKSBAW0pBJTNEEphFgLZEW5qVDtwkARI4LQK0pdPCxINIIDEEaEu0pcQkMwMhga4RoC11DTVvRAKxIEBboi3FIhFZCBLoKwK0pb6qLhaWBBZMgLZEW1pwEvECJJA6ArSl1FU5A045AdoSbSnlTYDhk8A8CNCW5gGNp5BAHxOgLdGW+jh9WXQS6BEB2lKPwPO2JNAjArQl2lKPUo+3JYE+JkBb6uPKY9FJYB4EaEu0pXmkDU8hgZQToC2lPAEYfuoI0JZoS6lLegZMAgsmQFtaMEJegAT6igBtibbUVwnLwpJALAjQlmJRDSwECXSNAG2JttS1ZOONSCAxBGhLialKBkICp0WAtkRbOq1E4UEkQAKzCNCWZsHgJgmkgABtibaUgjRniCSwyARoS4sMlJcjgZgToC3RlmKeoiweCcSQAG0phpXCIpFABwnQlmhLHUwvXpoEEkqAtpTQimVYJNCGAG2JttQmNbibBEigLQHaUls0fIMEEkmAtkRbSmRiMygS6CgB2lJH8fLiJBA7ArQl2lLskpIFIoHYE6Atxb6KWEASWFQCtCXa0qImFC9GAqkgQFtKRTUzSBKICNCWaEtRMnCDBEjgNAnQlk4TFA8jgYQQoC3RlhKSygyDBLpIgLbURdi8FQnEgABtibYUgzRkEUigzwj00pYajYaiZVnWzMxMoVA4cOBAxK/RXNRL3/ej/dwgARJYCAHaEm1pIfnDc0kgnQR6aUuKeLFYVBsArrvuuje96U233nprpVJRO2u1mmVZ6awbRk0CnSBAW6ItdSKveE0SSDaBntmS53mKrO/7tVqtXC7ncrldu3bNxh11KQVBMHs/t0mABOZNgLZEW5p38vBEEkgtgZ7ZkoiUy2XXdRX6/fv3A2FhGo2G1Vwcx4lqhd1LEQpukMACCdCWaEsLTCGeTgIpJNBLWwqCwG8uIlKpVADs3bt3dh2YphmNbZq9n9skQALzJkBboi3NO3l4IgmklkDPbCl6ElepVBqNRqVSWbp0qYi4zSV6V1WMaZqprSEGTgKLS4C2RFta3Izi1UggDQR6Zksi4nmeaZrqiVu1WgUwOTkZQQ+CYPbX4qL93CABElgIAdoSbWkh+cNzSSCdBHpmS9EjNjUmaXp6GoBt26oaZvctua7LvqV0Ziej7gQB2hJtqRN5xWuSQLIJ9MyWVN9SBLdYLOq6XiqVoj3cIAESmE0g+kqEiKhvidq27YXfFrXEEzFFwv/X2CMyJY5I4LZcbV82bduIAvLZtVpBYPiGITpMDUHLFRkx4ORxN7J6DpuBqpYRoNjyYA2BjgDwAbOgC3A78oUMxjT47Y6H7mrwjPAUH9m6Hl7hPmQA7ABmwpeaILymG65aeHHNqIUbmo9MNRMW3oFxJww9i1HdCKA5miY5VYyM1e6+BnxDuws5DGFch4dMCfDaHawhiB+HRohFC6CXoDcMXTJhDW4BBnfv2eqbvj+t8mG3yJGT5EPddR0RN1ythhxpuMckCBOKCwmQwHEEaEvHAeFLEogpgciWfN9XtuR5niXiyFGRYihM4aQcxzyp2Y4E4rdcGw0ZHdkCA8A6oApUcwX/rLy0E4X4WQJtSVljfZYt2YYuRqikE9CzG7Y+YtqHonxwpOJ6bfMhEDHNwPdDRwpCa7JCceKELTH9DGCxekmAttRL+rw3CZw+gejxtOM40VRkViANMW054vvieeIGYQdTzZbAb736TnVs3bZlS19wtnEwlxNkq9BngBptqd/6luqaJtAFehm6siUXGM0s+T+bdm205Ui97pdKUqxI1Za60zoZgvAnEhzPssUXuy6+LY4d9ixZ3vTppyWPJIGUEKAtpaSiGWbfE4gMybZt1bcUhJNwSCBVT/a4ciRo9i654ltSlcBpvcqhx3/+SNY4C1gDHMOSmcxgI2ewb6nvnsTVnrGlGjSr2bdkNfsLlz257mci+wKZjvKhIZXWyRA4DfPXnnM0fNcV3wwTKBDXk6d/X6Hv2wwDIIHFI0BbWjyWvBIJdJLAbFtS9zFNc++2Xds3bdo0tnpk5PHR0dGxsW3jE+vHtv73xOjaluvoxCP//L3vnnfeOWdh2EAZg1VodcBm31Kf9S1pFT3sWBLoNWiOrokePld94txlK/71n/95zaqfj4w8vnr16tHRretHVj2+9p6WyTAxunbt8Krh0Ud+tWe9BGYoTLZ4vtS8cicTmdcmgb4kQFvqy2pjoVNIILIlNYDJ87zJyclsHhoArAAGYWShDUHPIAdomdYrLgFeCAM5/EzX6igIED7HoS31ly1petOWDIFuPmNLJeCRTA7Lz1oKrNBzZ0X5kF/RNh/07NuAFy1fObRh+KcSOFZdXDccvsSFBEjgOAK0peOA8CUJxJRAZEvqMVyj0di5c2cu94cD+NdBHB7Avow2amBrFrsGMJHHzpZrIX/fwOBfYcmKpcZqwAI8oDGQb/2FuFh+F4yjvMNR3ppeCvuWQluylC1pmAYeBi7L4fvA5jMyhwvZTVlsBzYZGGmZDHnsBP5H0z8HXLBz16hIWQIJArHC8UxcSIAEnkOAtvQcHHxBArElENmSKmG1Wt24cSOyZwI3I/wWvSB/GCiG2/CgOS1XHTbwjzD+Tw7rdE2yQwI0NP0Q+5b6rW+pZBjH2dJR4KfInrlk2Z0DhmTDXsOd+oBl5CT0qjb5AJSfd+448IbxiQ216q9EnECkWK/HthWwYCTQKwK0pV6R531JYM4EookD1JkjIyPpm2eIfUuLOe8UDC/sf9IyGzesDn93qjn3hHhPzxI85wTlCSSQXAK0peTWLSNLHAHaEmenXNxZOmlLifuQYECdIkBb6hRZXpcEFp0AbYm2RFta9GbFC5LA6RCgLZ0OJR5DArEgQFuiLdGWYtEUWYj0EaAtpa/OGXHfEqAt0ZZoS33bfFnw/iZAW+rv+mPpU0WAtkRboi2lqskz2PgQoC3Fpy5YEhI4BQHaEm2JtnSKRsK3SaAzBGhLneHKq5JABwjQlmhLtKUONCxekgROTaBnttRoNFTpLMsSkenpaQC2Hc7zEQSB+m0HdYDnedHBpw6IR5BAcgnQlmhLtKXktm9GFmsCPbMlEfE8zzRNx3FEpFqtApicnFR/D5QzNRoN5VKxRsjCkUC3CNCWaEu0pW61Nt6HBJ5DoGe25HmeKkilUmk0GpVKZenSpSLiNJfoXXWMaZrPKTVfkEAqCdCWaEu0pVQ2fQbdewI9syXVe+Q3FxGpVCoA9u7dOxuJaZp8BjcbCLdTToC2RFuiLaX8Q4Dh94pAL22pXC5H45P2798PhIVRT98sy1JP6BQXPo/rVX7wvrEiQFuiLdGWYtUkWZj0EOiZLUXP2nzfr9Vq5XI5l8vt2rVrNvrZx8zez20SSCcB2hJtibaUzrbPqHtOoGe2FEVeLBbVNoDrrrvuzW9+82233VatVtXOarXKh3ERK26knABtibZEW0r5hwDD7xWBXtpSpEGWZc3MzBQKhQMHDkQgLMuKDog6maJ3uUECKSRAW6It0ZZS2PAZchwI9NKWZjtQsVjUdb1UKsUBCstAAvEkQFuiLdGW4tk2WarEE6AtJb6KGWByCNCWaEu0peS0Z0bSVwRoS31VXSxsugnQlmhLtKV0fwYw+p4RoC31DD1vTAJzJUBboi3Rlubaang8CSwKAdrSomDkRUigGwRoS7Ql2lI3WhrvQQInEKAtnYCEO0ggrgRoS7Ql2lJcWyfLlXACtKWEVzDDSxIB2hJtibaUpBbNWPqIAG2pjyqLRU07AdoSbYm2lPZPAcbfIwK0pR6B521JYO4EaEu0JdrS3NsNzyCBNrqwPgAAIABJREFURSBAW1oEiLwECXSHAG2JtkRb6k5b411I4DgCtKXjgPAlCcSXAG2JtkRbim/7ZMkSTYC2lOjqZXDJIkBboi3RlpLVphlN3xCgLfVNVbGgJEBboi3Rlvg5QAI9IUBb6gl23pQE5kOAtkRboi3Np+XwHBJYMAHa0oIR8gIk0C0CtCXaEm2pW62N9yGB5xCgLT0HB1+QQJwJ0JZoS7SlOLdQli3BBE5mS57nBc1FRGZmZkTE9/1araZwNBoNEanX6yfSaTQalmWp/a7rikipVFKni4jjOL7vi4jnedG5xWJR13V1WLSTGyRAArMJ0JZoS7Sl2S2C2yTQNQJtbUnpkeM4kdMo71ElU7ojIrZti4hlWfV6PdqpjnEcp1arHTlyRL2sVqsiomSLttS1CuaNkkSAtkRboi0lqUUzlj4i0NaWHMdRYSjLMU1zampK9Q/Ztl0ul9W7yn4io6pWq6ZpiohpmlG3U7lcPnTokDo+OpJ9S32UJSxqTAjQlmhLtKWYNEYWI20E2tqSiFQqldn9SbPRRLZk27YSIOVGs4+fmZkJgiBypuhxXvRgbrY58UncbLzcJoGWBGhLtCXaUsumwZ0k0GkCbW0p6lsSkWPHjinFcRznwIEDqkyRBnme57quGtKkBh5NTk5G2qSGNzUajRN1irbU6drl9RNGgLZEW6ItJaxRM5x+IdDWlkQkCILogdqXvvSl3/iN3xgaGnrve9979913qxFLkRKpaB944IHLLrvMMIzf/d3f/clPfqLGM0WDu0Xk6quvPvvssz/96U+r0U60pX7JEpYzJgRoS7Ql2lJMGiOLkTYCbW2p1lyU8dx7770veMELvvvd705MTFx99dW/8zu/s3v3bjVSO/ru22OPPQbgK1/5yq9//etPfepTK1euHB8f95tLEATVavXf/u3fXvOa1zz/+c///ve/ryjTltKWbYx3gQRoS7Ql2tICGxFPJ4H5EWhrS+pyanzSq1/96uuvv15E1GO15cuX33rrrepLc6p7ybbtq6+++gMf+IDTXETkJS95yV//9V97nqd06tChQxdeeOHatWtf/vKXf+tb31LXoS3Nr854VmoJ0JZoS7Sl1DZ/Bt5bAm1tKeo0EhEAP/vZz9Q8SbVa7c/+7M/e/va3Rw/a1Cf4+eeff+ONN0bB3HzzzS996UsjwbrssstuvfVWEXnBC15w8803q3FO6iGdGupk2zaAo0ePqu/KNRoN27bd5hJdkxskkHICtCXaEm0p5R8CDL9XBNrakipQpVLZtGkTgIcfflhNJSAi11xzzdve9jY1altJled555133l133eV5XrFYFJHvfOc75513nrrIV77ylXe84x2VSqVWq73uda+76aab1P5arRY52aFDh4CwMGoCggiH7/uu687uhYre4gYJpI0AbYm2RFtKW6tnvDEhcApbEpH9+/efc845ExMTak6Bcrn85S9/+fLLL1cTeauJlCzLAvDAAw+oqEzTvP32288991zbtletWnXBBReouZpEJJPJfO973xOR2SPETdMsl8v5fP7QoUP1el39SajX6+VyWY0HjwksFoMEekuAtkRboi31tg3y7qkl0NaWyuWyGsftui6AH/zgB4qR4zgf+9jH3v3ud6sPbvU0zXGcSy655KabbrIsSz2w+9SnPvX6179eRP7+7//+3HPPxTNLLpcbai4R8ejXTgBcddVVH/rQh97+9re/4Q1v+OAHP/gf//Efqlcp6taKzuIGCaSQAG2JtkRbSmHDZ8hxINDWllThVNfOFVdc8fGPf7xer6sHZ6p/aHJyMvrsDoLgLW95y/vf/34RUQPDX/Oa13zmM59xXdeyrJGRkaeeemrLli2HDx9+0Yte9JnPfEZN2hQ9hiuXy8eOHVu5cqXqvopuXSwWTdP0fZ9P4uKQKyxDzwlELU6VZGRkBIaexahuBNAcTZMcAsBHxtIQtFwN+IZ2F3IYwrgOD5kS4LU8Uu1ERgw4edyNrJ7DZqCqZQQotjtFVwWAWdAFuB35QgZjGvx2x0N3NXgG/LDY2bqOQMd9yADYAcyELzVBeE13cS2BHJ6uX8PLYju0zMYNq8Mef0cC8cULf8+KCwmQwGwCbW2pWq2qCSo9z7vtttsuvPDCW265Zf/+/Z/4xCde8IIXHDhwwPO8D3/4w3/xF3+hupd27NgB4Ktf/erevXs/+clPnn322RMTE6qfqV6vu65r27bjOCtWrLjtttvUd+KKxaLaEJGpqSkA+/bti7qsZpcymglz9k5uk0DaCNCW2Le0uNYI2lLaPkQY73wJtLUl5UDqZ+BE5Etf+tJLXvKSbDZ7xRVXROOTrrjiive9731qHksRue+++1772teeffbZL3vZyx5++OETi3TkyJFXvvKV3//+9x3HicYtqe1SqVQoFNS04OpE3/et5tLSn068OPeQQOIJ0JZoS7SlxDdzBhhPAm1tKbKZIAgqlYqIqMFD0UOxSqWiOp/UxEvqXdu2o34g9aBNfb6rcdyqD0mBiK4f/QovADUYPAiC6F2lYhSmeGYPS9VlArQl2hJtqcuNjrcjAUWgrS11AVAkXiLCX9XtAnDeot8J0JZoS7Slfm/FLH+fEqAt9WnFsdhpJEBboi3RltLY8hlzDAjQlmJQCSwCCZweAdoSbYm2dHpthUeRwCIToC0tMlBejgQ6R4C2RFuiLXWuffHKJHASArSlk8DhWyQQLwK0JdoSbSlebZKlSQ0B2lJqqpqB9j8B2hJtibbU/+2YEfQlAdpSX1YbC51OArQl2hJtKZ1tn1H3nABtqedVwAKQwOkSoC3RlmhLp9taeBwJLCoB2tKi4uTFSKCTBGhLtCXaUidbGK9NAm0J0JbaouEbJBA3ArQl2hJtKW6tkuVJCQHaUkoqmmEmgQBtibZEW0pCS2YMfUiAttSHlcYip5UAbYm2RFtKa+tn3D0mQFvqcQXw9iRw+gRoS7Ql2tLptxceSQKLSIC2tIgweSkS6CwB2hJtibbU2TbGq5NAGwK0pTZguJsE4keAtkRboi3Fr12yRKkgQFtKRTUzyGQQoC3RlmhLyWjLjKLvCNCW+q7KWOAkEPB93/M8EanVarPj8TzxAwnk+NXx3EDE98P9ntR8qdquNTHxFAw9i1HdCKA5miY5BICPjKUhaLka8A3tLuQwhHEdHjIlwGt5pNqJjBhw8rgbWT2HzUBVywhQbHeKrgoAs6ALcDvyhQzGNPjtjofuavAM+GGxs3UdgY77kAGwA5gJX2qC8Jru4loCOTxdv3oAjOp40ZZ1u0UmA5F63Rc5IL60XKcruzw54MlkyTziieuJ5dqehInMhQQSToC2lPAKZnixJWDbtoiofz3PazQa9Xo9ECcQR55erWc2nEAaIq7r2s09NZGq7VTGxsZoSzocGHeSw/w4YGAGeABaZt1jT4pMBb5Y1aaqP5uEUTY2NxwRV3xPAl+CQLUtP/QqLiSQdAK0paTXMOOLKwHlSap0pmmqjcCVwA27j47/P/vmHqse/q1S77qWbBxh35LMzxLYt/R031J2Brh7cAWG1/xcZHcgbr1mi5TDNGu1WrVQp7xGmJ+Vomk1xPMCX0Lv50ICySZAW0p2/TK6mBLwPM91XREJgsD3fWVOGzduHB753w0jT46MrhsZGR4Nlw3hdnMdHVu3es3jIyNjIxs2j45sGRkZ/vED7FOhLfnIVDPGPDkAjQy2Ll1x4b/c+vCqtcMjG3evX795y6Yw/VquY1t/vHHTY9u3rtu7d5XIMWn2MHmhWHEhgYQToC0lvIIZXmwJeJ7n+75lWaqEIyMjv/mbv4k8nl5zQF57zstBINwJ6APQ8/oZwAD4BIp9SwuxJU33MvnvYhBDZz4f+QEMLENGD8eNRXl43Ia2DHgJcO45K7Fz5y/NauDYYnql2LYyFowEFosAbWmxSPI6JDA3AuoLbo1GQ532xBNPADDwSwNPZDCcxUQOW3PYnMVoFhsMbCxgQwarBrBVwy5g2xmZ9eEwao7y5rilBfQt5Qw5c/Ax4PkF3AT8yMC6nL5uCdYYGG+5Dub/exCPAJ8Dzj18cLvXCAcweTI5t9Tn0STQhwRoS31YaSxy/xNwHEcFEXUvbdu2bcmSJRkcyaCYhZuDPLP6OTg5yIDhZlEayob7DXjLho5Be4i2xL6lhfQtAWXgNuCFg9oqA362IJomGQRGmGMt1nxOVg7KGfrjwEvGNz5aOhoOb/LkQP+3SEZAAqcgQFs6BSC+TQIdIqDGLUk4L0C4jI6OAoA2CRQBO/xG/bOrAwSa7gDHcnkxDAE8Y2AfcBdtiba0EFtavqSuaV9DZtlA5rEwr3IClGA0oPmtV1jNKSfuMwbPWzX8r0Hze3I1e3+H2ggvSwLxIdBLW1IjNqzmIiIArr322iuvvPLuu+9WXxEKvzDd/JZ1fHixJCSwiATUwzglTOPj46EtcZ4hzrcU53mn4GXCab0mkMXY2Eg4z4A4AedbWsQPBV4qrgR6aUvRiI1yuTw5OZnJZPbs2RP9D3f0h0RESiWOIoxrBrFcCyAQJbnv+7Qlzk7ZB7N00pYW0N55al8T6KUtRd8GEpHJyclcLhehtG27Xq9H5uT7nP4sYsON5BCgLXEu72fm1O6TOc1pS8n5+GEkcyPQS1sSEc/z1EM3x3EAHDhwoFwuRwNg1UzH6gci5hYWjyaBfiBAW6It0Zb6oaWyjCQgPbOlqGOpVCoFQVCv1wGUy+Xj6iT6Oa3j9vMlCSSAAG2JtkRbSkBDZghpINAzW4p6jNTjtpmZGQCNRiMIAsuyarWaaZqO4/AZXBqyMLUx0pZoS7Sl1DZ/Bt5fBHpmS+FXKZqL4lWpVABMTU1Ffz/UfjXf8XE7+wsxS0sC7QhEic1R3uF0CXH+LlhGDDh53I2snsNmoKplBCgq1znxXx1BcwIIs6BLOIlovpDBmAb/xCNpS+1aB/eTQKwI9MyWor8TypmKxWKhULBtO9ofdT5J87fXY0WNhSGBRSEQZTttibakweN34halWfEiJNAJAj2zJTXEOwqpWCzqus6ZAiIg3EgDAdoSn8SxbykNLZ0xJoAAbSkBlcgQ+pUAbYm2RFvq19bLcqeMAG0pZRXOcONEgLZEW6ItxalFsiwk0JYAbaktGr5BAp0mQFuiLdGWOt3KeH0SWBQCtKVFwciLkMB8CNCWaEu0pfm0HJ5DAl0nQFvqOnLekASeIUBboi3Rlp5pDfwvCcSaAG0p1tXDwiWbAG2JtkRbSnYbZ3SJIUBbSkxVMpD+I0Bboi3Rlvqv3bLEqSRAW0pltTPoeBCgLdGWaEvxaIssBQmcggBt6RSA+DYJdI4AbYm2RFvqXPvilUlgEQnQlhYRJi9FAnMjQFuiLdGW5tZmeDQJ9IgAbalH4HlbEhChLdGWaEv8JCCBviBAW+qLamIhk0mAtkRboi0ls20zqsQRoC0lrkoZUP8QoC3RlmhL/dNeWdJUE6Atpbr6GXxvCdCWaEu0pd62Qd6dBE6TAG3pNEHxMBJYfAK0JdoSbWnx2xWvSAIdINBLW7JtO/prcezYMQDVatV1XRWm21zUtuM4HYidlySBHhOI8t/3/fHxcYTLDmBGR6BrAgSAG65aAPiaUQs3NB+ZasYQHQ6MO2HoWYzqRgDN0TTJhaf4yFjqb/CJ/xrwDe0u5DCEcR0eMiXAO/GwaA8yYsDJ425k9Rw2A1UtI0AxOuC4DV0VAGZBF+B25AsZjGnwjzsseklbUij6hgO8TJhmE8hibGxEwg9mJ/B63I54exLoAoFe2pIKz2ku5XI5l8sVi8UTY47+opz4FveQQF8TiHKbthRKXrYeaiLuQ4bWGFcOtKW+/sRh4RdAIBa25Pt+vV4fGhoyTVNEbNu2LEsF5TiO5/H/XBZQwzw1xgRoS33Tp8I+NgRa2HHIvqUYf6CwaJ0k0Etbsm3b930V3fT0NICnnnoq+vuh9lvNJTqskyh4bRLoNoEo29m3xL4lDZ4BP+4caEvd/pDg/eJCoGe2pLqRRMTzvGq1Oj09fcYZZ0RUGo3GzMyMbdtqT71ej97iBgkkhgBtiX1LHLeUmObMQJJNoGe2JM2JjOv1ejRWCcB73vOeN77xjXfccYf6K2JZVrlcjv6iJLsmGF0KCUS5zb6luPep8Ekcn8Sl8BOKIc8i0DNbikYm1Wq1crlcrVaXLl0amZNyqaictVot2uYGCSSGAG2JfUvsW0pMc2YgySbQM1sSEdM0o6kBpqamAFQqFd/31Z+Q4Jkl2RXA6NJMgLZEW6ItpfkTgLH3EYFe2tLsL7sVi0Vd10ulUh+xY1FJYIEEaEu0JdrSAhsRTyeB7hCgLXWHM+9CAi0I0JZoS7SlFg2Du0ggfgRoS/GrE5YoNQRoS7Ql2lJqmjsD7W8CtKX+rj+Wvq8J0JZoS7Slvm7CLHx6CNCW0lPXjDR2BGhLtCXaUuyaJQtEAq0I0JZaUeE+EugKAdoSbYm21JWmxpuQwEIJ0JYWSpDnk8C8CdCWaEu0pXk3H55IAt0kQFvqJm3eiwSeQ4C2RFuiLT2nSfAFCcSVAG0prjXDcqWAAG2JtkRbSkFDZ4hJIEBbSkItMoY+JUBboi3Rlvq08bLYaSNAW0pbjTPeGBGgLdGWaEsxapAsCgm0J0Bbas+G75BAhwnQlmhLtKUONzJengQWhwBtaXE48iokMA8CtCXaEm1pHg2Hp5BA9wnQlrrPnHckgacJ0JZoS7QlfhyQQF8QoC31RTWxkMkkQFuiLdGWktm2GVXiCNCWElelDKh/CNCWaEu0pf5pryxpqgnQllJd/Qy+twRoS7Ql2lJv2yDvTgKnSYC2dJqgeBgJLD4B2hJtiba0+O2KVySBDhCgLXUAKi9JAqdHgLZEW6ItnV5b4VEk0GMCtKUeVwBvn2YCtCXaEm0pzZ8AjL2PCNCW+qiyWNSkEaAt0ZZoS0lr1YwnoQRoSwmtWIbVDwRoS7Ql2lI/tFSWkQSEtsQkIIGeEaAt0ZZoSz1rfrwxCcyFAG1pLrR4LAksKgHaEm2JtrSoTYoXI4FOEeilLdVqNdu2VWRHjhwBUKvVfN9Xf0KCZ5ZOhc7rksDiEQhkt8guqya2VZUwqV27IUHQ9gamG0jgimOL63uuGYg1tm5bARcDO4AZHYGuCRAAbrhqAeBrRi3c0HxkqhlDdDgw7vz/2XsT4EiO897zn1lHHzjm4piXJJKmLFmSuZbk8Erap4ukbDks60kO0WGvImjGMryWtXLshqW3forQi/X6PUtem5YlW5JpSrJIikNRHJLiIZIzABpH4xwMjsY1903MjRkAjW70UVduZCWmWAN0AYPh4P4qajDZ1VlZmf/M+vLXX2ZlQeMG+rnmgVmMCVOe4kIvqT547l8NrsZ2wEQ1Bjgc6JOAMzdacAS60GDF8DQMbmIEyDFdABNBhFkBrjKAQpwL4AnE4joyDO6saMFHoiUlxZrRQbMMQwAp8Kqetn5REGJaONOR7VxGKAtRtoQ4JTzhif2WI6bF5egT6BtSYJUqsGK0FHBSPp/PZrO5XK6mpmZiYiLQKfjZLYTI5/PBcQqQAqtQgakpp1AoebLbKAhXDB/6ZUdPc+bA3kzfUMW9eW9vb1+mr61n/8DhlvauuraGH/740a3xzURLHDuhg3RYpTogr+siru1ObGdP7vhed+/LIwf6+4+8VLGRZ/qG0u11g5mj/b0H9u3bN9hT7Oprs3LCdlfhHUxZIgUWUGDFaEnlq1AoTE5OqjCAL3zhC5/4xCd++tOfKlQqlUrZbDaMTQuUhr4mBVZIAccVniu8ohBirKO9ZcvbANwO/Bo4Ku83x1AdB9NhxGFw1GDb3WDVRAneKqUE8rHBY/AQE1VJAfwMMVRveTeL3QH8Kozayo2cAzWACeg6dA79tl95F3oznZ7Yv0K3KV2WFLh+BVaMlkqlksq14zi5XO7y5cu1tbVBOYrF4vj4eOB/mp6ex9UbnEQBUmDFFCiLc5Y75Th5IUb3DR+Haej4+yrtF0kMVNyBBg39HP2bcTSGw0BTQvsHDR8hnwrREoxpORS7On1sOAs4wE7Eb4+xb8bYs8BuJFIVG3kSA5s37UsY+zj6TaQ5dgDbB3uKInqEesVuYLowKbCQAitGS0KIYrHoOI7K4fj4OICjR4/O8iSV/M11yXW7UE3S9yuqgC1OecIWYlyI88OZi8DNcQzH4ALliH26RhM1EJt1kTAFUAAeA95DtLRKKYF8S8q3pI8bEMCzbNMHdexJyrDL4iKikZeBKSDL4P5KrdiS7IWOgwcPuu6RFb1Z6eKkwPUosGK05PqbEMKyLNd1i8ViTU2NcjiVy+XA82RZVkBU11M+OocUWBYFyqLslYX/oznf33sasaQm52s7iIuKuxa3dDmPuwRcACxdE4nE4+amWqIloqVV7VtiZU3+Bvg+zK0Me0wZtsDsio0ccVG9SUCTDyv40//3QNeHB48Kh379LotVoovcUAVWjJaCUlj+ls1mTdMMz/IOIszyNgXHKUAKrB4Fpj3bnVa0VOjs2IctAPbAzAPTlXc2AZQSpkhuugxTcPkE2SOI0byl1ToCRb4l37fEuFNtCm7+M+KoQqYagptjiBcqN3LZ+AvARaCoccHQh1q9r+eg/9Do6rl3KSekwDUpsJK0ZFlWkMexsTEAU1NTtm2rg7a/qXA4ZnAKBUiB1aNAWYy6cuGAy0JMtLT04iYAe/VaEYNXcecxAUzJLiR+0e9pygxPsSTREtGSu6p9Szib1IWe/BYSSOCwJgeai2BuxUYeg2dwoWsC8seACzRhO5pbdxEtrR7DRTm5dgVWkpbCQ2wTExOc8+D5uGsvAMUkBVaFAk7ZE64t+d8e7O0E0w0chBa5lNGaWV+HfCoz83Vo3Sn/mbhFtoe4nNg0Dd0BFwZ6wJHpG1oVNyxlghRYpAJES4sUjKKTAhUVIFryqYJWp1SrTZIOSgeipYrWgg6uRQWIltZirVGeV58CREtES2pmD+kQ0oFoafWZKsrRdSpAtHSdwtFppMBVChAtESWEKIF8S+Rbuso+0Ie1rwDR0tqvQyrBalCAaIloiWgppADR0mowS5SHG6gA0dINFJOS2sAKEC0RLYVYgXxLREsb2Bquz6ITLa3PeqVSLbcCREtES0RLIQWIlpbbBNH1llgBoqUlFpiS3yAKEC0RLYVYgXxLREsbxPJtnGISLW2cuqaSLqUCREtES0RLIQWIlpbS3FDaK6AA0dIKiE6XXIcKEC0RLYVYgXxLREvr0Mpt7CIRLW3s+qfS3ygFiJaIloiWQgoQLd0o00LprBIFiJZWSUVQNta4AkRLREshViDfEtHSGrdolP3ZChAtzVaEPpMC16MA0RLREtFSSAGipesxI3TOKlaAaGkVVw5lbQ0pQLREtBRiBfItES2tIetFWb0WBYiWrkUlikMKLKQA0RLREtFSSAGipYVMBn2/xhQgWlpjFUbZXaUKEC0RLYVYgXxLREur1FJRtq5XgUhaKpVKKk3P8yYmJoQQ2WxWCHH58mUhRKFQUN+6rqsCk5OTQgjLsqamptSRcrkshCgWi+qjOsVxnHK5bFlWcGK5XC6VSuPj47FYLLio67qlUslxHHWuZVkqQH9JgVWqANES0RLRUkgBoqVVaqkoW9erQCQtCSEcx5menlYpf+Mb37j77rtN0/zUpz71/PPPq2+FEJ7nBSjz1FNP3XPPPbfddts999zzyiuvBJz01a9+9e67737nO98J4KGHHgozUHDu1NQUgAsXLgQcJoSwbVuhVXDK9RaTziMFllgBoiWipRArkG+JaGmJLQ4lv9wKRNJSNptVKOM4zr//+7/fcccd3/ve90ZHRx9++OH3ve99+/fvV56kfD6vsCaTyQB45JFH9u/f/+d//udve9vbjhw5Mjk5mc1mf+d3fueJJ544efJkX1/fPffc86EPfWhsbCzwLanA5OQkgFKpVCwWw2wURFtuYeh6pMCiFCBaIloiWgopQLS0KPtBkVe/ApG0pLKuRtPuvffeL3/5y9PT06VSqVAo3HbbbX/7t3+rIihaKpVKn/vc5z7/+c8rhBJCvPvd7/7Sl76k4ih30cWLF4UQZ8+eBTA1NRUMuqkhvEKhAEAN9nmeVyqVbNt2XdeyLBVe/VJSDje0AkRLREshViDfEtHShraH67HwkbSUzWaVX8e2bQCPP/54UPw/+7M/+5M/+RNFP0IIxT133XXXY489JoQYHx/PZrPf+MY37rvvvkKhUC6XgyG5QqGwc+dOzrmCMOWUUixVLpcBjI6OqjE+27aDy1GAFFgDChAtES0RLYUUIFpaA1aLsrgYBSJpKUhkdHT05ptv3rdvnxBiamqqUCh87Wtfu//++2eNkQHYsWOHIifP837wgx/U1NQoHhJCTExMKCr6wAc+8MUvflHxU3iK0rlz53RdD1xT6urKsVT2tyA/FCAFVqMCREtESyFWIN8S0dJqNFOUp7egwAK0NDk5OTg4CCCVSqlBNyHEgw8++JGPfEQIkc/nFR45jrN58+Znn31WCHHu3DnLsh599NF3vOMdKmNnzpzxPE8Icf/99//mb/6meqou/LhcNptVtHT8+HEFYerZOvIwvYWapVOXVwGiJaIloqWQAkRLy2uA6GpLrkAkLSlSUZQDoLGx0bZtx3Fs2/7Lv/zL3/u931MPxAkh1LDa7bff/sgjjwT5/fa3v3333XerOAqA7r333g996EPqITu1yoA6MXAdAXjwwQc/97nPfeYzn/n0pz/90EMP7dixY3x8XAgRPJoXpE8BUmB1KUC0RLQUYgXyLREtrS4DRbl5ywpE0pJKWU27/uAHP6imbCtP0q233vpv//Zvana2GmvzPO+BBx740z/9U8dxFBu9613v+sY3vuG6bjBP/Ld/+7eVVylYkCn87NvExATnPEjzLZeLEiAFllcBoiWiJaKlkAJES8trgOhqS65AJC3l/E2Nl+2Ow0TIAAAgAElEQVTcufMd73jHo48+um/fvocffviOO+544403hBAPPPDA17/+deVAamlpAfB3f/d3Z86c+drXvrZ9+/aBgQFFTp/5zGfe9a53ZTKZXC7X3d1tWZbyFREtLXn10gWWTQGiJaKlECuQb4loadlsD11oeRSIpCXFQIVCQZHN3/zN39xzzz01NTX33Xffk08+qTL3u7/7u1/5ylfUYJkQ4sUXX/zEJz5hGMaHP/zhXbt2qcfl3njjDQDxeBz+tn37dgBNTU3B+pYqKfItLU9901WWSgGiJaIloqWQAkRLS2VqKN0VUiCSltTSlGre0qVLl4QQk5OTtm2rwbJsNlssFoPpRJ6/TU9Pq28vXryovEpCiGBRAFXAsbGxoKTkWwqkoMCaV4BoiWgpxArkWyJaWvM2jQpwtQKRtKTWC6j4VJpiIzW/e9rfglWXgjeZKLpSsKWumM/nFXWph+nIt3R1RdCnNa4A0RLREtFSSAGipTVu0Sj7sxWIpKWAk3K5nHoq7fz58+rsCxcuzEomoKJsNqscTsGilMViMZfLBVCllq9Up5NvaZaM9HENK0C0RLQUYgXyLREtrWFrRlmvpEAkLU1MTKjn3QKmUX6jYEnJfD6vHnlTS01alhUwk7qQ67qKtILr5nI5law6EqSslq+kZ+ICoSiw9hQgWiJaIloKKUC0tPaMGOV4XgUiaSlYTkkxkJrKHTicbNsOD7qplQWCC5VKpYCE1AoChUIhzFLBmpbBKTTLO5CCAmtSAaIloqUQK5BviWhpTdoxynS0AvPRUvRZN+abgKjIt3RjBKVUVlABoiWiJaKlkAJESytojejSS6EA0dJSqEppbjwFiJaIlkKsQL4loqWNZwTXeYmJltZ5BVPxlkkBoiWiJaKlkAJES8tkeegyy6UA0dJyKU3XWd8KEC0RLYVYgXxLREvr2+BtwNIRLW3ASqciL4ECREtES0RLIQWIlpbAylCSK6kA0dJKqk/XXj8KEC0RLYVYgXxLREvrx7hRSXwFiJaoIZACN0IBoiWiJaKlkAJESzfCrFAaq0gBoqVVVBmUlTWsANES0VKIFci3RLS0hq0ZZb2SAkRLlVShY6SAVCBr54Xw7MJlT4jLoiCE5dmeqLhb7lTZEUWvIERhcKAXOmJsGvyM6jPm/gW3GRwNLuDCmObwOHZCB3AIGJcfmQA8wJY78wCXaXkZYC70nK4JDgvaU9C4gX6ueWAWY8KUp7jQS3OvqI5ocDW2AyaqMcDhQJ8EnKjIDB50ocGK4WkY3MQIkGO6ACaiTiFKUMqQDkELAfcQmwJOJvAGULN/f79TqnwTqTvLcYXnCaF2UXBF0XHk3eh5XrA8slrfOHh3O5krUmAZFCBaWgaR6RJrTwHLvWSJE8KVK6eKkhCiYE8KYctXJlbebVHKC9t2hSv2trZAAzDCqk8HfcasANGSEoR0WN86ACXJ93EB5IGDzDDbu58tO9nKN5GYtt1Jz8sLkRfetLAKnpWVAXkbyi1Y0FjRUvj9EDMx6D9SYMkUIFpaMmkp4TWtgOX/unXEwEjDns4j3f27B4b37Dva2N+3p+J+8PBr/Zmuvkx6uOfgj/7pyW21W+PIbakSsyAp+EiUsL4pgXxLM02dTwJFGML3hu6/9a6bnnzuHwaP9lS8ifr79vT2NQwMNQ4Ndwz07enr6hroHDyYGTl1uEu9jXQWLa1pA0OZX3MKEC2tuSqjDC+HAp5bFmJi5HDLLe8C8HYYDEkNMYDVVt5NQOeIa2bs7ph2E2Jg6AYuBng0K0C0RLQUbhLrtT0ABSCHuNi+VQD1MABsB3678k3EasE3IRaHcZMfrRa409A2m5tx9uxZz/MCWlJDcjQStxymkK5xRQGipStK0P+kQEgBzxLCEZmBM8DtwGsJ7NseH2c4y7G34h7H5aQ2AWSADuBvzK2/DpwCyuEeMRxer70j+VRULZMOSofNNUL6lpADLgE/4LW1NclvbK1ur3gT+QePMnkHDUPOq2tK4oCJZ2H86vDwcLlctm1bjb6pv8E0ptCNS0FSYKkUIFpaKmUp3TWuwGXLye4ZqofJNuFIEgUdBROCG/mKu8YFNAFzLJGcgvZdJAG8Fts0HiakcJhoSalBOqxvHfzpSnkeE9s2Wab2r4hvAV5gKFW8ibiR15nQYhNyYjhzjarRakMYaEECe/bssSzLdd2AkMKTvte4qaHsrw0FiJbWRj1RLpdbAUt4ltgz3IEk36RdMFEC9kMvAE7EPgWMgZ1KxkRV/EXo1RqGNsdp3lJcR4bBDZNiOEy0tL5picMzq0vQhCZvnH+EVmugI6GJiJvI0eEZsSkYAszlxmQ1FwaGEUNXV5eyAGp+t3pEjmZ5L7dV3NjXI1ra2PVPpY9QwCmV5dNtB3chDuCNhCmAcb1G6PAq7gkmEvLBn3EgX8tego5tfK+GqTAZhMNECeueEuRSDijEuQCeQGyDUiOQ1RNjQEmHvbnqaehVyXgaKFa8ifyDViJ+0jSEXDKDjVVDJHEUCfT29qo7tVAoECpFGC06vLQKrBgtWZYVbv3FYhHAxYsXPX8LCh12vQYHKUAKLLUCjnxceWpwoAesVme94Fn4nBQmnnCY5qkoNUgH0uEt3Rd6CXBNeIwJMItrnoF+aLyvr0/d8mqiN3mVltoAUvpzFVh5WlJz97LZbCKRUM84OI4z5W/lcnlujukIKbAMChAtqT6PVqckHcL0s+TtgWhpGawbXeK6FFgxWpKr/k1MKLeqEOLChQsATp06FUziU8VRT42qxTauq4B0EilwPQoQLRElLCsl0Nru/ntjQLR0PeaKzlkOBVaSloL5etls9tKlS9u3bw9Wa3UcJwApIUQ+n18OMegapMAVBYiWiJaIlsIKLFN7IFq6YoLo/9WmwErSktJicnJSBQA88MADf/iHf/izn/1MzWpSQ3I0RL3aGs1GyA/R0jL1juRTUT4V0oF8SxvBsK7lMq4YLQWrsspXcBUKk5OTsVjszJkzARsFC5EJIWgkbi23sTWZd6IloqWwZ2XJ5+sQLREtrUlLuYEyvWK0JF9POj0dDMadOXMGQBiVLMtSwOR5Hq1wv4Ga5OooKtES0RLRUliBZWoPNBK3Ogwg5WKuAitGSwqMPM9TI3GlUkmtIOA4TsBMQohyuUyoNLfa6MhSK0C0tEy9I/lUaCTOV+BKe6MVBJbatlH616nAitFSMKFbZXxiYoJzHsxhus7S0GmkwA1SgGjpSu8lNFgxPA2DmxgBckwXwIT6du5fWm9JaUI6XKcO5Fu6QRaMkrnhChAt3XBJKcH1oADRkurtaL4O6aAUWCYdiJbWg/lcn2UgWlqf9UqleosKEC0tU+9II3E0EkcjcW/RWtHpy6IA0dKyyEwXWWsKEC0RLS2rT4WoUVEj+ZbWmqncOPklWto4dU0lXYQCREtES0RLYQWWqT0QLS3CSlHUZVWAaGlZ5aaLrRUFiJaWqXcknwqNxNFI3Foxixs7n0RLG7v+qfQRChAtES2FPSs0232Z2gP5liIsEh1ecQWIlla8CigDq1EBoqVl6h3Jt0S+JfItrUYTSHmarQDR0mxF6DMpIBcDE8JxpgYHesBqddYLngU8PWTWw44HBo/W11GCkA6kQ/jWWHR7IN8S2d/VqgDR0mqtGcrXiipAtKT6PBqBIh3C9LPk7YFoaUXtHl18HgWIluYRh77auAoQLRElLCsl0IikGpEkWtq4Rne1l5xoabXXEOVvRRQgWiJaIloKK7BM7YFoaUXsHV30GhQgWroGkSjKxlOAaGmZekfyqdAs79B0QBAtbTxju1ZKTLS0VmqK8rmsChAtES2FPStLPl+HqJFG4pbVwtHFFq0A0dKiJaMTNoICREtES0RLYQWWqT2Qb2kjmNe1WUaipbVZb5TrJVaAaGmZekfyqdBIHI3ELbE1o+RviAJESzdERkpkDSjgeZ7jOLZtO47jed78OXbk14XhoT6wWqALek7XhQEx99e2OrLodWWIEogSwpRA7UG1hwjfUm9vr+u6QgjbtoUQC96/C0aY//anb0mBuQoQLc3VhI5sCAVc11WWt2JpS7aw7axanZKhG0aeaMnECJBjugAmiBpJhyVpDxG01N/fr+5TxUwV79nwwVnRCJ7C4lD4+hQgWro+3eisNaZAuVy2LEt5lTzPc11X+Zm8iM33LU3vG8nMrOWt5xgTHA5RAlHCklAC+Zbm9S319PQoALIsSy6178gb1HXdiNtX3uABIak4a8xgUXZXnwJES6uvTihHq0CB8LwlDT3qzScaXKIloiWipRiehsGXRIcI39LAwICyCgEDXbuRIFq6dq0o5jwKEC3NIw59tW4VUO4l5WFyKm22J0ql8b7eLrBaORKHCcZEjNG8JRqJWxpKIN/SvL6lYN5SuVxWs5fUSHqle1cem2W5roOxZqVAH0kBoiVqAxtCAcuyZk1lCPz5FcuvZnnLkTh9i6n1AxOATb4lmre0VD4VoqV5aWlwcFDdp8Q9Fe0VHVwGBYiWlkFkusQqUkD5k1x/i5r04Hle2RGFwqVMfzf0LXFjwKcli+YtES0RLWmwln8kLpPJKCOinsxQExCDaYhzb+RisTjPMxyryB5RVtaOAkRLa6euKKdvTYHp6enR0dHh4eG9/pbJZEZGRvojtp7+4f7+9ldefh6sVs1bYkwkdRqJo5E4GolbAVp64oknBgcHh4aGent7h4aG+vr6MplMX19fxO3bn81mp6en5w7JvTUTQmdvaAVWkpaKxaLSvlQqjY+Px+Px06dPB7VR9Df1ce4YShCNAqTANSmQE8dHjhmboOOjwG/CTCAOmICuVd6TALvDYLehFjE0X/GpWDTLm2Z5L8nsZhqJUyNxUTrEAB3gcfBqcF2GNUAzoBsyLL/SwaplBA0wkEgkDh06FFgG1YPQKF4gCAWuQ4GVpCWV3YmJCRUA8PDDD993332PPvro1NSUOpjP50ul0nUUjE4hBa5SwBHD+zOogYZ/A5o42jX0aDipobfiDvZkHK9W4R+g6TEcBaa5IcAvEC0RLREtLeFIXBQt4SWOZh0ZHcP+nduhoUv3b16OLo4ODT0mhk1kDDRreEnTtOHhYWUB1CMdV1kD+kAKLF6BFaOlwEfqum4+n89ms6ZpHj16NFyEwKVEvwnCslD4OhSw3ELPSAbVADoYbI0LTRPcEFzzKu6GLqohqtEH3K3hNDBpmoKbo0RLREtESytAS9opxqc0LnRNcOZyXtI0W9eEbI26zbQS466uCZ0JzqY4OwWgv7/ftu3g6dfrMBp0CikQVmDFaEkIkc1mg4l4o6OjgMxMsVgs+ZtahUzlldxL4Tqj8HUo4Npe38ABJHUNvRxlmONIHkPyDDSn8m4IDa6OFxAzGPrBLpim0LUi0RLREtHSCtCSfhTaJXAPmgCzwQtglgxrAtyCVvAPCjAP7BL4UQB9fX1ES9dhKumUKAVWkpbC1D81NQXg5MmT4YwWCoVgblP4OIVJgUUrYBeH+oahJxM4Gofnv9atBNiMiYo7jPPAaca+hypw3gp2QdclPxEtES0RLa0ALWEUyHPpOpJPWsC/E2WYCVz5qEH4ex4yMjKZTDA6oQLBx0VbDzqBFBBixWgpGImbmpoqFotTU1M1NTVq2TH13tNw7RQKhfBHCpMCi1bALo30DIAbNThUC2FCAA5nQodTcYfmcTgx/AJxw9DkCgKcC6BMtES0RLS0/LTEcEDDOROWCWHA1lEwYJs+HnG5ENrMxzgsA+d0HAAQLNGk3pEy//pqi7YndMLGU2DFaEm13UKhoEbccrkcgPPnzwdV4Hle+LG44DgFSIHrUcATvX0ZmIijI8kLuj4O/Q3dzAJu5V0TcXhJpGBsMrAfbFzTBFAiWiJaIlpafloCzgIFBtf3CjuQb2yUYeVnAuQRHZ4mDxb8yBgYGAgmvKpA8BP9egwInbPhFVgxWgqG2NScpMuXLwNQq9rP+hFg2zb5ljZ8Q32rAtjC7hjsQwLAHk06llzAlpMe9FLFnfPJBCYTeAomdPSoeUtcyxMtES0RLa0ALcUyME/AyEMvQ89Dn4RegO76e8H/mOd6mcsIJ2Bk1CzvYOhN0VLw8a1aEzp/QyqwYrQ0C4kmJiY455OTkxuyFqjQy6FApm8IHIZ8Ra6A7gDTcUSuNgk5S2kpV+GLfFL6EDDO4fGZCRm2pDrmT9TQ8v4kVhd6Tj4ZBAvaU9C4gX6ueWAWY8L053BAj/SBaXA1tgMmqjHA4chuRv5Ml7/RK+6kg5KFdFilOshbw79H/FvG9zyNA4cA6VsK8ChwMi2HoaFrrFMFiJbWacVSseYoQLTE/KEKoiXSISDjNU/PREtzDB0dWCIFiJaWSFhKdtUpQLRElLB+KAEuI1+jXC+AfEurztKu1wwRLa3XmqVyzVaAaIloiWgpUEAFyLc020zQZ1IgQgGipQhh6PC6U4BoiWgpYIU1TwnkW1Lz+ci3tO4M9aotENHSqq0aytgNVoBoiWiJaClQgHxLN9i+UHLrXQGipfVew1S+KwoQLREtBaxAviWipSuGgf4nBa5JAaKla5KJIq0DBYiWiJaIlgIFiJbWgU2jIiynAkRLy6k2XWslFSBaIloKWIF8S0RLK2mM6NprUAGipTVYaZTl61KAaIloiWgpUIBo6bqsCJ20cRUgWtq4db/RSk60RLQUsAL5loiWNpoBpPK+RQWIlt6igHT6mlGAaIloiWgpUIBoac1YLsro6lCAaGl11APlYukVIFoiWgpYgXxLREtLb3LoCutKAaKldVWdVJh5FCBaIloiWgoUIFqax1bQV6TAXAWIluZqQkfWpwJES0RLASuQb4loaX2aOSrVkilAtLRk0lLCq0wBoiWiJaKlQAGipVVmnyg7q12BFaOlYrGotCmVSkKIy5cvAyiXy0IIz/Ns2w6UcxwniBwcpMAGUcB1XdUkhBCWvwkhisXiudGD+w4d7thX3zHYMNh96lDf4P7hVwcGBoYynRX3fYdTf////fWt7wRHL1A0tp/TTAEUZ3UewUfoQoMVw9MwuIkRIMd0AUwEEWYFODzABQpxLoAnEIvryDC4s6IFH8FtBkeTp7gwpjk8jp3QARwCxuVHJiDTtOUuX4ZF75wnHag9zL0vHKblwQWYC21K44LDgfbC5mr2zX/4x+HRPb0HWzub9h/qGzx8YHd3d3dF4zCU6Ww98Hjf3mNnzjwtHNfzRNESrlcQzgaxslTMa1JgxWhJCOE4TqFQsCxLCJHL5QCcP3/e8zyVcc/zisWiYqlrKgpFWr8KBPSsmseZM2f0OKBxGDr0GPAOhgQ0ALcCiYj9f9H4exHHFn5GUkjsLOAmmAjwZVaAaEkJQjqQDuFbY/W1B4dphbm0pMWg11QjmbjKPmhvjzAOCRjvBf7z297G25v2Oo4oOqJsjwtH/lSjjRRQCqwYLTnODLdPTU0Vi8WpqamamprAfxB8q3JZKBSowjayAmFoLpfLg4OD1fiDJHbGcDjBjm/G2S3oq0argfFq7Ku4A8/r7L8ghiTeAArABOBuShAtTQJOuDucFV59vSP52MjHFvaxhWhJn7ziW3o+jt9jeBLoM3FkuzaWRCfwqo7LFY1DNfZtveV1YAdQvW9o1BGuLVzLvixK5FzayN3O7LKvGC2p4RXX34QQU1NTAE6ePBnOYKFQoDG4sCAbNqwckKr4xWJx7969wDZgB4fNYGvIGTgGHAUsYLzivr1KJKt2IIG4dkQzBUsKwAHOzoKD4CNRgpKCdCAdgpuCwVt97cFhWmnGtxTQkr4T2FbNX9qSEDFTxFgxoZ1KJM5s2iQqGgf/4FlN2pDbu/b0TRROl0RRiIKQwx60kQIzCqwkLWWz2WCEZXR0FJCZUaNvpVIp3EGGXQtUdRtKATX0pmYvqYKXy+VMJgND0/GKpgkYwp8wVGLcgiagR+yYAh5FNRJGD2N+HOaZfDrcE4TDq69XIJ8K+VTCPhVqD6o9OPLGV/OW3qSln4NjU6xR2gfpRZ7i3AIrA6Vo+1C8eUsR2rbDx4am7VOWKAvh2hMbytZSYRdQYMVoKRhrc103n89ns1nTNI8ePRrObzhO+DiFN44CQRsQQihmchxnZGQEMWj4hZx5bdhAUQ4nyZ+YXtRekxSJmp+iCiaagWl5iiaSNBKn00jcgJwXTDpgjergMO7MoaWfQQfD8/J4UsQ2iURCSPugiyj7AFwGhsH1g4d6hJiYGYF781mjjWNxqaSRCqwYLQU5mpiYAXgADz/88P333//YY4/lcjkVIZfL0WBcoNUGDMylJdu2BwcHwbfpaGOmQKwAODoTcfk4jM25qLyjDPwIBmoxWKUJozbrP26WD/uTwmHyLSk1SAfSYXXfF5VpSY/dkuTd0vGsTfm/puTf6mSEceBi222iWjsIGAf6M8KxiwVRKOU8Vz6jTRspoBRYSVoKMKhUKo2Pj8fj8dOnTwcVUyqVggjhLjOIQIGNoIDyJ6n5bWpUzrKsnp4eYDtDvRx6SxwDy8UhquDpOCGBqdJeBVHFXgS2bcIRjjLMo9AdI06zvMm3tEZ9KjQSF4zEuVf7liwYTwPbpRfZEDAP81h5c1wk5WodRyoaBy7X6bjAkUmaNx/ce0RYwnOEIwpCXN4INpbKeI0KrCQthRloYmKCcz45OXmN+aZoG0oBxUlBg+nr64PGDfRzzQOzGBOmWu5IL4V/B4fDtHazUoN0IB3ovggroMLQHAMHwfTB3k4hbNsSnnCFQ76lDdXPLFBYoqUFBKKvV4MCREu0OiWt0kmrlS7dqq1ES6vBzq/yPBAtrfIKouxJBYiWiJaIloiWiJaoP1hBBYiWVlB8uvS1KkC0RLREtES0RLR0rRaT4i2BAkRLSyAqJXmjFSBaIloiWiJaIlq60ZaV0luEAkRLixCLoq6UAkRLREtES0RLREsrZYHpukIIoiVqBmtAAaIloiWiJaIloqU1YKzXbxaJltZv3a6jkhEtES0RLREtES2tI6O+9opCtLT26mxN5zhYM0kBkHpR4IkTJ3oz9f0DHQMDAwODvZnBtv7BVGawbWCwp3fgxf6+fZm+N3qH9vQNNfV097Y2tO5+5ae03hKHBe0p0oF0gJ7TNUE6vBUdTPm6yaduurn20X95fGikq2/oYFfX8KGD+4cynRX33uGXRw51ZAZ6jpx6zS0KIc5eHj/r0Vt413TntFDmiZYWUoi+v6EKKEhyXTebzaqE29ra3va2t8EANAOsVu6aAY2Dx2TYAHAzcCf0GAwGvhWohgaiBOod30rvSKt00iqd4TUqY6aIsQZwXp14F2IcJhADEvD/JSr9/S3gI8D/dOc7t3W3nRHirBA5b+b1cjfUYlJiq0YBoqVVUxUbIyNTU1OqoOXyzDq5cmFuIMYaE+ipwuEqHEliXwKDSRyowokqbW8SZ02c19AX13s2Gye2aCO17CWiJaIloiUwD8wlHd66DsCJmPES2K/F8B3guYR2akt8ejOfqMa+ivvWra0mXkhq3+Tm1uFMvuScsr3L2cnSxrDiG7SUREsbtOJXsNiWNeOwLvlbb29vbW0tWC/YUeASkPXfB34RmATKYGcABygBR/19AjgMvEC0RLRElPDWKYF8bMrDlEgUjdizwHs2mW0m8pAvlcv7tmgcqLhPMuSrY3XA9sH+y8XyKSFKwltBs0qXXnIFiJaWXGK6wCwFcrmcmq7keV6pVGprawMA8zj0SehC7poA9+RfXXBD8JiAKWCWYLjMFNJ4sdeJloiWiJaIlm7U0w+1cQH8APxWXdvFYxeQOI+qA/Ftp2YskrJL4b8JsXmzMHgavHpw4KQQE7btOvYsU0cf15UCREvrqjrXRGEKhUI4nwcPHuScQxsBPxs89wRY8ucd86RjiXtyNydhuNwQ4Oeg7SRaIloiWiJaulG0pKFkxL4LfauBfqAAZkMTsZj/s03Zn1l/UdRjAngVGu/ZOyBE3ioJi3xLYcu+7sJES+uuSld3gdQsbyFEoVDI5XKu6/b29krfEjvBMKVBaBAcHoPL4WkQkp+kV9yRJgyewYWGHPAK0RLREtES0dKNoiVg3ND/Ccl4TbzL/6nmAFkNDuei4g5MmaZI8m49afZ39wmv6HnCFvnVbX0pd29JAaKltyQfnXwdCriu6/ibOrezs1P6ljDEcVaHrcOVRkqSU1ZHPgbPhGBy3tJ5wDbgGTjPsINoiWiJaIlo6UbR0k26MLV/holqo11n8kcaw+XN8pebXXFH3ALKJnrA+FDvgF3KeZ6Ylk/G0bZuFVhyWlLr6xSLRcdxlF9hcnJSCKGOB09IZbNZAMWiXLniRm3qEmrcR106cGzMvUTwiJYQolSSjzbYtu267tyYwZFFpR8U+RrzM+vSuVwuuG7FwGLjB4kozVWlBGWfnp5WCqhoSpDglHAg7wwLcVTYolzKibJw7KJjCc8TV6R2hXCFsIWw5CxIUSrYnvBsYZWFHOYveKKU6T4Qx93g/b6Fcjgv+fMuHaaf49JsuUzLV+gVdOjoZ8quMRHTcwweTCv8VHA4DDa1GS/LJQn4a9DKNQl/5njNZDhOOAzuctgxPIEYYugFJuQgIJsKx7k67Po+sFycC+BHSOg6urm0uV7FHdxmcDTpNnNhTMtl97ATOoBDwPjcVfgYPK5Pg4vQM1AO+KLXnWJy7sUOVKMaozqy0KW2BhcVMykllXmzY/gpEjBxALgsdYATFZ+j6LsDS74OjyIOHRkGNyo+mMu0S5ryIGpCY46GJ8GronSo1B6c+dadihflJcwCMxxgWron/fxHzm5mZSZrTdZOOM/QhQYrhqdhcBMjQE4qiYlwHP8U/1xW5vD89lDwdXgCsXglHZyZa7FydHs4JjX3W5E/Tl0AL8tmEHVfxJE0++T9opd1XejI+SsJla/O55tt0pDu28dh6iYGY/JuGpczdeZpt9ekw5vpA2VfqKkYPB07EEsAHVyPzA94QeOunwC8dykAACAASURBVCsbWk6D0LFTrhgScV8YUoqLcqQ+Juc76rqIaRb4E9G/ppxZNet/lHeixnZIWsIAhyPnUM40gMrxoVl+Q0qBV/W09YuCENPCkVbT8s2dsnsh62cLURTCcUul/cITnthvuyInxsK2NBwO9z7elS0cQfUjgd0OfxUOL7ZfWGx8da2gg5h1ejgn4fCi4i9YxnDK15efuSlUPLLktDRLFzW9d2pqSj0Ypf56npfL5QBchy4VSyWEKJfL4ZpTnbe6etQpKqvqr+M44dPnnrLY9BcbX10xn5eu3SvkMTcXs49ce3ylvOM4ChNd1/U8L8jkxMREOAOzLxP6XCwK23aF/JsVrjhyqmHoYG/r3sa+noH+3kG1Z/oGMn0DA/2DA/2DzXt7e/syfW09+wcOt7R31bU1/PDHj26Nbw7R0hXi0cbmoyXjalrSCn7X/qaZntU9gOc24SWwGrA6cKdWzjkoomp6VrTgo09LZUkJJmIYAKZ8SoiMf6V3VLT0OOIxHX3zUcIK0RLnAvxZJCUtachDKwGuzuahpaJPS08jDlP2WAvSkho5tX1KeMynpXl1YC7jkzPU+CYtJaJ6R58SSlfoOX9lVcYnI3tHw5/6ptt+n11amJai6PZaKUF1rvaV9jA/LXmqq2awo2npuCT1GVpy5cOhzJmPlkwk9CE5cq05usxz3pD0E0knV2iJm8gsDS05vvLSSazjZ4hVAV1cm4eeLY17V2hp2qel5+ehJV2TzCppSc5o9CQtMXEdvyKiaamySQHyui7i2u7Edvbkju919748cqC//8hLytZl+oZCu7R+Q/v2ZvoOHz44mslkDg2LoYP9zrSwotdnirL5gd1WAWWJw+GQbX4zeO39gjpnsfGDvtKyLMdx5u9nhRCLiq+8Eq7rTk9Pu/6mfsy/Wbw5oUWlP+fsyANLTktCiIsXL869vhqOUcdLpVKxWAQQdNJz4y/2yKwKUygwfyLq6srXEkb7imctNv3FxlcXVSijshS0gIr5WWx8dYOpNAO/WoC2wSXy+byKc+Xnzez/HVfYlrDzwhUXBjI9W98OsHeAvxccc3YOznFzDNVxMB1GHAZHDbbdDVYN8N4Z3xKTv+llp8il4yfyN7QBA/2y74fNmDB5Wf6U16N7fW26Bi+AxcGawZxa2YVMIx7t+9E8DTO05PsSCj4tXSG5OX3q1b3jT2FW6xi40bRUvNq3NP9v6MpWnrEJDS8jjiROSj+Q5gKWPqc4b1Kj5vi09BxiMHFsxsd2td8liCwdYDM+FUVL/4E4W4AamcvY9Bxais1HS9yf/i/XGSosSEt+C7kEyH5UzYHzA+6ie8drpaUZ2a/osCAtzcS/ZlqyJSnO41vSeBLDEiCY+yYtzfhrKzSJK7QEE30+LV32fUvRNLNIHaSHRipfmKElswbo4fP4MpmrcXE1Lb0kLUmEb0mTUvj3BRfQTmpc0dLSr3EfE1VJAcl/qN7ybha7A/hVGLVzjN4VM5iEXPFS16FzYPtN70TfQJcn9s+2p6HPgRH2PE/9mpWeK3/5FWWTA0ia1bkEJwaBpetHgjGT8K/6+fOj6Oca4wdJeZ6nGC4oVFRgUelHJVLx+JLTkkIQVc7gYSh1sFQqBb11uVy+4SNxqsCKACzLUteqqII6qDLpuq4aHwza4jynBENX15L+ovITVLkQQi17PRdlwhlbbPzwua7rBl49NeSn7q7wFUN38VXBaW+0ZE/6o2yj+4aPyzW48f8k+QsJZBIY9PehBEb8fX8C+4EGDf0c/ZtxNCZXTmpKaP+g4SPQ+vxfwA6/Qktq2OtaaYn5Lo35aKlUjeclpaELzK2Rgw4j89KVoqUd/sjLgSsDCvPSknyCT41A/QxmjYbBK878Cr1UdO84z0jcLFoqg/8k0qcSAUAa7zXwGkwkpfi2/FGOHI+mH8zQ0i98WvL9HAuMxKkRKEVLT/i01DMfNUpaKl5NS4/LZdwjekfZHpi44lsKaOnxKB3kgwK8C3B8F4scfvU777VLSz4pzkNLqE5iX1BkjmnpfeHS81pxn6ElicJ7fVoaW3pa6l0kLb0MFklLPg276i+MOg0+LbFoX2OEDoumZ5z1Hz3ZifjtMfbNGHsW2I1EKoH9vq0butr67de1bpMPba0+XqV3xrET2N7dNiGH5CI2hUeKk2x/U8Md4V6sXC5funQpbMnnhhfbLyw2fgBwajxHZSCcyblZCjrW4Ff6PPHDfZAip/Hx8blpho8sKv3wiQuGl5yWAjUfeeSR3/iN34jFYrfffvvRo0dVzlTBFDYCCMq5YL6vJUJ4ZDcsesVzg0vbtr1z50710FbFmMHBRaUfJKi4ZMH8qAjKH6vClmVFuWcDaLv2+EKIsBft2WefDTdZ1Y7D5BSUelbAFqfksyBiwnHe6N0zypN33ZIcTcjJEFbEPl2jiRqIzbpIyMWTCsBjwHt8WnI4c0O0NOHP/IiYt2TARMa3ks4V35IDbR7fklWF53yzmwFzq2UOn/aRpXIv4s9TKcblPBXdn69TVAMKFbscph7fu4qWqjX5KPJVc1/C514XLfkTVt5cu7kM7cdRlBC+VjjM+U9MvA7DSGJIVpDsSifmm19lqJG4531aOglMLjRvKTwS9wTimo4FaWmub2nekTjuXKGlhUfiJIeZ/w5YMenhcMEmoXlg3qJ7x0X6VG6cb+kIMBYaiVuQlrYlkYH5A8A2DcFQkN4XvRhuA+FwiJY6fVq6sDS0pEbifurPW7pGWipDkw/J6nIAPZKW/JmLnj8eZyP+iAbXH4mLpOdQ2a+akHQN7eGq+NDHfemeZZs+qGNPUtoTl8lFmyrbvSuwbjFcNtAiZ/NlMkKcmmVOK35UQBV8pfody7LK5fJTTz0V9FxBhHBgGfoRBTGWZamMBdM5wtkIhxcbP5hBq+aN/PznPw8wK5xsEL6O9INz5w8sBy0dO3bsmWee0XX9Bz/4waVLl/7qr/4qHo+fOHEi7MS7dOkSgAXHI+cvzKxvVeWFIWAeRlESO44zPT390EMPqYUTZyU46+Oi0g9o6Rrzo641a3K3yuSsbIQ/Liq+Ulu1vIcffrhUKnmeZ1lWLpcLF21sbMzzPPUU29y/ZVH2yqKYywuR7+o4Jt/mJudEl5AUSIT2uEBcftTilv/ISQm4IMeANJFIPG5uqoU+APi05I8a+MssnVuIlgYCWjJ4Vp6iR/p+oHtJPO+79EfAPJ+W/guYnBtecYecIVu6Qkv75aq+cobE+YqRGTxZKPmLv+zP19kB0+BoB+aZRb74Wd6affVIXBHaDxdLS9D+zxhehG7Eeae07HLS9yV9nlm9sUv+SNwz10pLfBLMAgLf0jXQkjZ+tW/pSfB5aWn2rP/5ZnkbcFD1ZaAU8/2OYOfBXWgiunesMMVbjghH0pLqRGdjcTQtVY4fSc9sP3Be4ax/OywwEqfhpiQ6UfVnChAZCnLy3wK09B9+5bb7tHRuaWhpMgZHx38gbgLd1+ZbykO/5NPSL+ahJQm+XPg3XQlVDxlw4hDQHlvovrAZK8r9SsuPbg/KPsyOD1b2G+33YW5l2GPKxzUsuUpTYPSSDpLOmx/lWwosPSZqkiKp70cy2ZbuFc7M08Fz7aqaoKPmq9i2HXb5KONs27bneQ899FChUJjnV/Qy9CMK14K+dVYfFO6eVHix8QOHixAil8t96UtfUgrMTfm6049KatbxJaclNar14Q9/+Ctf+UrgrLvlllu++93vhrMyNjamadrly5fDB99iOGhDJ0+eVEnNw6QqsvJ/fvKTn1SjqmGymZuZRaUfHqa9lvyoywXN4vjx43MzMPfIYuMHKXz84x8Pw6sQYt++fQP+Njw8PDg4mInYuocyfR1eV1v78cODz/zsdVQD6Epu8X/HSwtiy1kFLOdPpBgDuwA2AZQSpkhuugxTrmUCPCJfYKkNAq70LfmjBkAO2nH/h9o8vqUhTRNgFuOWoV2UtGSMR9EMdC+B56BBwwFwuwoutM/MQz8whA7LpyVuSjfMJd8Nczwq/atpST5Jx9EAnI6KH9k7RoxAySlBmjtDS0bWn68zfV20dH8cz8Dgcb1BvljGEFy/ZFzpM+bmFok3fFp6wp/lfXxh35J+BtoEcGW+zoK+JV5ihj/fXNaI5z8T91M5GT9CByDPjEszvqUZHRzwyBUldJSw6V6gmNCF5AZ2Ss6SnoeW+CTjU4xNM/lw3JsMFElLqtNlZT/+m0/SRdJSRPzI9sAHwN7gbJrJJccsf5b3fPOWTGxJIoVN/wko++60ael9if4V4TtI/sOv3LSkJXZ2aWhpLIaijn/331PbsRAtqVneEzDPaHDlM3HR85bAy7omaYmhiNqP6bAlLRnfX4CWWFHWsqzoGa/bArQ0Jz7jTrUpuPnPiKMKmWoIbo4hXvCH58pgWfBLcmdZeZf5A8G10iqW/Qcz04jhxz985vTByQizOnN4YGAgk8n09/cPDAyMjIwcOHBg1hzqj370o7M8T4FJDwcW2y9ce3z1AzvwBQghgt4tnIEgfB3xVQEDT8G9994bpDY3sNj056Ywz5ElpyUhRD6f1zTtF7/4hZoM77ruQw899Ad/8AcqW0qF8fHxTZs2VZwPPk/uF/xKce7LL7+sqn9+p2XAUvfff79KOWg0URdaVPoKjYUQ15If5fhRDcV13RdeeGF+dFtsfFVY9dfzvA9+8IMBy5bL5SNHjtx2221y0Uhg27ZtKlD5bxxbat6vcegMsdg2VMFMvAHk4hBxiBg8f8Ek10TJQM5AVr7GBFMaFyx+0TccZYanWBLQR3xacriW9yd3T8I4IJkp6klpg8Uw7NNSmWkFQz8tB/XMc3P7e3UEhkjIt8spWipWw0Hst4DReeLP0JIph/yAc/6bWPZFxQ9oKSFdUI8jDs5eBT8WFT+yd4yghAhaWvA39GzPGbR7YngSOuLGq4qWNHPMDGHBrAwjeYjLKbo/ulZaMo5Cl+/483/uP77wSJyWZeZxTb4c0IXuaszSMC8t8cvMPCufomcWjAmfGh3wn0X1jgZy2Po+oJA05MKnYCcWoCVtjGmX5BMGElDefAggkpZ4jvGcT1fFEDA5kbQUET+yPfA+sBNcOkFtH5UK4L6LMeK+MFFbhVex7dcCWoJ0jL2JfbPqN0RLzT4tnb7xtCQfSzwXQ07H931aauPa7GYZ5ArM1jTbz9UYYm9ozNHx7Ly0JEdjk/KmK2DTe3x/sID5L1Htwb+QLatMG5c7l8L6I+lRKwh4MsKc+MDZpC705LeQQAKHNYlBcq0KE2q3TRT83VZHODx/MG4yZorammEkEa+CCaOyUa10VNf1eDx+/vx5y7KUI8d13fe///3BQFXFTmqx/cJi4wcXVZNrp6enU6nUgu6lYDLugvGDXi+YWfue97wnuOg8gcXmZ56kgq+WnJZc171w4YKu6729vcFV/+Iv/uKjH/2obdsBjkxOTgIyM+opwSBm8CS/cuSoVqIm3ARxKgY8z7NtW8X/zGc+o+LMQ0vK1amGnBTJBWtBVUw//Eyf8kXN32oXG19BZOBl/fSnPz3/EwFR8VUjO3DgwNDQ0LFjx9LpdH9//+DgYFtb2/79+3t6ejo7OwcGBu644462trb+/v7+PSMH9g898p3vxqs+CfwtQ3tMOwn0Q3sVOMdjbdD2wtiBqv8KnoLRgPiPpd9IOwi+C4k/xpZ3ATsNjMP0h640gepefwQhj03fBPZLvjGySB5FfIrJ0a6TjH8d5s2IN/qOKE+r6dLkcpQ2tvxfwBG5vBCX4yDyCWE5bJSDfgb6YUiE62LckeusyJ/d+7D5qzEclExTaU/E3wDqcLOcACF/feI0brtV4kKlyL7vwWE4DP1fsP0maM8lmNDhYvPHouLDzMEQWk2/zLn2r9hyB7CTJe+Nih+pQ2wU5hi0aXli8F4qQ8iDspjScOtMGPLRs3Yk/gKJWuA7Bkq67iD5BkzfB2ZUFkGmGd8K/C22bwFGNExosUvyKsl9UflE1W/Jl4zy/8C2W6A/I1da1y9Lj2CEbtj0mwxWdXzalAMi/8MXfCTBouPjBLY9KN+grAkWL/plfA6bgCgd8AY2/b/gh+SSVOaRmZ/yVf8aqQPyuPk9gFzRSt+ckuigTXOJzh7iD2HT22H83PDXa4bhozzrQ+0PZH54HonD0pknC2tBm5Lts+rruOl2hs4EhFFz1K+jE3KUtubbkqfjp+SkLqnMGGKDTBf+kjw2jG9h+x1Mf1aO/+qV40e2B/N12Q3f9Of+MxAlTT8vq8A4GnlfbAGwC7dXyfnssUPQPfmORX8toopVZrAxxL6K6q2If4xhr6ley5jcXzGyfzBCh6j2oHkwT2qw2Lb/BPwVfmUL5Hoc0r1Xedf9tQCQQ/U3gJMJ+ZRler72oI8ZhuDJQblS1F1gsOTYa/IfI9sDk7PWEDso7/1tfw2+H/r5edtD5fiR7SEifcQmERM87smmFftvuGkr9P+ewLFIu8oy0Dqgt0PfB/0otF3Q/hLaex9//PG+vr6hoaGOjo6enp677767u7u7t7e3J2IbHBwMj2Tdd999Fbuz4GBUPxJEmBtQQKM60HK5PL/vJxjBUBeybfvee+8NRmnmJh7ED5xGiUSiYrTwQZW4OvKxj31McUV4NDN4xlARQhBflSVAtHCaQoglpyUhxMjICIDOzk7FH57nfetb3woI0XGcvL9t27ZtbOzN1bpyuVw2mw3rGNDVkSNHyuXy9PT0+Ph4NmITQpw/f765ufmZZ555//vf/8wzz7z44oupVOq16O2FF16or69Pp9Of//znOzo6UqlUZ2dnS8TW5G/t7e2NjY2f/exnu7q66uvrW1tbI6K3LDZ+KpXq6OhoaGhobm5Op9Nf+MIXdu3aNU9+ouKPjIz85Cc/2b59O+TjqzrnPB6PA/CXz575axjyJ46maaZpMuhVNdxIasCvVSf+m4GdMbTWVu3l2GniQBwNJlo4fgJ8neM1E7uAH2k4aqCD4UXg/4B+n4afJbBPvkEJBzgGuPYjjgxHKzMfBp43cIChE2gGhjlOm9ir4280fMyf6z3A0avrPzTwhoYeZv4J8ALQArRKMMIehjb54AmeBZ4A3wo8oeE1rr8InAIe1/T/LYHX/Mitc//G2ePATxHbouGJOFIMzUjeoyE1N6Y6YqDJwMvAP8G8G/gfSeyVa1Ty34+KD7yk4YTOn9Ll5O7/CuPdHI/F8Nmo+NE6PAupZL1/YheksGmGRol66AY6OXbH0RXDgJwFgs8D/7OG78dxzMAhX9g+JldF7466LvAbMnuJWzRZF/U6dnOMgv04Ov4nqpEx8Y/Q7wS+aaKP4+X50tc/oWFvAi8Zcvra15G8DXg+hqao9HU0If6Hfms5yLSnNbRx/CPYLX4tV9ThNRhf4viZjhMGntfQzXAc+lejdGBIo/pdQKeJw4bxGHAQqGfI1OIN4I9h3M3x9zHs41Lh5zSZ56f81Jo50hqe1TCsoYPL5voaw3HG/nfEbjPw/Sr0xfTngCEmG0kT9C8Dr2p4ycSgjmEm74uXGAZN7NZkA/5rxN6n41u1MreV40e1B4bvAX1IfJ6hQ0faRMrARTk4FXVfGElgB6rfxtGt4zku753mK5Er3Rfyhvoq8FvA7+qyIWUY+vwWWCGyX4mVdYiqX8g5/jtNjJja72v4v2HcDTyhy4tGpd/g5/ZV6P8rw4tVUsOn/FVbK98XHD0xHDfljdyP6rfpOBnHWY7/HtUeOFo1uWzsz4HjiP8x8CzHKyb2RbWHqPhR7SE6fivDOV0+DpyRP1f09+v4p6Q0jJXtqi5nPdYBrwMdBgYMvMbxdeD+RCKhLLmu67FYTDmhYrEYj9je8Y53fOc731Eo9cILL3z84x/fvXt3R0dHVD8V1Y9ExW9ubladVHt7e3Nzc2Nj4xe+8IV0Oh0VP51ONzQ0NDY2trW1tbS0NDc3P/DAA1GRW1pa2trampqagshNTU3vfe97m5qaok5Jp9P19fVNTU3pdLq1tbWxsfGP/uiPmpubz507d/ny5Vwul8/ns9ns+Pj4xMSEYgfHcQqFwqlTp5QX5vz587MgKfi45LSkPHs1NTVPPfWUEGJycvL8+fMPPvjgZz/7WSHEhQsXAqwD8KlPfer3f//3P/WpT33yk5988MEHd+7cqQqgSqgyffLkydtvv121kpqaGhaxBb7MTZs2AaiulhNq5OvIIjbFEIlEQg08cc41Ta4gq0VsnHPGmK7L1ZdVNADxeDwiurbY+CpNdQuoS8yTmSCrc+MD2Lx5s0pBSWH4mzqi7j0Ad911lxIH2CrnVBpydZDNt9wGbIYmV3HWDBj8rlhsk2lu5SZYAppWYxrbeBIav0szazQ9IRczqoKmGTrbKl3u2iamJ1g1ONvGWUwuDMlhGP5T/IYOYzNit2pmja4hpgNyPRKdxWK8GkxPcC0mp0Bxf5GSGFgMzJR/5Qwnf9d1MCRkuAYwa2CAadBxcxBhVkCThuVWxGQ0TZ57B0xwVM2KFnzUNM3g2xhukUc4YjHD5G+Xq+RdycDsAAfYr+gSM++CJtd10rDN1CPjR+oQv3KKKcsuCx6XaqOKwZTPASIOLc5NfYtmyHWqdBOcwdBu1c2tMBLgtdBMLUhkTm41ORapsyowVGusWpPQeZtMdk5MdUTnqMY9JouzuNSBazfLBWO06qj4zADHrVwDx02M+ZnHFs7kgugVdwO/KkvHEtAN1IAZps5garKYM/Fn6cCZbBgJMENmiRlxmZloHbgBbAHXoRlbtCpAj/tt26jC+zRVTQa4dgu41JZVyTaEKjBucs3Q4rKRcx3cBBIM7E7ZxhIySkzbqiVi0H5FMyGbVDWg+2kbNZpWw+Svj1thbFeNWd5ZMRga4gai4s/XHjRTOld0eQtwM8b1LfLm8qts7n0hNcHtUh/cynkt0zbLhc2i6ytmbOMya7IQTPeXbjBroN1UsbLkwQgdIuMb1TB1A++MMZiolY2W+ZP4I9qDzISpM8P0x+ySJr9dxxY5Uh/VHrSEbm7XYiZQjVoYfLvBt8OIvC+4rO64FgfHrylVeQy6kYxqD1Hxo3SIjB8HDDn2Jg2WLjOraTBwe5Rd1Y2bmZlETOfmFsN4u6lv1TWYMZimTCLod+68884rdjvoJWYHGJOPFKqzNm/evGWLdD9G9VOL7XeCxFUPq36Ez5O+6qoAVFVVqWgqb/PkJ4gQ0CFjLCq+UsY0zeBC6nT1lzEW5FAdUX4E1UuqItTW1kYN4yw5LQkhJiYmPvCBD3zxi18MGO2d73znt7/97eDj2NjY6Ojo29/+9rCvrFAoKNIKfHG2batiHD58OJfLjY+Pnz59eipis217cnJyeHhYrp166FA6nR4aGhocHOyN2IaGhtrb2/v6+g4cOLB///7GxsbW1lblakpHbApv0+l0JpNJpVItLS2tra0RceXhRcVvamoKUmtpaenv729ra2tsbIxKPyr+7t27e3t7G/ytsbHxpZdeSqVSra2t7e3tHR0d3d3dHR0d6XT6pZdeamxs7OjoaGrau2dvR7rj1dfqnmtt6+hoH+rq7O/t7W1OvZZu6Gpr6mhtbGtO/bKp8bmWhtbWhr7WpsZ0qq0lVZdOtci9aVdzfVNz/evpxlfTu4bSdZ3p1Outrx+V4abn2l4f6Gr+eXvja00NrY1Nrc2tdS2tr6ab6lp3p1sa+1ua21sa9zQ3NjU1NjQ1dDY1tDY39KYbGtINza0NbW0Ne9oa9rQ2tKUbmlvqU+2/PNmya29T06uN6VeaWhqbG7pbdu1Nv9rRmmqpuDelXmytH2qrO95S396c2pVu6G6t25+u760YuTXV0pJqbG/qbd19rOn1vqZd3W3NTe2NmZZdI1Hxm+sa0vWtbbv3t+3e39KQluLUjbQ2HI2KH6VDuqExXZ9O17W31nfJvaGtNdXU2ljf3DTQ2NiVSqUam+paGve0NQy3NextbdzVXN+SbmxKp+vS6V3pVEtLfWdrY11HekfUddN1b6TrBpsb6pvr01LVuiFf0sao+K2/HOhpOtixeyj1yt50fW+6qbsx1drc1BYZvz6Trt/bUtfdUtctm4f82CvDEfXSWT/QWre3cXd/qqmuqe3FdEtDR0Nn+y9PROpQP9Cc6mhuqmtqbGhu6G6u729p7GxpbojSoaWprbmxqaWpLd3Yn04NNKfaUqmmVENbV6q3bXd3endPW6o/3dDdUNeUatzd2l6XrtsjL70r01rXn65rT+/uTte3phsaZVtN7U2/PtL2+p6O+qb2ppaWxs6Gho62usH07p7m1AstdS2t9epjX/Pulsa6gabGtuaWV1pTnbIl1O1tr+tqb9wVFT+yPaSGmlNdTU2vN6faWho70w37mhtbmxrrou6LlvqR5t0H0nUDLfWdLXU9fhNqba2P1L+jrq/99QNtrx5J7xpIp1p8YdsaGwaj6itKh6j4qVRnc6qtPdXd8fq+tleOt/7ycLqhq6X11aj4Ta+3tTe1djZ3pRvrW+o725ra06mhxt39Ue2hqeH1tuZUW3OqJVXXkmpoT9e3texqSf0ysj3Up9K7ZJtvffVCuvnn6d096dTu9O6eqPbQEhE/Soeo+O3pV1qbXmlp3NnckGppSLc2v97SlG5ubImyqy1N3U1NqcbGXzY1NrSm9rbV97XVpdO7X6yrq+vo6Ni7d68ac2hsbOzs7EylUu0RWzqdTqVSg4ODHR0dr776aktLyy9+8Yvu7u7F9iNR8Ts7O5uamtrb2zs7O1977bV0Oj04ODhPv9nV1aV8RR0dHa+99lpra+v88VWXV19fry6RSqUOHDigyl4xS3v27GloaOjq6gqcTCMjI3V1dWNjY+Pj41NTU2rMatLfstnsuXPncrlcuVw+duyYmhd05syZwIMTIIoKLDktqRykUqna2tof/vCHBw4c+PKXv1xdXX3x4sVisRgMtKn3xJ05cyabzQazizzPKxaLahAxaq7Swmp4NgAAGjxJREFU3Gcv1ZFSqeQ4TrA4uMqGGqScJYH6qHISyBTmtorx1cEgmko5yHnUKdceX8WcNYA6T/rzx591oprcbdv2xMSEyvmZM2fUHPyyIxwhPGEXCvnpqbL8UBTFyZJ8ZaRQ76orCJHzRFm+EcmTJwkx4cmvLOEKzxWeKNjigoxs+996QsZ1ZaIyNSGX/ZYx5afLjjjvCUue5R/xhO0fzzvCdWzheP5Z6m1Ljn96+K88d9RP5LInX0JXEGJYJT73rytGPXHYTy/vijOe6PNEwROFuTGvZO+iJ0855QnXjznhf5Rvd6m8i/NCvlOzJMRZT1x0RM4RJ2xRqhxZvn6wsg5SovCuLufr4h8uODI/wvP8bDhSL0fkPTEqxMTMtWSlRF7XlsmfdWQN7hfyrMtCnH7z3LmlE1NCHBbiomMLT2Q9ee4lR5yNKpcnLnnitJ9fFZjwNZwpbIWzxIjwFXbEhCMb0jEhLspoYRGcK5p7fjtxhF8pef91hLKtyte/R+jgCNuxZhK70sbkKUJkhMj6DbjgifOuGPNka/TLZc1oK09TLVC4jjjmiVPyo2zVF4U46EtxVn6cadj2zGX8zPvxT3uyai77Ipf8v5ei4ke1B0/KLjxZZFlMvwglmX/VAOYI5ct2ws/1Mb9BnhXikrz03JpVR2RZZARPip/1/170ous3UoeI9P2WdlGIQb/4sok64rItRqPzI82LUswTJzxx2BGnpdmIag/y7Wt5v8IKoqya6ISspYj2IM2U7Ucv+xUna7MgE49qDxHxI3WIiC9rThooS0izIytUtkxxMcqu+t/mXTHpm1ZXyjXTFGXfYtu26hDVUo3T09PqeaC5f9V86qCfVUY+qnsKHBPX3u8Es3XVO09UykE3WvFC6ttw/KBbrBg/nGdV6uB5rIrxg8wHzOC6bqlUUldUDxXatm1ZlspJkFqhUAiAoWLKS05LQojR0VEhxPe+970777xT1/Vf//VfHxoaUhOvlBBKLAAqUC6XJycngwoOlr1SdamGFZXrKJCjYtmC2W2Tk5NKF4VQFQFLJaWanQKIBaswaCiTk5OqhmZBydxcqWxcS3yVYFDxqhaDj3NTnj++67rFYnFycjL8tIJ6z/GsNHPTolAWhaIPQ2LS7xhOCzFqSwuds11hC0caLnW3++bbFVOuNIISbmxbWKJcFGVXjDuOsMRY2XXKriiLfMknLGn3/SRsedAui5Il5PuSHOHasicaKwu7KPJFMVaUb5/z/H5xxlBIcyFXv5W7fOOKEJYryrawXf+jJyxpfUKRQ2FL5v+yvIQrM2eLs7awLdkJVd79+DKa5frvyXSELSxLWFHxZfH9LNmiYPnsVhJjpYjEZSIROsxN3/UlKElDO1n29SkL1xJTtrDkC/pcURJFS4w5rvAsaZNlLUSXqyzZNV+U4p/3BbccT54y97rqSMEp2SIrK8XvZWyh1IuMXxJFJbKMKUolWb9l+SblCClscVa9htn5/9u79tioiu9/aWyxID4aTCNiSykQtQqIwVd8VEUTRM1XQf8TH/yhBFEUCVEjFCPwBxANURMlGHyQaoIGBUNFgSgGxcgvRRQpT4G+2+2+d+97fjnzKYfrdu/ysLvbvbkbUmbvzp075zNn5nzmnLkzBlWbQLaF2kud/3UXcJB1FgYhENfo0B1dJ/FdcYgLYvoaWaoeTRDXNAnJLk20URObvZoDFTJJjRNUqAjrQtVImYM6sX9NngutUn6NbtFFRLOTVALpVZdU+06pKoYuFUCXykaZydAnTMlrSUCX/G76IJ8b1UyhiS4pe1gXSZXIriTNjOqpfmFQL+g4pb1J4nvuykCsgqhkwhBR2RllV6LGoklL2n9uOKTNbAuhGyAuAYOeompyPpF0KZwKQb8QwiTwA6qtayKmgTL++y7og2kKS861CGeDxgRDCNV21QdDRHRTUNsJlTRfKoNqWm764JbfDQe3/CSXTTWUNIgGPnnMeMhtXNWkIETFMcZaBKNGE6HeA+nZBLCh5Ct9E6ZphsPhaDQKO5LBtGW2I31LZiPLtjjz21Gcnz0XmfPDYrKRwirntNVwXkR+3HvGbYkYQE3TIIVz/bSz2KyzJd6n3DTNFDKBr/F4HEu2FUXp7u52NiSWdTuvgCRCAAjZl03jCmgBhOf35LmFnBD0TeOus8mMVoHjCm3TtzTnlXPNj3ux/72znMzplPzMnfku7APLXxHxhKtPzgUtQ4468ZAwYyIZkJM9GkNP0ARJBMn09M6w5ZxPtMrJWdQSUYt4T7NJUyE6HNASh3UymWFNHFLJfLYbNk0vbZGkSRWZd/gNdJpHGsIS+y3RI3nJYUmbuizRw/9OTX+jtoiBHFA1zN5i4KCyRCjtP6IyxGaSZBFN4me6IOOXNrMlQqYtdNp5M2nQABc2dcnM3PPTqKfSvFIXqqWRTbaEZpJE6evjjkNQihk8JXVIOl3CpkhY4qglTsjqJ3RxUBfHdElSbXJrddHoS3axzRAhleai6Z9LLgmbTD5VjyylFM1dLtUkuDSDpILp1VTiZG7l6xZID6FNIOMrNXr6+sBokM1SqR1N29BV4nMAwRapOEjfVadNBtGwRJdFjq6YhEikxSEhWojlk5E+pguapEnCfJCsLFw1fGa8KWwiN8ck9TmgiZNUefGPLDwqNDJ1lq2R2ZNp04oL4lUxQ/xBRyWKvw2h6cRp2kyhEimz6Fx6QQ0XNqOkEjbRrPT53fRBCthuWKYpjlCFxV6pAJ2n1IN6h7NfUI+wNeoLCWELzbKEpQrTtlzx12j2IjkWTQWo2pLnZsifFgfX/BJeU1JtnZicqZlCde8XND1SiY9aSWGLEP2V/MlNH6Qu2qQ6hHeH1ctfJU1M1y9M0S3la9HFnyCyhvhHs5Pu+pA+v5s+uJUvNVa1adg8LsRxW6P9ZISI0OEn6cZVOQ6rJBORwaQgHU4aglxKbJgikYht2853/vtaQ7Z9PNozX3FeSZtOsSNp8+Ais5kzFs7UhEtLYQV8HQn4hPgVtpRf+35FTZgb8LY42O8Q+OAuSIeDzlB+5prk6J24cDjMDQzqg22jUWlc6enpKSkpiUaj4Bx4XZCRRZPjuBzetagvUs4rKNZJC/iNvL4qhQdhd1T2GEELeU/VlATKh0MPz8WRPSnZ+Ou55nduj4nVWuBwXGBKwi2/cy4Si8WSyaTzSLtEIoGmAbmk0KcetISp6TRqheOt0jgFDBGi6bnooECTLaM8CUmbZJxO2GGyCpYh7CBlEJ2YspGPXNoTSaGipia5DY0XUXL+2+Q5p/wUpzOEEaGYj4iS+cSNctaIuflpv70c4SQ5O07FWboMN4Tl33YqijOkJARxGYuCSmEyCCTESfLhp2Tjr6LTTgrTSMpn7aIKiIgl/ftpb7FFq0XlH6DwFjn5VVk4fG5pamW64ZAS0cBkGUCRU06CQyBHbDtGQFHFwsQc4OanaONJLRMOAWke5V1kYvba5NHpTiuUpF8R2UDCJtHCwrJNvas3eMFYORMyQmSJfbYIS+gIAVsccyufFICg2Ec80wrAkNCz3HAgeYlakbx4bpIuuOFAIUtB4FjkcPuHFDUhhJqkWxCFtKnZ5Bygm9iOiFFgRwRpTCA9lC0o2ZYwE0L8nxDt8nFhIQ5T6Icq304aDdVFxAQMzI4RdGIPhTLDMuIjOt3yZ9IH9AjLpJqLk6cF5wClMx5nxYSVoOgqSXGSgubEjA+74g+HDLWR1utItiIEr7NNnWn6KQ0OrvlFQEBRbYqT2eKwLaIWdMNZLKfFSRl8PEYqLQ6SsFaMerebPuhyAJGuHoqmwSeOMLdbv1AlcxUtvWKSRZUqlFYfTBnWJnz+nT8DDunKt0UXqRZp1GEh9lNCuiilhqQbVyVzp18xQhLmSUucPvwKNhFmhRf4Oi2gM435fDgc5hBeivngr252hDOkJFABlA8LBcKUko2/gpHA6CQSCZAbPgKPs3GCzTFuhJ1CcIbzOBPMH6jryojKGQkcqg0RhBBujqUcsSVns3EaVQQEOG1DURRnnIhz5ibBLR2LxVArvpKbCuT4KZBR0zQ+25k9lileQCapOa5h/z7OsiyIjGLRuKCh7P7EAHTGoad/K5al0pj+8vsd4XAYYxN+ymNfy4bIzj7LLci2gf2+GYbCbNQqe2XybD5lSgkcYrEY2hcqnb1q5L1klpdrwt2Zr3gswdN49pdkDmYVtPhgY2yUedtCKHZvPITWhtDHOcJnQ+qsR+LcKg0U8BdrmC666CIe5tzuyur1rVu3zpgxY8yYMUVFRd9+++3Ze/+yWqvsFR6JRFatWjV58uQLLrigsrJy1qxZf/31Fz8OhJ3HYr5eoAk2G6tXr7711lsVRbnsssvuvPPOjRs38hpA9sOxKSpQYVFtVVXRiMFgEGsHhRB1dXWXXHLJrFmzyD0ViYBGMKMqXHkxkvCJWrZtL1myxPkW8eTJkyEd7/hauMKi5qylzvhCa2vrfffdV1VVNWzYsKqqqqamJue6z0IXuW/9x44dW1paiobG2+N1dXWZ1+r2LaSArsANs2zZsquuumro0KEjR45cunRpAdX/XKuKpcZgQi+99FJFRcWFF15400037dmzx3ncCro/94hzfcpZ5s8bW4JlYmPc0tJSXFyc+YiZsxTpvLNt2rRp0aJF9fX1xcXFmzdvzi91O28pzv5G27bvvvvu+vr61tbWnTt3jhs37pprrunp6YHm8d6pZ1/gAM8JX+v333//9ddft7W1/fHHHwsXLlQUBdudt7W1MVsa4IKcTfUQj3fmNAxj165dY8aMqaioWLhwIb04p1JIj3mkM3PBpcELUW2cjb148eIJEyZEo9FAIBCPxzET4AGn4ATsW2E4htGOaMTDhw+PHTt23rx527ZtCwQCv/zyy9GjR73Rvn3Fx5W2trbjx493dnYmEol169aVlZXt3r3bLbMHrsfj8TVr1lx55ZX19fXRaHTjxo2lpaXLly/3gGhuInR0dAghpk6det111/3www8tLS2LFy8uKys7dOgQbuns7ARPynY4KJ9siSOFWIpUVFTkvOKGXVavY6qtKMrmzZuz+qC8F464m9N1GY/HS0pK9u/fz35dpuocyMh7tc+7AnjbEQ4VZ0i7pqZmxYoVzigkTjY87wcNnBuxDg+kv7OzMxwOV1ZWNjQ0TJkyZcmSJWhTLGLzRnyqp6eH10cKId54440JEybAzYATjUCV+MCpgdNS51cTZkt4UUYIsXTp0htvvBHqjbEUio0zs87vKQVxF8ScPXt2VVUVB2sKoubnWkld1/8nP5jamab58MMPz50791zLKbj8gwYN2rZtG8/uJk6cuHLlyhMnTkAQVVVzYKTyyZbYGNN6y0BAUZQ89mpntFtRlC+//DKRSOSxPjnQZrAiphF79uwpKipqamriuAw3kDemp/xCpWVZWNWxfv36wYMH//jjj3DqQl4ng8xBK2TpEUx5eQYyb968F198UQhxxx13zJw506nbHBDPUmVyUyzIELvuFyxYMHTo0KqqqhEjRjz55JMci8TcLDdVyupT2J0GjTUM4/rrr6+rq5s6deqQIUNqa2tXrlzpjZbNACMExEGzVVVVK1aswIkRGW4p9J9effXVmpoaxGF27dpVUVHxySefFLpQbvXHgu5oNKooyo4dO3jjodra2ilTpvAg5nzdyq2o/349n2wJtdd1PZlMdnZ2VldX532OG41GVVUtKyvbsGEDc4X/jvLALIE5UGtrqxDi0Ucfra2tdS7+5bfnPABFZyftaIDP7t27R44cOWTIkNLS0oaGBszSMDVhJ9OpvIX6P48jcJWtW7fu6quvxm4ljzzyCE9GA4EA86pCFVXW2zmz7O7u1nV9586dX3311f79+zds2DBt2rSKigq8tZptd31uYGSGxLFFy7KwfGfVqlW//vrrF198cfnll3/wwQehUIgZc27qluOnQLr3338fe9B4YLDKACDafenSpThoq6SkZMmSJRnye+CnYDBoWdbUqVNvu+22v//+Wwixdu3aQYMGjRgxAm5U9hbzPD9LUueNLcEqOzUbU/wsyXnGYpmoISC1detWeLzOeGOBZojH47xjghDiqaeeGj169NGjR1kcOLSdDcQ/FWhC1/X29nZN0yzLOnjw4L59++bPn3/xxRf//vvvOFgRcvHhzQUqJle7u7sbvSwajV566aUc5n/ggQfmzJmDloUnhi0u31uIiVgs5vQQOynC8ePHy8vLP/zwQ29QQ379h7diQQsOHTr05ptvRttpmvb4448/+OCDhdiUZ19nbDUshJgyZcr06dPxBriXRq0UKCzL+vjjj6uqqrZv397Y2Lh+/fry8vKPPvooJZuXvoID7du376GHHiotLS0uLr7rrrtmzpw5fvz4aDTKk58cxATyxpYwF7QsCx4OyJzfhdWapsGvqyhKfX29lxTOTRZN0wzDeP7550ePHs1L7DVNc67/cL5x41bOwL/OqgVxQCN0Xa+trX399dehhHAseWOoZV9LMBj87rvvcJYk/g4ePPgC+cHySc458BsxQw3Rc6G3PMXEC0S4q7q6etGiRQjDsVc1Q4ED/CdoKTNC0MSKiooXXniB7ceaNWsw//YMR+zbKGjKpqam4uLiLVu2sOx9c3rmyqhRo9auXcsTg7feemvMmDGekS5FEGcoWdf1np6eQCBgGMZjjz02Y8YMTH1xC4/wKSX049e8saV+lKFfikKkRtM0XdfLyso2btzojGX0yyMGVCGsW3PmzCkvL3e+O4O34UCkvOF1APKYfMRiMadQkyZNevPNN9va2pg0sK0dUO11rpXhUQanAZ44caKpqenPP/9sbGysqal5+umnjxw54gHSwLCA/rJW0x6pp2KvOBBq+PDhWNTibH2+vUATYEto61gsNmvWrHvuuSeRSODKs88+e//99/PLjwUqY+ZqQ9JFixYNHz4ce6p5mzCpqlpeXo4z6aHJ77zzzrXXXpsZpYL+lVdwc88NhUKKonz22We8dyWvZ8qqpD5bOg1vKBRqbGzcu3evoih1dXUHDx7EW+Wnc3grFQqFFixYMGjQoAMHDrS2tpqm2dTUhLUdKYLyFDblegF9tW1blZ/Vq1fv2rXr0KFDjY2Nr7zyyrBhwz7//HMIwh41DoQXkIApVWW2hC3ssAoSfPH222+fP3++M78HfA/sETRNs6WlJZFIvPvuuw0NDR0dHdu3b7/33nsrKyvxBk0sFmNm7AShsNLgBGhlFuenn34qKipavnx5OBx+++23q6ur165d6w32n6F1gsHgqFGjsHwHZ6ayMmS4q3B/euaZZ8aNG7dp06bm5uY1a9ZUVlYuWLCgcMXJXHPouaZpDfLT3Ny8YcOGCRMmPPfcc01NTZgJoLm5F2Qu8L/86rOl0+h98803ivyUlpYOHz5cUZTZs2ef/tlzKdu2S0pKIDI2disrK9uxY0dzczNmacwenKa3oGGIx+MzZswYOXKkoigTJ0685ZZbtmzZwhKpquoB3sDipE10dHRMmzbttddeCwaDnmlWSJpyaPT06dOvuOIKRVFuuOGGJ5544sCBA87t7NKCU0AX0TdhJ3RdhyPcsqyff/65pqYGUr/33nve5g1CiLa2toaGhtLS0t9++42bz2OKzXIJIbq7u0Oh0Msvv1xdXa0oyqRJk5YtW+bhVgbXV1X1008/HT9+fFFR0aRJk+bOnXvkyBHAgnCQE6LspX221IutZVnsQQmFQrCa7PrLXgPksWRnIAaBDMMwOjo6WGre0CWPlezHR0NGLpCb2xm1SSaTTlg4c+EmcI4NolEYVSORiNPfwAsgCldG9sNDQOzojagcZpyxWIybOxKJcLqgRXaG2BBfNk0zpTU5+lzokmauPzwQkUiko6MjB6t9M1cm27/qus50EC8neUaf00IXj8d53h6Xn5Rga87Ios+WUhuopaWFL+XAucfPynHCNE2oYDgcRt8zDMO57AMvZ3LMOMfVy+rjIpGIpmmYjicSCbQyD0DxeDxn3S97YmIznr6n9/AWCaFQCLQ4ZejJXpWyWjIaMSWECuIL88kDrjc6NdQ1pXtCb2FRmBBji5asgp/HwrEsTwjR3NzM1WDZ+YpnEtxb29vbMUTzX8/ImFYQbDCLnzBwRaNRZsacSHtvf1302dJpJLu6unBKHx1BHgzmpgFOPz6vKT5gyzTNiPxg5IVPIq9V67eHw5Q6F+87WVE8HscUjc1qvz04TwWxj5Cfn3IFB8k5XRScsxATaDjbtlPasaurixkSdODYsWOFKKCzzuwB5U0E8GtKEztv8WSaJzmQrqenh5HxpLzYHM4po7cX1yaTSY4J2LYdCoXYLvNAjTWpOdB8ny2l6VPsYvHw6Yx4mwATFJ6v9MUC78exgvbNUEBXICaG13g8jq/xeDwSifCG5qAOOeh4ucfNNE0MsslkkokFaASTidzXqh+fyKMn1DWRSFiWBQ3n02ycZqYfH52XoqCl2IRFlx9UA8uYMBNApMYb/dcNZNM0+d0UnvW5ZfbAdR6u8S69ByQ6GxGctIl7Om60bbuvE/1syjzXPD5b6kUMg0soFGLLkeLVP1dkB3h+HlbYa40VD+xdy+XquRxg5exgIMHO8D97WeCW8AZbsm2bW5kR5pkAA8JXOE8hJtB/2XGIdYewK7FYjGkiWpbtTSFKynVOCRmzl4V7NG9i6SWOyOJzAn3WsixufQ+zQz6+iRcSeP6kF94RA/psmiaf+G6aprMvcxdg3ejfhM+W+hdPvzQfAR8BHwEfAR8BHwGvIeCzJa+1qC+Pj4CPgI+Aj4CPgI9A/yLgs6X+xdMvzUfAR8BHwEfAR8BHwGsI+GzJay3qy+Mj4CPgI+Aj4CPgI9C/CPhsqX/x9EvzEfAR8BHwEfAR8BHwGgI+W/Jai/ry+Aj4CPgI+Aj4CPgI9C8CPlvqXzz90nwEfAR8BHwEfAR8BLyGgM+WvNaivjw+Aj4CPgI+Aj4CPgL9i8D/A7HVOZg+7ik8AAAAAElFTkSuQmCC)" ], "metadata": { "id": "1Gk9-UjdhW0k" } }, { "cell_type": "markdown", "source": [ "\n", "\n", "```\n", "number_of_sample:=10\n", "size_of_product_of_population:= 9765625\n", "size_of_sample_space_of_product_of_population:= 9765625\n", "size_of_range_of_sample_mean_as_duplicates:=9765625\n", "range_of_sample_mean:=[1, 6/5, 7/5, 8/5, 9/5, 2, 11/5, 12/5, 13/5, 14/5, 3, 16/5, 17/5, 18/5, 19/5, 4, 21/5, 22/5, 23/5, 24/5, 5, 26/5, 27/5, 28/5, 29/5, 6, 31/5, 32/5, 33/5, 34/5, 7, 36/5, 37/5, 38/5, 39/5, 8, 41/5, 42/5, 43/5, 44/5, 9]\n", "size_of_range_of_sample_mean:=41\n", "distribution_of_sample_mean:=[[1, 1/9765625], [6/5, 2/1953125], [7/5, 11/1953125], [8/5, 44/1953125], [9/5, 143/1953125], [2, 1992/9765625], [11/5, 981/1953125], [12/5, 2178/1953125], [13/5, 4422/1953125], [14/5, 8294/1953125], [3, 72403/9765625], [16/5, 23672/1953125 , [17/5, 36401/1953125], [18/5, 52844/1953125], [19/5, 72633/1953125], [4, 473694/9765625], [21/5, 23496/390625], [22/5, 27738/390625], [23/5, 31207/390625], [24/5, 33484/390625], [5, 171389/1953125], [26/5, 33484/390625], [27/5, 31207/390625], [28/5, 27738/390625], [29/5, 23496/390625], [6, 473694/9765625], [31/5, 72633/1953125], [32/5, 52844/1953125], [33/5, 36401/1953125], [34/5, 23672/1953125], [7, 72403/9765625], [36/5, 8294/1953125], [37/5, 4422/1953125], [38/5, 2178/1953125], [39/5, 981/1953125], [8, 1992/9765625], [41/5, 143/1953125], [42/5, 44/1953125], [43/5, 11/1953125], [44/5, 2/1953125], [9, 1/9765625]]\n", "mean_of_sample_mean:=5\n", "variance_of_sample_mean:=4/5\n", "[4/5, 1, 6/5, 7/5, 8/5, 9/5, 2, 11/5, 12/5, 13/5, 14/5, 3, 16/5, 17/5, 18/5, 19/5, 4, 21/5, 22/5, 23/5, 24/5, 5, 26/5, 27/5, 28/5, 29/5, 6, 31/5, 32/5, 33/5, 34/5, 7, 36/5, 37/5, 38/5, 39/5, 8, 41/5, 42/5, 43/5, 44/5, 9, 46/5]\n", "[0, 1/9765625, 2/1953125, 11/1953125, 44/1953125, 143/1953125, 1992/9765625, 981/1953125, 2178/1953125, 4422/1953125, 8294/1953125, 72403/9765625, 23672/1953125, 36401/1953125, 52844/1953125, 72633/1953125, 473694/9765625, 23496/390625, 27738/390625, 31207/390625, 33484/390625, 171389/1953125, 33484/390625, 31207/390625, 27738/390625, 23496/390625, 473694/9765625, 72633/1953125, 52844/1953125, 36401/1953125, 23672/1953125, 72403/9765625, 8294/1953125, 4422/1953125, 2178/1953125, 981/1953125, 1992/9765625, 143/1953125, 44/1953125, 11/1953125, 2/1953125, 1/9765625, 0]\n", "\n", "```\n", "\n" ], "metadata": { "id": "PaKgbx3_hZa9" } }, { "cell_type": "markdown", "source": [ 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)" ], "metadata": { "id": "Cxq9GevahdMq" } }, { "cell_type": "markdown", "source": [ "자료는 나름 잘 만들었다고 생각했는데, 오히려 알고 있던 내용이 혼란스럽다.\n", "\n", "과연 모집단이 뭐지? 조사는 뭐지? 확률에서 말하는 이상적인 상황에서\n", "\n", "표본공간에서의 사건과 혼돈하는 듯 하고?\n", "\n", "이상적인 상황에서 조사와 시행이 같아 보이기는 한데... 오히려 모집단이 뭔지\n", "\n", "모르는 상황이 되어버렸다.\n", "\n", "나름 합리화로 답을 만들었지만, 자신이 없다.\n", "\n", "아래 예는 \"모평균은 표본평균의 평균과 같다.\"를 설명하는\n", "\n", "잘 알려진 예인데 이것에서 모든 통계용어를 써가며 분석해보니\n", "\n", "더욱 모르겠다, 나만 이런 생각을 하나?" ], "metadata": { "id": "LE4cfceYhg-y" } }, { "cell_type": "markdown", "source": [ "아래는 Sage Math의 Text 파일이다. 위의 Nims 서버와 같은 내용인데, 혹시나 Nims 서버가 없어지는 경우를 대비하여 Text 형식을 아래에 붙여 놓았다.\n", "" ], "metadata": { "id": "0j9PUNichh7f" } }, { "cell_type": "markdown", "source": [ "\n", "\n", "```\n", "$\\text{지금은 작업중 입니다.}$\n", "sage: population=[(1,1),(3,1),(5,1),(7,1),(9,1)]\n", "sage: #population=[(1,1),(2,1),(2,1),(3,1),(3,1),(3,1)]\n", "sage: print(\"population := %s \" % population)\n", "sage: size_of_population=len(population)\n", "sage: print(\"size_of_population:= %s\" % size_of_population)\n", "population := [(1, 1), (3, 1), (5, 1), (7, 1), (9, 1)]\n", "size_of_population:= 5\n", "$\\begin{array}{l}\n", "\\text{모집단이 수가 아니라 대상이란 의미에서 순서쌍의 $y$좌표가 $1$인 순서쌍으로 표현했다.} \\\\\n", "\\text{여기서는 모집단의 원소를 카드나 공으로 생각하자. } \\\\\n", "\\text{그러면 같은 순서쌍이 여러개 있는 것을 } \\\\\n", "\\text{같은 순서쌍의 $x$좌표의 수가 써 있는 여러개의 카드나 공으로 생각할 수 있다. } \\\\\n", "\\text{모집단의 원소를 선택하는 것을 시행으로 보고}\\\\\n", "\\text{순서쌍의 $x$좌표의 원소의 글자를 얻은 것을 시행의 결과로 보자.}\n", "\\end{array}$\n", "sage: sample_space_of_population=[]\n", "sage: for i in range(size_of_population):\n", "... sample_space_of_population.insert(i,(population[i][0],population[i][1]+1))\n", "...\n", "sage: sample_space_of_population=sorted(list(set(sample_space_of_population)))\n", "sage: print(\"sample_space_of_population:= %s\" %sample_space_of_population)\n", "sage: size_of_sample_space_of_population=len(sample_space_of_population)\n", "sage: print(\"size_of_sample_space_of_population:= %s\" % size_of_sample_space_of_population)\n", "sample_space_of_population:= [(1, 2), (3, 2), (5, 2), (7, 2), (9, 2)]\n", "size_of_sample_space_of_population:= 5\n", "$\\begin{array}{l}\n", "\\text{모집단의 표본공간이 수가 아니라 시행의 결과란 의미에서} \\\\\n", "\\text{순서쌍의 $x$좌표는 시행해서 얻어지는 모집단의 원소인 순서쌍의 $x$좌표이고} \\\\\n", "\\text{순서쌍의 $y$좌표가 $2$인 순서쌍으로 표현했다.} \\\\\n", "\\text{모집단의 원소를 선택하는 가능성이 같다고 보자.} \\\\\n", "\\end{array} $\n", "sage: probability_of_sample_space_of_population=[]\n", "sage: j=-1\n", "sage: for i in sample_space_of_population:\n", "... j=j+1\n", "... probability_of_sample_space_of_population.insert(j,1/1*population.count((i[0],i[1]-1))/size_of_population)\n", "...\n", "sage: print(\"probability_of_sample_space_of_population=%s\" % probability_of_sample_space_of_population)\n", "sage: print(\"sum of probability_of_sample_space_of_population=%s\" % sum(probability_of_sample_space_of_population))\n", "probability_of_sample_space_of_population=[1/5, 1/5, 1/5, 1/5, 1/5]\n", "sum of probability_of_sample_space_of_population=1\n", "$\\begin{array}{l}\n", "\\text{모집단의표본공간의 원소를 그 원소인 순서쌍의 $x$좌표로의 대응을 확률변수 $\\mathrm{X}$ 라 하자. } \\end{array}$\n", "sage: random_variable_X=[]\n", "sage: j=-1\n", "sage: for i in sample_space_of_population:\n", "... j=j+1\n", "... random_variable_X.insert(j,[i,i[0]])\n", "... #random_variable_X.insert(j,[i,1+floor(log(j+1)/log(2))]) \n", "... #일단 위의 경우처럼 특별한 경우에 대하여 진행한 후 다시 가정에 맞게 가기로 한다.\n", "...\n", "sage: print(\"random_variable_X:= %s\" % random_variable_X)\n", "random_variable_X:= [[(1, 2), 1], [(3, 2), 3], [(5, 2), 5], [(7, 2), 7], [(9, 2), 9]]\n", "sage: range_of_random_variable_X_as_duplicates=[]\n", "sage: j=-1\n", "sage: for i in random_variable_X:\n", "... j=j+1\n", "... range_of_random_variable_X_as_duplicates.insert(j,i[1])\n", "... \n", "...\n", "sage: print(\"range_of_random_variable_X_as_duplicates:=%s\" % range_of_random_variable_X_as_duplicates)\n", "range_of_random_variable_X_as_duplicates:=[1, 3, 5, 7, 9]\n", "sage: size_of_range_of_random_variable_X_as_duplicates=len(range_of_random_variable_X_as_duplicates)\n", "sage: print(\"size_of_range_of_random_variable_X_as_duplicates:=%s\" % size_of_range_of_random_variable_X_as_duplicates)\n", "size_of_range_of_random_variable_X_as_duplicates:=5\n", "sage: probability_of_range_of_random_variable_X_as_duplicates=copy(probability_of_sample_space_of_population)\n", "sage: %latex\n", "sage: probability of range of random variable $\\mathrm{X}$ as duplicates $\\displaystyle=\\sage{latex(probability_of_range_of_random_variable_X_as_duplicates)}$\n", "sage: print(\"sum of probability_of_range_of_random_variable_X_as_duplicates=%s\" % sum(probability_of_range_of_random_variable_X_as_duplicates))\n", "sum of probability_of_range_of_random_variable_X_as_duplicates=1\n", "sage: range_of_random_variable_X=copy(sorted(list(set(range_of_random_variable_X_as_duplicates))))\n", "sage: print(\"range_of_random_variable_X:=%s\" % range_of_random_variable_X)\n", "sage: size_of_range_of_random_variable_X=len(range_of_random_variable_X)\n", "sage: print(\"size_of_range_of_random_variable_X:=%s\" % size_of_range_of_random_variable_X)\n", "range_of_random_variable_X:=[1, 3, 5, 7, 9]\n", "size_of_range_of_random_variable_X:=5\n", "sage: probability_of_range_of_random_variable_X=[]\n", "sage: for i in range(size_of_range_of_random_variable_X):\n", "... sumtemp=0\n", "... for j in range(size_of_range_of_random_variable_X_as_duplicates):\n", "... if range_of_random_variable_X[i]==range_of_random_variable_X_as_duplicates[j]:\n", "... sumtemp=sumtemp+probability_of_range_of_random_variable_X_as_duplicates[j] \n", "... probability_of_range_of_random_variable_X.insert(i,sumtemp)\n", "sage: %latex\n", "sage: \\ \\\\\n", "sage: probability of range of random variable $\\mathrm{X}$ $\\displaystyle=\\sage{latex(probability_of_range_of_random_variable_X)}$ \\\\\n", "sage: \\ \\\\\n", "sage: sum of probability of range of random variable $\\mathrm{X}$ $\\displaystyle=\\sage{latex(sum(probability_of_range_of_random_variable_X))}$\n", "sage: distribution_of_population=[]\n", "sage: for i in range(size_of_range_of_random_variable_X):\n", "... distribution_of_population.insert(i,[range_of_random_variable_X[i],probability_of_range_of_random_variable_X[i]])\n", "sage: %latex\n", "sage: distribution of population $\\displaystyle=\\sage{latex(distribution_of_population)}$\n", "sage: population_mean=0\n", "sage: for i in range(size_of_range_of_random_variable_X):\n", "... population_mean=population_mean+range_of_random_variable_X[i]*probability_of_range_of_random_variable_X[i]\n", "...\n", "sage: print(population_mean)\n", "5\n", "sage: population_variance=0\n", "sage: for i in range(size_of_range_of_random_variable_X):\n", "... population_variance=population_variance+probability_of_range_of_random_variable_X[i]*range_of_random_variable_X[i]^2\n", "...\n", "sage: population_variance=population_variance-population_mean^2\n", "... \n", "...\n", "sage: print(\"population_variance:=%s\" % population_variance)\n", "population_variance:=8\n", "sage: population_standard_deviation=sqrt(population_variance)\n", "sage: %latex\n", "sage: population standard deviation $\\displaystyle=\\sage{latex(population_standard_deviation)}$\n", "$\\text{모집단의 확률분포는 확률변수}\\mathrm{X}\\text{의 확률분포이다.}$\n", "sage: number_of_sample=2\n", "sage: %latex\n", "sage: $\\displaystyle\\overline{\\mathrm{X}}=\\frac{1}{\\sage{number_of_sample}}\\sum_{i=1}^\\sage{number_of_sample} \\mathrm{X}_i$\n", "$\\begin{array}{l}\n", "\\text{복원추출을 할 경우 표본개수의 제한이 없지만,} \\\\\n", "\\text{비복원추출일 경우 표본개수의 제한은 모집단 크기가 된다.} \\\\\n", "\\text{복원추출로 표본을 추출했다고 가정한다.}\n", "\\end{array}$\n", "sage: product_of_population=[]\n", "sage: for i in range(size_of_population^number_of_sample):\n", "... temp=[]\n", "... for j in range(number_of_sample):\n", "... temp.insert(j,population[mod(floor(i/size_of_population^j),size_of_population)])\n", "... product_of_population.insert(i,temp)\n", "...\n", "sage: size_of_product_of_population=len(product_of_population)\n", "sage: if size_of_product_of_population*(number_of_sample+1)<600:\n", "... print(\"product_of_population := %s \" % product_of_population)\n", "... else:\n", "... print(\"자료가 너무 많아 product_of_population을 표시하지 않음\")\n", "... \n", "...\n", "sage: print(\"size_of_product_of_population:= %s\" % size_of_product_of_population)\n", "product_of_population := [[(1, 1), (1, 1)], [(3, 1), (1, 1)], [(5, 1), (1, 1)], [(7, 1), (1, 1)], [(9, 1), (1, 1)], [(1, 1), (3, 1)], [(3, 1), (3, 1)], [(5, 1), (3, 1)], [(7, 1), (3, 1)], [(9, 1), (3, 1)], [(1, 1), (5, 1)], [(3, 1), (5, 1)], [(5, 1), (5, 1)], [(7, 1), (5, 1)], [(9, 1), (5, 1)], [(1, 1), (7, 1)], [(3, 1), (7, 1)], [(5, 1), (7, 1)], [(7, 1), (7, 1)], [(9, 1), (7, 1)], [(1, 1), (9, 1)], [(3, 1), (9, 1)], [(5, 1), (9, 1)], [(7, 1), (9, 1)], [(9, 1), (9, 1)]]\n", "size_of_product_of_population:= 25\n", "sage: sample_space_of_product_of_population=[]\n", "sage: for i in range(size_of_product_of_population):\n", "... temp=[]\n", "... for j in range(number_of_sample):\n", "... temp.insert(j,(product_of_population[i][j][0],product_of_population[i][j][1]+1))\n", "... sample_space_of_product_of_population.insert(i,temp)\n", "...\n", "sage: sample_space_of_product_of_population=sorted(sample_space_of_product_of_population)\n", "sage: temp=[]\n", "sage: temp.insert(0,sample_space_of_product_of_population[0])\n", "sage: j=0\n", "sage: for i in range(1,size_of_product_of_population):\n", "... if not(sample_space_of_product_of_population[i-1]==sample_space_of_product_of_population[i]):\n", "... j=j+1\n", "... temp.insert(j,sample_space_of_product_of_population[i])\n", "... \n", "...\n", "sage: sample_space_of_product_of_population=temp\n", "sage: size_of_sample_space_of_product_of_population=len(sample_space_of_product_of_population)\n", "... \n", "...\n", "sage: if size_of_product_of_population*(number_of_sample+1)<600:\n", "... print(\"sample_space_of_product_of_population:= %s\" %sample_space_of_product_of_population)\n", "... else:\n", "... print(\"자료가 너무 많아 sample_space_of_product_of_population을 표시하지 않음\")\n", "...\n", "sage: print(\"size_of_sample_space_of_product_of_population:= %s\" % size_of_sample_space_of_product_of_population)\n", "sample_space_of_product_of_population:= [[(1, 2), (1, 2)], [(1, 2), (3, 2)], [(1, 2), (5, 2)], [(1, 2), (7, 2)], [(1, 2), (9, 2)], [(3, 2), (1, 2)], [(3, 2), (3, 2)], [(3, 2), (5, 2)], [(3, 2), (7, 2)], [(3, 2), (9, 2)], [(5, 2), (1, 2)], [(5, 2), (3, 2)], [(5, 2), (5, 2)], [(5, 2), (7, 2)], [(5, 2), (9, 2)], [(7, 2), (1, 2)], [(7, 2), (3, 2)], [(7, 2), (5, 2)], [(7, 2), (7, 2)], [(7, 2), (9, 2)], [(9, 2), (1, 2)], [(9, 2), (3, 2)], [(9, 2), (5, 2)], [(9, 2), (7, 2)], [(9, 2), (9, 2)]]\n", "size_of_sample_space_of_product_of_population:= 25\n", "sage: probability_of_sample_space_of_product_of_population=[]\n", "sage: j=-1\n", "sage: for i in sample_space_of_product_of_population:\n", "... j=j+1\n", "... temp=[]\n", "... for k in range(number_of_sample):\n", "... temp.insert(k,(i[k][0],i[k][1]-1))\n", "... probability_of_sample_space_of_product_of_population.insert(j,1/1*product_of_population.count(temp)/size_of_product_of_population)\n", "...\n", "sage: if size_of_product_of_population<600:\n", "... print(\"probability_of_sample_space_of_product_of_population:=%s\" % probability_of_sample_space_of_product_of_population)\n", "... else:\n", "... print(\"자료가 너무 많아 probability_of_sample_space_of_product_of_population을 표시하지 않음\")\n", "...\n", "sage: print(\"sum of probability_of_sample_space_of_product_of_population:=%s\" % sum(probability_of_sample_space_of_product_of_population))\n", "probability_of_sample_space_of_product_of_population:=[1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25]\n", "sum of probability_of_sample_space_of_product_of_population:=1\n", "sage: sample_mean=[]\n", "sage: j=-1\n", "sage: for i in sample_space_of_product_of_population:\n", "... j=j+1\n", "... temp=0\n", "... for k in range(number_of_sample):\n", "... temp=temp+i[k][0]\n", "... sample_mean.insert(j,[i,temp/number_of_sample])\n", "... \n", "...\n", "sage: print(\"sample_mean:= %s\" % sample_mean)\n", "sample_mean:= [[[(1, 2), (1, 2)], 1], [[(1, 2), (3, 2)], 2], [[(1, 2), (5, 2)], 3], [[(1, 2), (7, 2)], 4], [[(1, 2), (9, 2)], 5], [[(3, 2), (1, 2)], 2], [[(3, 2), (3, 2)], 3], [[(3, 2), (5, 2)], 4], [[(3, 2), (7, 2)], 5], [[(3, 2), (9, 2)], 6], [[(5, 2), (1, 2)], 3], [[(5, 2), (3, 2)], 4], [[(5, 2), (5, 2)], 5], [[(5, 2), (7, 2)], 6], [[(5, 2), (9, 2)], 7], [[(7, 2), (1, 2)], 4], [[(7, 2), (3, 2)], 5], [[(7, 2), (5, 2)], 6], [[(7, 2), (7, 2)], 7], [[(7, 2), (9, 2)], 8], [[(9, 2), (1, 2)], 5], [[(9, 2), (3, 2)], 6], [[(9, 2), (5, 2)], 7], [[(9, 2), (7, 2)], 8], [[(9, 2), (9, 2)], 9]]\n", "sage: range_of_sample_mean_as_duplicates=[]\n", "sage: j=-1\n", "sage: for i in sample_mean:\n", "... j=j+1\n", "... range_of_sample_mean_as_duplicates.insert(j,i[1])\n", "...\n", "sage: size_of_range_of_sample_mean_as_duplicates=len(range_of_sample_mean_as_duplicates)\n", "sage: if size_of_range_of_sample_mean_as_duplicates<600:\n", "... print(\"range_of_sample_mean_as_duplicates:=%s\" % range_of_sample_mean_as_duplicates)\n", "... else:\n", "... print(\"자료가 너무 많아 range_of_sample_mean_as_duplicates을 표시하지 않음\")\n", "... \n", "...\n", "sage: print(\"size_of_range_of_sample_mean_as_duplicates:=%s\" % size_of_range_of_sample_mean_as_duplicates)\n", "range_of_sample_mean_as_duplicates:=[1, 2, 3, 4, 5, 2, 3, 4, 5, 6, 3, 4, 5, 6, 7, 4, 5, 6, 7, 8, 5, 6, 7, 8, 9]\n", "size_of_range_of_sample_mean_as_duplicates:=25\n", "sage: probability_of_range_of_sample_mean_as_duplicates=copy(probability_of_sample_space_of_product_of_population)\n", "sage: if size_of_range_of_sample_mean_as_duplicates<600:\n", "... print(\"probability_of_range_of_sample_mean_as_duplicates:=%s\" % probability_of_range_of_sample_mean_as_duplicates)\n", "... else:\n", "... print(\"자료가 너무 많아 probability_of_range_of_sample_mean_as_duplicates을 표시하지 않음\")\n", "... \n", "...\n", "sage: print(\"sum of probability_of_range_of_sample_mean_as_duplicates=%s\" % sum(probability_of_range_of_sample_mean_as_duplicates))\n", "probability_of_range_of_sample_mean_as_duplicates:=[1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25, 1/25]\n", "sum of probability_of_range_of_sample_mean_as_duplicates=1\n", "sage: %latex\n", "sage: probability of range of sample mean as duplicates $\\displaystyle=\\sage{latex(probability_of_range_of_sample_mean_as_duplicates)}$\n", "sage: range_of_sample_mean=copy(sorted(list(set(range_of_sample_mean_as_duplicates))))\n", "sage: print(\"range_of_sample_mean:=%s\" % range_of_sample_mean)\n", "sage: size_of_range_of_sample_mean=len(range_of_sample_mean)\n", "sage: print(\"size_of_range_of_sample_mean:=%s\" % size_of_range_of_sample_mean)\n", "range_of_sample_mean:=[1, 2, 3, 4, 5, 6, 7, 8, 9]\n", "size_of_range_of_sample_mean:=9\n", "sage: probability_of_range_of_sample_mean=[]\n", "sage: for i in range(size_of_range_of_sample_mean):\n", "... sumtemp=0\n", "... for j in range(size_of_range_of_sample_mean_as_duplicates):\n", "... if range_of_sample_mean[i]==range_of_sample_mean_as_duplicates[j]:\n", "... sumtemp=sumtemp+probability_of_range_of_sample_mean_as_duplicates[j] \n", "... probability_of_range_of_sample_mean.insert(i,sumtemp)\n", "...\n", "sage: print(probability_of_range_of_sample_mean)\n", "[1/25, 2/25, 3/25, 4/25, 1/5, 4/25, 3/25, 2/25, 1/25]\n", "sage: %latex\n", "sage: \\ \\\\\n", "sage: probability of range of sample mean $\\displaystyle=\\sage{latex(probability_of_range_of_sample_mean)}$ \\\\\n", "sage: \\ \\\\\n", "sage: sum of probability of range of sample mean $\\displaystyle=\\sage{latex(sum(probability_of_range_of_sample_mean))}$\n", "sage: distribution_of_sample_mean=[]\n", "sage: for i in range(size_of_range_of_sample_mean):\n", "... distribution_of_sample_mean.insert(i,[range_of_sample_mean[i],probability_of_range_of_sample_mean[i]])\n", "sage: %latex\n", "sage: distribution of sample mean $\\displaystyle=\\sage{latex(distribution_of_sample_mean)}$\n", "sage: mean_of_sample_mean=0\n", "sage: for i in range(size_of_range_of_sample_mean):\n", "... mean_of_sample_mean=mean_of_sample_mean+range_of_sample_mean[i]*probability_of_range_of_sample_mean[i]\n", "...\n", "sage: print(mean_of_sample_mean)\n", "5\n", "sage: %latex\n", "sage: mean of sample mean $\\displaystyle=\\sage{latex(mean_of_sample_mean)}$\n", "sage: variance_of_sample_mean=0\n", "sage: for i in range(size_of_range_of_sample_mean):\n", "... variance_of_sample_mean=variance_of_sample_mean+range_of_sample_mean[i]^2*probability_of_range_of_sample_mean[i]\n", "...\n", "sage: variance_of_sample_mean=variance_of_sample_mean-mean_of_sample_mean^2\n", "... \n", "...\n", "sage: print(\"variance_of_sample_mean:=%s\" % variance_of_sample_mean)\n", "variance_of_sample_mean:=4\n", "sage: %latex\n", "sage: variance of sample mean $\\displaystyle=\\sage{latex(variance_of_sample_mean)}$\n", "sage: histogram_data = []\n", "sage: histogram_data.insert(0,range_of_sample_mean[0]-(range_of_sample_mean[1]-range_of_sample_mean[0]))\n", "sage: for i in range(size_of_range_of_sample_mean):\n", "... histogram_data.insert(i+1,range_of_sample_mean[i])\n", "...\n", "sage: histogram_data.insert(size_of_range_of_sample_mean+1,range_of_sample_mean[size_of_range_of_sample_mean-1]+(range_of_sample_mean[size_of_range_of_sample_mean-1]-range_of_sample_mean[size_of_range_of_sample_mean-2]))\n", "sage: histogram_weights = []\n", "sage: histogram_weights.insert(0,0)\n", "sage: for i in range(size_of_range_of_sample_mean):\n", "... histogram_weights.insert(i+1,probability_of_range_of_sample_mean[i])\n", "...\n", "sage: histogram_weights.insert(size_of_range_of_sample_mean+1,0)\n", "sage: print(histogram_data)\n", "sage: print(histogram_weights)\n", "sage: histogram(histogram_data,bins=11, weights=histogram_weights)\n", "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n", "[0, 1/25, 2/25, 3/25, 4/25, 1/5, 4/25, 3/25, 2/25, 1/25, 0]\n", "sage: #아래는 위의 내용을 함수로 만들어서 한번에 결과를 보려고 만들었다.\n", "sage: def function_of_population(population):\n", "... print(\"population := %s \" % population)\n", "... \n", "... size_of_population=len(population)\n", "... \n", "... sample_space_of_population=[]\n", "... for i in range(size_of_population):\n", "... sample_space_of_population.insert(i,(population[i][0],population[i][1]+1))\n", "... sample_space_of_population=sorted(list(set(sample_space_of_population)))\n", "... print(\"sample_space_of_population:= %s\" %sample_space_of_population)\n", "... size_of_sample_space_of_population=len(sample_space_of_population)\n", "... print(\"size_of_sample_space_of_population:= %s\" % size_of_sample_space_of_population)\n", "... \n", "... print(\"size_of_population:= %s\" % size_of_population)\n", "... probability_of_sample_space_of_population=[]\n", "... j=-1\n", "... for i in sample_space_of_population:\n", "... j=j+1\n", "... probability_of_sample_space_of_population.insert(j,1/1*population.count((i[0],i[1]-1))/size_of_population)\n", "... print(\"probability_of_sample_space_of_population=%s\" % probability_of_sample_space_of_population)\n", "... random_variable_X=[]\n", "... j=-1\n", "... for i in sample_space_of_population:\n", "... j=j+1\n", "... random_variable_X.insert(j,[i,i[0]])\n", "... #random_variable_X.insert(j,[i,1+floor(log(j+1)/log(2))]) \n", "... #일단 위의 경우처럼 특별한 경우에 대하여 진행한 후 다시 가정에 맞게 가기로 한다.\n", "... print(\"random_variable_X:= %s\" % random_variable_X)\n", "... range_of_random_variable_X_as_duplicates=[]\n", "... j=-1\n", "... for i in random_variable_X:\n", "... j=j+1\n", "... range_of_random_variable_X_as_duplicates.insert(j,i[1])\n", "... \n", "... print(\"range_of_random_variable_X_as_duplicates:=%s\" % range_of_random_variable_X_as_duplicates)\n", "... size_of_range_of_random_variable_X_as_duplicates=len(range_of_random_variable_X_as_duplicates)\n", "... print(\"size_of_range_of_random_variable_X_as_duplicates:=%s\" % size_of_range_of_random_variable_X_as_duplicates)\n", "... probability_of_range_of_random_variable_X_as_duplicates=copy(probability_of_sample_space_of_population)\n", "... range_of_random_variable_X=copy(sorted(list(set(range_of_random_variable_X_as_duplicates))))\n", "... print(\"range_of_random_variable_X:=%s\" % range_of_random_variable_X)\n", "... size_of_range_of_random_variable_X=len(range_of_random_variable_X)\n", "... print(\"size_of_range_of_random_variable_X:=%s\" % size_of_range_of_random_variable_X)\n", "... probability_of_range_of_random_variable_X=[]\n", "... for i in range(size_of_range_of_random_variable_X):\n", "... sumtemp=0\n", "... for j in range(size_of_range_of_random_variable_X_as_duplicates):\n", "... if range_of_random_variable_X[i]==range_of_random_variable_X_as_duplicates[j]:\n", "... sumtemp=sumtemp+probability_of_range_of_random_variable_X_as_duplicates[j] \n", "... probability_of_range_of_random_variable_X.insert(i,sumtemp)\n", "... \n", "... \n", "... distribution_of_population=[]\n", "... for i in range(size_of_range_of_random_variable_X):\n", "... distribution_of_population.insert(i,[range_of_random_variable_X[i],probability_of_range_of_random_variable_X[i]])\n", "... population_mean=0\n", "... for i in range(size_of_range_of_random_variable_X):\n", "... population_mean=population_mean+range_of_random_variable_X[i]*probability_of_range_of_random_variable_X[i]\n", "... print(\"population_mean:=%s\" % population_mean)\n", "... population_variance=0\n", "... for i in range(size_of_range_of_random_variable_X):\n", "... population_variance=population_variance+probability_of_range_of_random_variable_X[i]*range_of_random_variable_X[i]^2\n", "... population_variance=population_variance-population_mean^2\n", "... \n", "... print(\"population_variance:=%s\" % population_variance)\n", "...\n", "sage: def function_of_sample(population,number_of_sample):\n", "... print(\"number_of_sample:=%s\" % number_of_sample)\n", "... size_of_population=len(population) \n", "... sample_space_of_product_of_population=[]\n", "... product_of_population=[]\n", "... for i in range(size_of_population^number_of_sample):\n", "... temp=[]\n", "... for j in range(number_of_sample):\n", "... temp.insert(j,population[mod(floor(i/size_of_population^j),size_of_population)])\n", "... product_of_population.insert(i,temp)\n", "... \n", "... size_of_product_of_population=len(product_of_population)\n", "... \n", "... print(\"size_of_product_of_population:= %s\" % size_of_product_of_population)\n", "... \n", "... for i in range(size_of_product_of_population):\n", "... temp=[]\n", "... for j in range(number_of_sample):\n", "... temp.insert(j,(product_of_population[i][j][0],product_of_population[i][j][1]+1))\n", "... sample_space_of_product_of_population.insert(i,temp)\n", "... sample_space_of_product_of_population=sorted(sample_space_of_product_of_population)\n", "... temp=[]\n", "... temp.insert(0,sample_space_of_product_of_population[0])\n", "... j=0\n", "... for i in range(1,size_of_product_of_population):\n", "... if not(sample_space_of_product_of_population[i-1]==sample_space_of_product_of_population[i]):\n", "... j=j+1\n", "... temp.insert(j,sample_space_of_product_of_population[i])\n", "... \n", "... sample_space_of_product_of_population=temp\n", "... size_of_sample_space_of_product_of_population=len(sample_space_of_product_of_population)\n", "... \n", "... print(\"size_of_sample_space_of_product_of_population:= %s\" % size_of_sample_space_of_product_of_population)\n", "... probability_of_sample_space_of_product_of_population=[]\n", "... j=-1\n", "... for i in sample_space_of_product_of_population:\n", "... j=j+1\n", "... temp=[]\n", "... for k in range(number_of_sample):\n", "... temp.insert(k,(i[k][0],i[k][1]-1))\n", "... probability_of_sample_space_of_product_of_population.insert(j,1/1*product_of_population.count(temp)/size_of_product_of_population)\n", "... \n", "... sample_mean=[]\n", "... j=-1\n", "... for i in sample_space_of_product_of_population:\n", "... j=j+1\n", "... temp=0\n", "... for k in range(number_of_sample):\n", "... temp=temp+i[k][0]\n", "... sample_mean.insert(j,[i,temp/number_of_sample])\n", "... \n", "... range_of_sample_mean_as_duplicates=[]\n", "... j=-1\n", "... for i in sample_mean:\n", "... j=j+1\n", "... range_of_sample_mean_as_duplicates.insert(j,i[1])\n", "... size_of_range_of_sample_mean_as_duplicates=len(range_of_sample_mean_as_duplicates)\n", "... \n", "... print(\"size_of_range_of_sample_mean_as_duplicates:=%s\" % size_of_range_of_sample_mean_as_duplicates)\n", "... probability_of_range_of_sample_mean_as_duplicates=copy(probability_of_sample_space_of_product_of_population)\n", "... range_of_sample_mean=copy(sorted(list(set(range_of_sample_mean_as_duplicates))))\n", "... print(\"range_of_sample_mean:=%s\" % range_of_sample_mean)\n", "... size_of_range_of_sample_mean=len(range_of_sample_mean)\n", "... print(\"size_of_range_of_sample_mean:=%s\" % size_of_range_of_sample_mean)\n", "... probability_of_range_of_sample_mean=[]\n", "... for i in range(size_of_range_of_sample_mean):\n", "... sumtemp=0\n", "... for j in range(size_of_range_of_sample_mean_as_duplicates):\n", "... if range_of_sample_mean[i]==range_of_sample_mean_as_duplicates[j]:\n", "... sumtemp=sumtemp+probability_of_range_of_sample_mean_as_duplicates[j] \n", "... probability_of_range_of_sample_mean.insert(i,sumtemp)\n", "... \n", "... distribution_of_sample_mean=[]\n", "... for i in range(size_of_range_of_sample_mean):\n", "... distribution_of_sample_mean.insert(i,[range_of_sample_mean[i],probability_of_range_of_sample_mean[i]])\n", "... \n", "... print(\"distribution_of_sample_mean:=%s\" % distribution_of_sample_mean)\n", "... \n", "... mean_of_sample_mean=0\n", "... for i in range(size_of_range_of_sample_mean):\n", "... mean_of_sample_mean=mean_of_sample_mean+range_of_sample_mean[i]*probability_of_range_of_sample_mean[i]\n", "... print(\"mean_of_sample_mean:=%s\" % mean_of_sample_mean)\n", "... \n", "... variance_of_sample_mean=0\n", "... for i in range(size_of_range_of_sample_mean):\n", "... variance_of_sample_mean=variance_of_sample_mean+range_of_sample_mean[i]^2*probability_of_range_of_sample_mean[i]\n", "... variance_of_sample_mean=variance_of_sample_mean-mean_of_sample_mean^2\n", "... \n", "... print(\"variance_of_sample_mean:=%s\" % variance_of_sample_mean)\n", "... \n", "... histogram_data = []\n", "... histogram_data.insert(0,range_of_sample_mean[0]-(range_of_sample_mean[1]-range_of_sample_mean[0]))\n", "... for i in range(size_of_range_of_sample_mean):\n", "... histogram_data.insert(i+1,range_of_sample_mean[i])\n", "... histogram_data.insert(size_of_range_of_sample_mean+1,range_of_sample_mean[size_of_range_of_sample_mean-1]+(range_of_sample_mean[size_of_range_of_sample_mean-1]-range_of_sample_mean[size_of_range_of_sample_mean-2]))\n", "... histogram_weights = []\n", "... histogram_weights.insert(0,0)\n", "... for i in range(size_of_range_of_sample_mean):\n", "... histogram_weights.insert(i+1,probability_of_range_of_sample_mean[i])\n", "... histogram_weights.insert(size_of_range_of_sample_mean+1,0)\n", "... print(histogram_data)\n", "... print(histogram_weights)\n", "... show(histogram(histogram_data,bins=size_of_range_of_sample_mean+2, weights=histogram_weights))\n", "sage: population=[(1,1),(3,1),(5,1),(7,1),(9,1)]\n", "sage: function_of_sample(population,1)\n", "number_of_sample:=1\n", "size_of_product_of_population:= 5\n", "size_of_sample_space_of_product_of_population:= 5\n", "size_of_range_of_sample_mean_as_duplicates:=5\n", "range_of_sample_mean:=[1, 3, 5, 7, 9]\n", "size_of_range_of_sample_mean:=5\n", "distribution_of_sample_mean:=[[1, 1/5], [3, 1/5], [5, 1/5], [7, 1/5], [9, 1/5]]\n", "mean_of_sample_mean:=5\n", "variance_of_sample_mean:=8\n", "[-1, 1, 3, 5, 7, 9, 11]\n", "[0, 1/5, 1/5, 1/5, 1/5, 1/5, 0]\n", "sage: population=[(1,1),(3,1),(5,1),(7,1),(9,1)]\n", "sage: function_of_sample(population,2)\n", "number_of_sample:=2\n", "size_of_product_of_population:= 25\n", "size_of_sample_space_of_product_of_population:= 25\n", "size_of_range_of_sample_mean_as_duplicates:=25\n", "range_of_sample_mean:=[1, 2, 3, 4, 5, 6, 7, 8, 9]\n", "size_of_range_of_sample_mean:=9\n", "distribution_of_sample_mean:=[[1, 1/25], [2, 2/25], [3, 3/25], [4, 4/25], [5, 1/5], [6, 4/25], [7, 3/25], [8, 2/25], [9, 1/25]]\n", "mean_of_sample_mean:=5\n", "variance_of_sample_mean:=4\n", "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n", "[0, 1/25, 2/25, 3/25, 4/25, 1/5, 4/25, 3/25, 2/25, 1/25, 0]\n", "sage: population=[(1,1),(3,1),(5,1),(7,1),(9,1)]\n", "sage: function_of_sample(population,3)\n", "number_of_sample:=3\n", "size_of_product_of_population:= 125\n", "size_of_sample_space_of_product_of_population:= 125\n", "size_of_range_of_sample_mean_as_duplicates:=125\n", "range_of_sample_mean:=[1, 5/3, 7/3, 3, 11/3, 13/3, 5, 17/3, 19/3, 7, 23/3, 25/3, 9]\n", "size_of_range_of_sample_mean:=13\n", "distribution_of_sample_mean:=[[1, 1/125], [5/3, 3/125], [7/3, 6/125], [3, 2/25], [11/3, 3/25], [13/3, 18/125], [5, 19/125], [17/3, 18/125], [19/3, 3/25], [7, 2/25], [23/3, 6/125], [25/3, 3/125], [9, 1/125]]\n", "mean_of_sample_mean:=5\n", "variance_of_sample_mean:=8/3\n", "[1/3, 1, 5/3, 7/3, 3, 11/3, 13/3, 5, 17/3, 19/3, 7, 23/3, 25/3, 9, 29/3]\n", "[0, 1/125, 3/125, 6/125, 2/25, 3/25, 18/125, 19/125, 18/125, 3/25, 2/25, 6/125, 3/125, 1/125, 0]\n", "sage: population=[(1,1),(3,1),(5,1),(7,1),(9,1)]\n", "sage: function_of_sample(population,4)\n", "number_of_sample:=4\n", "size_of_product_of_population:= 625\n", "size_of_sample_space_of_product_of_population:= 625\n", "size_of_range_of_sample_mean_as_duplicates:=625\n", "range_of_sample_mean:=[1, 3/2, 2, 5/2, 3, 7/2, 4, 9/2, 5, 11/2, 6, 13/2, 7, 15/2, 8, 17/2, 9]\n", "size_of_range_of_sample_mean:=17\n", "distribution_of_sample_mean:=[[1, 1/625], [3/2, 4/625], [2, 2/125], [5/2, 4/125], [3, 7/125], [7/2, 52/625], [4, 68/625], [9/2, 16/125], [5, 17/125], [11/2, 16/125], [6, 68/625], [13/2, 52/625], [7, 7/125], [15/2, 4/125], [8, 2/125], [17/2, 4/625], [9, 1/625]]\n", "mean_of_sample_mean:=5\n", "variance_of_sample_mean:=2\n", "[1/2, 1, 3/2, 2, 5/2, 3, 7/2, 4, 9/2, 5, 11/2, 6, 13/2, 7, 15/2, 8, 17/2, 9, 19/2]\n", "[0, 1/625, 4/625, 2/125, 4/125, 7/125, 52/625, 68/625, 16/125, 17/125, 16/125, 68/625, 52/625, 7/125, 4/125, 2/125, 4/625, 1/625, 0]\n", "sage: population=[(1,1),(3,1),(5,1),(7,1),(9,1)]\n", "sage: function_of_sample(population,5)\n", "number_of_sample:=5\n", "size_of_product_of_population:= 3125\n", "size_of_sample_space_of_product_of_population:= 3125\n", "size_of_range_of_sample_mean_as_duplicates:=3125\n", "range_of_sample_mean:=[1, 7/5, 9/5, 11/5, 13/5, 3, 17/5, 19/5, 21/5, 23/5, 5, 27/5, 29/5, 31/5, 33/5, 7, 37/5, 39/5, 41/5, 43/5, 9]\n", "size_of_range_of_sample_mean:=21\n", "distribution_of_sample_mean:=[[1, 1/3125], [7/5, 1/625], [9/5, 3/625], [11/5, 7/625], [13/5, 14/625], [3, 121/3125], [17/5, 37/625], [19/5, 51/625], [21/5, 64/625], [23/5, 73/625], [5, 381/3125], [27/5, 73/625], [29/5, 64/625], [31/5, 51/625], [33/5, 37/625], [7, 121/3125], [37/5, 14/625], [39/5, 7/625], [41/5, 3/625], [43/5, 1/625], [9, 1/3125]]\n", "mean_of_sample_mean:=5\n", "variance_of_sample_mean:=8/5\n", "[3/5, 1, 7/5, 9/5, 11/5, 13/5, 3, 17/5, 19/5, 21/5, 23/5, 5, 27/5, 29/5, 31/5, 33/5, 7, 37/5, 39/5, 41/5, 43/5, 9, 47/5]\n", "[0, 1/3125, 1/625, 3/625, 7/625, 14/625, 121/3125, 37/625, 51/625, 64/625, 73/625, 381/3125, 73/625, 64/625, 51/625, 37/625, 121/3125, 14/625, 7/625, 3/625, 1/625, 1/3125, 0]\n", "sage: population=[(1,1),(3,1),(5,1),(7,1),(9,1)]\n", "sage: function_of_sample(population,6)\n", "number_of_sample:=6\n", "size_of_product_of_population:= 15625\n", "size_of_sample_space_of_product_of_population:= 15625\n", "size_of_range_of_sample_mean_as_duplicates:=15625\n", "range_of_sample_mean:=[1, 4/3, 5/3, 2, 7/3, 8/3, 3, 10/3, 11/3, 4, 13/3, 14/3, 5, 16/3, 17/3, 6, 19/3, 20/3, 7, 22/3, 23/3, 8, 25/3, 26/3, 9]\n", "size_of_range_of_sample_mean:=25\n", "distribution_of_sample_mean:=[[1, 1/15625], [4/3, 6/15625], [5/3, 21/15625], [2, 56/15625], [7/3, 126/15625], [8/3, 246/15625], [3, 426/15625], [10/3, 666/15625], [11/3, 951/15625], [4, 1246/15625], [13/3, 1506/15625], [14/3, 1686/15625], [5, 1751/15625], [16/3, 1686/15625], [17/3, 1506/15625], [6, 1246/15625], [19/3, 951/15625], [20/3, 666/15625], [7, 426/15625], [22/3, 246/15625], [23/3, 126/15625], [8, 56/15625], [25/3, 21/15625], [26/3, 6/15625], [9, 1/15625]]\n", "mean_of_sample_mean:=5\n", "variance_of_sample_mean:=4/3\n", "[2/3, 1, 4/3, 5/3, 2, 7/3, 8/3, 3, 10/3, 11/3, 4, 13/3, 14/3, 5, 16/3, 17/3, 6, 19/3, 20/3, 7, 22/3, 23/3, 8, 25/3, 26/3, 9, 28/3]\n", "[0, 1/15625, 6/15625, 21/15625, 56/15625, 126/15625, 246/15625, 426/15625, 666/15625, 951/15625, 1246/15625, 1506/15625, 1686/15625, 1751/15625, 1686/15625, 1506/15625, 1246/15625, 951/15625, 666/15625, 426/15625, 246/15625, 126/15625, 56/15625, 21/15625, 6/15625, 1/15625, 0]\n", "sage: population=[(1,1),(3,1),(5,1),(7,1),(9,1)]\n", "sage: function_of_sample(population,7)\n", "number_of_sample:=7\n", "size_of_product_of_population:= 78125\n", "size_of_sample_space_of_product_of_population:= 78125\n", "size_of_range_of_sample_mean_as_duplicates:=78125\n", "range_of_sample_mean:=[1, 9/7, 11/7, 13/7, 15/7, 17/7, 19/7, 3, 23/7, 25/7, 27/7, 29/7, 31/7, 33/7, 5, 37/7, 39/7, 41/7, 43/7, 45/7, 47/7, 7, 51/7, 53/7, 55/7, 57/7, 59/7, 61/7, 9]\n", "size_of_range_of_sample_mean:=29\n", "distribution_of_sample_mean:=[[1, 1/78125], [9/7, 7/78125], [11/7, 28/78125], [13/7, 84/78125], [15/7, 42/15625], [17/7, 91/15625], [19/7, 7/625], [3, 304/15625], [23/7, 483/15625], [25/7, 707/15625], [27/7, 959/15625], [29/7, 1211/15625], [31/7, 1428/15625], [33/7, 63/625], [5, 1627/15625], [37/7, 63/625], [39/7, 1428/15625], [41/7, 1211/15625], [43/7, 959/15625], [45/7, 707/15625], [47/7, 483/15625], [7, 304/15625], [51/7, 7/625], [53/7, 91/15625], [55/7, 42/15625], [57/7, 84/78125], [59/7, 28/78125], [61/7, 7/78125], [9, 1/78125]]\n", "mean_of_sample_mean:=5\n", "variance_of_sample_mean:=8/7\n", "[5/7, 1, 9/7, 11/7, 13/7, 15/7, 17/7, 19/7, 3, 23/7, 25/7, 27/7, 29/7, 31/7, 33/7, 5, 37/7, 39/7, 41/7, 43/7, 45/7, 47/7, 7, 51/7, 53/7, 55/7, 57/7, 59/7, 61/7, 9, 65/7]\n", "[0, 1/78125, 7/78125, 28/78125, 84/78125, 42/15625, 91/15625, 7/625, 304/15625, 483/15625, 707/15625, 959/15625, 1211/15625, 1428/15625, 63/625, 1627/15625, 63/625, 1428/15625, 1211/15625, 959/15625, 707/15625, 483/15625, 304/15625, 7/625, 91/15625, 42/15625, 84/78125, 28/78125, 7/78125, 1/78125, 0]\n", "sage: # population의 크기가 5라고 할 때 sample의 크기가 8 이상일 때는 상당한 시간이 걸린다.\n", "```\n", "\n" ], "metadata": { "id": "Doswn6G8hlQ8" } }, { "cell_type": "markdown", "source": [], "metadata": { "id": "SGI6fAuJhquT" } } ] }