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<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8" />
<meta name="generator" content="pandoc" />
<meta http-equiv="X-UA-Compatible" content="IE=EDGE" />
<meta name="author" content="Dr. Joseph P. Yurko" />
<title>Introduction to R demos</title>
<script>// Pandoc 2.9 adds attributes on both header and div. We remove the former (to
// be compatible with the behavior of Pandoc < 2.8).
document.addEventListener('DOMContentLoaded', function(e) {
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) 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BkBAXAcIVHfzgDwr+ogoPDwoBXgoPDwqvrwoPAAMAFwAXBJkEmQAPABsAMQAAADIeAhQOAiIuAjQ+AQQiDgEUHgEyPgE0JgUzMhYVETMyFgcDBiInAyY2OwERNDYB4+rWm1tbm9bq1ptbW5sBv+jFcnLF6MVycv58lgoPiRUKDd8NJg3fDQoViQ8EmVub1urWm1tbm9bq1ps7csXoxXJyxejFDQ8K/u0XEP7tEBABExAXARMKDwAAAAMAFwAXBJkEmQAPABsAMQAAADIeAhQOAiIuAjQ+AQQiDgEUHgEyPgE0JiUTFgYrAREUBisBIiY1ESMiJjcTNjIB4+rWm1tbm9bq1ptbW5sBv+jFcnLF6MVycv7n3w0KFYkPCpYKD4kVCg3fDSYEmVub1urWm1tbm9bq1ps7csXoxXJyxejFAf7tEBf+7QoPDwoBExcQARMQAAAAAAIAAAAABLAEsAAZADkAABMhMhYXExYVERQGBwYjISImJyY1EzQ3Ez4BBSEiBgcDBhY7ATIWHwEeATsBMjY/AT4BOwEyNicDLgHhAu4KEwO6BwgFDBn7tAweAgYBB7kDEwKX/dQKEgJXAgwKlgoTAiYCEwr6ChMCJgITCpYKDAJXAhIEsA4K/XQYGf5XDB4CBggEDRkBqRkYAowKDsgOC/4+Cw4OCpgKDg4KmAoODgsBwgsOAAMAFwAXBJkEmQAPABsAJwAAADIeAhQOAiIuAjQ+AQQiDgEUHgEyPgE0JgUXFhQPAQYmNRE0NgHj6tabW1ub1urWm1tbmwG/6MVycsXoxXJy/ov9ERH9EBgYBJlbm9bq1ptbW5vW6tabO3LF6MVycsXoxV2+DCQMvgwLFQGQFQsAAQAXABcEmQSwACgAAAE3NhYVERQGIyEiJj8BJiMiDgEUHgEyPgE1MxQOAiIuAjQ+AjMyA7OHBwsPCv6WCwQHhW2BdMVycsXoxXKWW5vW6tabW1ub1nXABCSHBwQL/pYKDwsHhUxyxejFcnLFdHXWm1tbm9bq1ptbAAAAAAIAFwABBJkEsAAaADUAAAE3NhYVERQGIyEiJj8BJiMiDgEVIzQ+AjMyEzMUDgIjIicHBiY1ETQ2MyEyFg8BFjMyPgEDs4cHCw8L/pcLBAeGboF0xXKWW5vWdcDrllub1nXAnIYHCw8LAWgKBQiFboJ0xXIEJIcHBAv+lwsPCweGS3LFdHXWm1v9v3XWm1t2hggFCgFoCw8LB4VMcsUAAAAKAGQAAASwBLAADwAfAC8APwBPAF8AbwB/AI8AnwAAEyEyFhURFAYjISImNRE0NgUhIgYVERQWMyEyNjURNCYFMzIWHQEUBisBIiY9ATQ2MyEyFh0BFAYjISImPQE0NgczMhYdARQGKwEiJj0BNDYzITIWHQEUBiMhIiY9ATQ2BzMyFh0BFAYrASImPQE0NjMhMhYdARQGIyEiJj0BNDYHMzIWHQEUBisBIiY9ATQ2MyEyFh0BFAYjISImPQE0Nn0EGgoPDwr75goPDwPA/K4KDw8KA1IKDw/9CDIKDw8KMgoPD9IBwgoPDwr+PgoPD74yCg8PCjIKDw/SAcIKDw8K/j4KDw++MgoPDwoyCg8P0gHCCg8PCv4+Cg8PvjIKDw8KMgoPD9IBwgoPDwr+PgoPDwSwDwr7ggoPDwoEfgoPyA8K/K4KDw8KA1IKD2QPCjIKDw8KMgoPDwoyCg8PCjIKD8gPCjIKDw8KMgoPDwoyCg8PCjIKD8gPCjIKDw8KMgoPDwoyCg8PCjIKD8gPCjIKDw8KMgoPDwoyCg8PCjIKDwAAAAACAAAAAARMBLAAGQAjAAABNTQmIyEiBh0BIyIGFREUFjMhMjY1ETQmIyE1NDY7ATIWHQEDhHVT/tRSdmQpOzspA4QpOzsp/ageFMgUHgMgyFN1dlLIOyn9qCk7OykCWCk7lhUdHRWWAAIAZAAABEwETAAJADcAABMzMhYVESMRNDYFMhcWFREUBw4DIyIuAScuAiMiBwYjIicmNRE+ATc2HgMXHgIzMjc2fTIKD2QPA8AEBRADIUNAMRwaPyonKSxHHlVLBwgGBQ4WeDsXKC4TOQQpLUUdZ1AHBEwPCvvNBDMKDzACBhH+WwYGO1AkDQ0ODg8PDzkFAwcPAbY3VwMCAwsGFAEODg5XCAAAAwAAAAAEsASXACEAMQBBAAAAMh4CFREUBisBIiY1ETQuASAOARURFAYrASImNRE0PgEDMzIWFREUBisBIiY1ETQ2ITMyFhURFAYrASImNRE0NgHk6N6jYw8KMgoPjeT++uSNDwoyCg9joyqgCAwMCKAIDAwCYKAIDAwIoAgMDASXY6PedP7UCg8PCgEsf9FyctF//tQKDw8KASx03qP9wAwI/jQIDAwIAcwIDAwI/jQIDAwIAcwIDAAAAAACAAAA0wRHA90AFQA5AAABJTYWFREUBiclJisBIiY1ETQ2OwEyBTc2Mh8BFhQPARcWFA8BBiIvAQcGIi8BJjQ/AScmND8BNjIXAUEBAgkMDAn+/hUZ+goPDwr6GQJYeAcUByIHB3h4BwciBxQHeHgHFAciBwd3dwcHIgcUBwMurAYHCv0SCgcGrA4PCgFeCg+EeAcHIgcUB3h4BxQHIgcHd3cHByIHFAd4eAcUByIICAAAAAACAAAA0wNyA90AFQAvAAABJTYWFREUBiclJisBIiY1ETQ2OwEyJTMWFxYVFAcGDwEiLwEuATc2NTQnJjY/ATYBQQECCQwMCf7+FRn6Cg8PCvoZAdIECgZgWgYLAwkHHQcDBkhOBgMIHQcDLqwGBwr9EgoHBqwODwoBXgoPZAEJgaGafwkBAQYXBxMIZ36EaggUBxYFAAAAAAMAAADEBGID7AAbADEASwAAATMWFxYVFAYHBgcjIi8BLgE3NjU0JicmNj8BNgUlNhYVERQGJyUmKwEiJjURNDY7ATIlMxYXFhUUBwYPASIvAS4BNzY1NCcmNj8BNgPHAwsGh0RABwoDCQcqCAIGbzs3BgIJKgf9ggECCQwMCf7+FRn6Cg8PCvoZAdIECgZgWgYLAwkHHQcDBkhOBgMIHQcD7AEJs9lpy1QJAQYiBhQIlrJarEcJFAYhBb6sBgcK/RIKBwasDg8KAV4KD2QBCYGhmn8JAQEGFwcTCGd+hGoIFQYWBQAAAAANAAAAAASwBLAACQAVABkAHQAhACUALQA7AD8AQwBHAEsATwAAATMVIxUhFSMRIQEjFTMVIREjESM1IQURIREhESERBSM1MwUjNTMBMxEhETM1MwEzFSMVIzUjNTM1IzUhBREhEQcjNTMFIzUzASM1MwUhNSEB9GRk/nBkAfQCvMjI/tTIZAJY+7QBLAGQASz84GRkArxkZP1EyP4MyGQB9MhkyGRkyAEs/UQBLGRkZAOEZGT+DGRkAfT+1AEsA4RkZGQCWP4MZMgBLAEsyGT+1AEs/tQBLMhkZGT+DP4MAfRk/tRkZGRkyGTI/tQBLMhkZGT+1GRkZAAAAAAJAAAAAASwBLAAAwAHAAsADwATABcAGwAfACMAADcjETMTIxEzASMRMxMjETMBIxEzASE1IRcjNTMXIzUzBSM1M2RkZMhkZAGQyMjIZGQBLMjI/OD+1AEsyGRkyGRkASzIyMgD6PwYA+j8GAPo/BgD6PwYA+j7UGRkW1tbW1sAAAIAAAAKBKYEsAANABUAAAkBFhQHAQYiJwETNDYzBCYiBhQWMjYB9AKqCAj+MAgUCP1WAQ8KAUM7Uzs7UzsEsP1WCBQI/jAICAKqAdsKD807O1Q7OwAAAAADAAAACgXSBLAADQAZACEAAAkBFhQHAQYiJwETNDYzIQEWFAcBBiIvAQkBBCYiBhQWMjYB9AKqCAj+MAgUCP1WAQ8KAwYCqggI/jAIFAg4Aaj9RP7TO1M7O1M7BLD9VggUCP4wCAgCqgHbCg/9VggUCP4wCAg4AaoCvM07O1Q7OwAAAAABAGQAAASwBLAAJgAAASEyFREUDwEGJjURNCYjISIPAQYWMyEyFhURFAYjISImNRE0PwE2ASwDOUsSQAgKDwr9RBkSQAgFCgK8Cg8PCvyuCg8SixIEsEv8fBkSQAgFCgO2Cg8SQAgKDwr8SgoPDwoDzxkSixIAAAABAMj//wRMBLAACgAAEyEyFhURCQERNDb6AyAVHf4+/j4dBLAdFfuCAbz+QwR/FR0AAAAAAwAAAAAEsASwABUARQBVAAABISIGBwMGHwEeATMhMjY/ATYnAy4BASMiBg8BDgEjISImLwEuASsBIgYVERQWOwEyNj0BNDYzITIWHQEUFjsBMjY1ETQmASEiBg8BBhYzITI2LwEuAQM2/kQLEAFOBw45BhcKAcIKFwY+DgdTARABVpYKFgROBBYK/doKFgROBBYKlgoPDwqWCg8PCgLuCg8PCpYKDw/+sf4MChMCJgILCgJYCgsCJgITBLAPCv7TGBVsCQwMCWwVGAEtCg/+cA0JnAkNDQmcCQ0PCv12Cg8PCpYKDw8KlgoPDwoCigoP/agOCpgKDg4KmAoOAAAAAAQAAABkBLAETAAdACEAKQAxAAABMzIeAh8BMzIWFREUBiMhIiY1ETQ2OwE+BAEVMzUEIgYUFjI2NCQyFhQGIiY0AfTIOF00JAcGlik7Oyn8GCk7OymWAgknM10ByGT+z76Hh76H/u9WPDxWPARMKTs7FRQ7Kf2oKTs7KQJYKTsIG0U1K/7UZGRGh76Hh74IPFY8PFYAAAAAAgA1AAAEsASvACAAIwAACQEWFx4BHwEVITUyNi8BIQYHBh4CMxUhNTY3PgE/AQEDIQMCqQGBFCgSJQkK/l81LBFS/nk6IgsJKjIe/pM4HAwaBwcBj6wBVKIEr/waMioTFQECQkJXLd6RWSIuHAxCQhgcDCUNDQPu/VoByQAAAAADAGQAAAPwBLAAJwAyADsAAAEeBhUUDgMjITU+ATURNC4EJzUFMh4CFRQOAgclMzI2NTQuAisBETMyNjU0JisBAvEFEzUwOyodN1htbDD+DCk7AQYLFyEaAdc5dWM+Hy0tEP6Pi05pESpTPnbYUFJ9Xp8CgQEHGB0zOlIuQ3VONxpZBzMoAzsYFBwLEAkHRwEpSXNDM1s6KwkxYUopOzQb/K5lUFqBAAABAMgAAANvBLAAGQAAARcOAQcDBhYXFSE1NjcTNjQuBCcmJzUDbQJTQgeECSxK/gy6Dq0DAw8MHxUXDQYEsDkTNSj8uTEoBmFhEFIDQBEaExAJCwYHAwI5AAAAAAL/tQAABRQEsAAlAC8AAAEjNC4FKwERFBYfARUhNTI+AzURIyIOBRUjESEFIxEzByczESM3BRQyCAsZEyYYGcgyGRn+cAQOIhoWyBkYJhMZCwgyA+j7m0tLfX1LS30DhBUgFQ4IAwH8rhYZAQJkZAEFCRUOA1IBAwgOFSAVASzI/OCnpwMgpwACACH/tQSPBLAAJQAvAAABIzQuBSsBERQWHwEVITUyPgM1ESMiDgUVIxEhEwc1IRUnNxUhNQRMMggLGRMmGBnIMhkZ/nAEDiIaFsgZGCYTGQsIMgPoQ6f84KenAyADhBUgFQ4IAwH9dhYZAQJkZAEFCRUOAooBAwgOFSAVASz7gn1LS319S0sABAAAAAAEsARMAA8AHwAvAD8AABMhMhYdARQGIyEiJj0BNDYTITIWHQEUBiMhIiY9ATQ2EyEyFh0BFAYjISImPQE0NhMhMhYdARQGIyEiJj0BNDYyAlgVHR0V/agVHR0VA+gVHR0V/BgVHR0VAyAVHR0V/OAVHR0VBEwVHR0V+7QVHR0ETB0VZBUdHRVkFR3+1B0VZBUdHRVkFR3+1B0VZBUdHRVkFR3+1B0VZBUdHRVkFR0ABAAAAAAEsARMAA8AHwAvAD8AABMhMhYdARQGIyEiJj0BNDYDITIWHQEUBiMhIiY9ATQ2EyEyFh0BFAYjISImPQE0NgMhMhYdARQGIyEiJj0BNDb6ArwVHR0V/UQVHR2zBEwVHR0V+7QVHR3dArwVHR0V/UQVHR2zBEwVHR0V+7QVHR0ETB0VZBUdHRVkFR3+1B0VZBUdHRVkFR3+1B0VZBUdHRVkFR3+1B0VZBUdHRVkFR0ABAAAAAAEsARMAA8AHwAvAD8AAAE1NDYzITIWHQEUBiMhIiYBNTQ2MyEyFh0BFAYjISImEzU0NjMhMhYdARQGIyEiJgE1NDYzITIWHQEUBiMhIiYB9B0VAlgVHR0V/agVHf5wHRUD6BUdHRX8GBUdyB0VAyAVHR0V/OAVHf7UHRUETBUdHRX7tBUdA7ZkFR0dFWQVHR3+6WQVHR0VZBUdHf7pZBUdHRVkFR0d/ulkFR0dFWQVHR0AAAQAAAAABLAETAAPAB8ALwA/AAATITIWHQEUBiMhIiY9ATQ2EyEyFh0BFAYjISImPQE0NhMhMhYdARQGIyEiJj0BNDYTITIWHQEUBiMhIiY9ATQ2MgRMFR0dFfu0FR0dFQRMFR0dFfu0FR0dFQRMFR0dFfu0FR0dFQRMFR0dFfu0FR0dBEwdFWQVHR0VZBUd/tQdFWQVHR0VZBUd/tQdFWQVHR0VZBUd/tQdFWQVHR0VZBUdAAgAAAAABLAETAAPAB8ALwA/AE8AXwBvAH8AABMzMhYdARQGKwEiJj0BNDYpATIWHQEUBiMhIiY9ATQ2ATMyFh0BFAYrASImPQE0NikBMhYdARQGIyEiJj0BNDYBMzIWHQEUBisBIiY9ATQ2KQEyFh0BFAYjISImPQE0NgEzMhYdARQGKwEiJj0BNDYpATIWHQEUBiMhIiY9ATQ2MmQVHR0VZBUdHQFBAyAVHR0V/OAVHR3+6WQVHR0VZBUdHQFBAyAVHR0V/OAVHR3+6WQVHR0VZBUdHQFBAyAVHR0V/OAVHR3+6WQVHR0VZBUdHQFBAyAVHR0V/OAVHR0ETB0VZBUdHRVkFR0dFWQVHR0VZBUd/tQdFWQVHR0VZBUdHRVkFR0dFWQVHf7UHRVkFR0dFWQVHR0VZBUdHRVkFR3+1B0VZBUdHRVkFR0dFWQVHR0VZBUdAAAG/5wAAASwBEwAAwATACMAKgA6AEoAACEjETsCMhYdARQGKwEiJj0BNDYTITIWHQEUBiMhIiY9ATQ2BQc1IzUzNQUhMhYdARQGIyEiJj0BNDYTITIWHQEUBiMhIiY9ATQ2AZBkZJZkFR0dFWQVHR0VAfQVHR0V/gwVHR3++qfIyAHCASwVHR0V/tQVHR0VAlgVHR0V/agVHR0ETB0VZBUdHRVkFR3+1B0VZBUdHRVkFR36fUtkS68dFWQVHR0VZBUd/tQdFWQVHR0VZBUdAAAABgAAAAAFFARMAA8AEwAjACoAOgBKAAATMzIWHQEUBisBIiY9ATQ2ASMRMwEhMhYdARQGIyEiJj0BNDYFMxUjFSc3BSEyFh0BFAYjISImPQE0NhMhMhYdARQGIyEiJj0BNDYyZBUdHRVkFR0dA2dkZPyuAfQVHR0V/gwVHR0EL8jIp6f75gEsFR0dFf7UFR0dFQJYFR0dFf2oFR0dBEwdFWQVHR0VZBUd+7QETP7UHRVkFR0dFWQVHchkS319rx0VZBUdHRVkFR3+1B0VZBUdHRVkFR0AAAAAAgAAAMgEsAPoAA8AEgAAEyEyFhURFAYjISImNRE0NgkCSwLuHywsH/0SHywsBIT+1AEsA+gsH/12HywsHwKKHyz9RAEsASwAAwAAAAAEsARMAA8AFwAfAAATITIWFREUBiMhIiY1ETQ2FxE3BScBExEEMhYUBiImNCwEWBIaGhL7qBIaGkr3ASpKASXs/NJwTk5wTgRMGhL8DBIaGhID9BIaZP0ftoOcAT7+4AH0dE5vT09vAAAAAAIA2wAFBDYEkQAWAB4AAAEyHgEVFAcOAQ8BLgQnJjU0PgIWIgYUFjI2NAKIdcZzRkWyNjYJIV5YbSk8RHOft7eCgreCBJF4ynVzj23pPz4IIWZomEiEdVijeUjDgriBgbgAAAACABcAFwSZBJkADwAXAAAAMh4CFA4CIi4CND4BAREiDgEUHgEB4+rWm1tbm9bq1ptbW5sBS3TFcnLFBJlbm9bq1ptbW5vW6tab/G8DVnLF6MVyAAACAHUAAwPfBQ8AGgA1AAABHgYVFA4DBy4DNTQ+BQMOAhceBBcWNj8BNiYnLgInJjc2IyYCKhVJT1dOPiUzVnB9P1SbfEokP0xXUEm8FykoAwEbITEcExUWAgYCCQkFEikMGiACCAgFD0iPdXdzdYdFR4BeRiYEBTpjl1lFh3ZzeHaQ/f4hS4I6JUEnIw4IBwwQIgoYBwQQQSlZtgsBAAAAAwAAAAAEywRsAAwAKgAvAAABNz4CHgEXHgEPAiUhMhcHISIGFREUFjMhMjY9ATcRFAYjISImNRE0NgkBBzcBA+hsAgYUFR0OFgoFBmz9BQGQMje7/pApOzspAfQpO8i7o/5wpbm5Azj+lqE3AWMD9XMBAgIEDw4WKgsKc8gNuzsp/gwpOzsptsj+tKW5uaUBkKW5/tf+ljKqAWMAAgAAAAAEkwRMABsANgAAASEGByMiBhURFBYzITI2NTcVFAYjISImNRE0NgUBFhQHAQYmJzUmDgMHPgY3NT4BAV4BaaQ0wyk7OykB9Ck7yLml/nClubkCfwFTCAj+rAcLARo5ZFRYGgouOUlARioTAQsETJI2Oyn+DCk7OymZZ6W5uaUBkKW5G/7TBxUH/s4GBAnLAQINFjAhO2JBNB0UBwHSCgUAAAAAAgAAAAAEnQRMAB0ANQAAASEyFwchIgYVERQWMyEyNj0BNxUUBiMhIiY1ETQ2CQE2Mh8BFhQHAQYiLwEmND8BNjIfARYyAV4BXjxDsv6jKTs7KQH0KTvIuaX+cKW5uQHKAYsHFQdlBwf97QcVB/gHB2UHFQdvCBQETBexOyn+DCk7OylFyNulubmlAZCluf4zAYsHB2UHFQf97AcH+AcVB2UHB28HAAAAAQAKAAoEpgSmADsAAAkBNjIXARYGKwEVMzU0NhcBFhQHAQYmPQEjFTMyFgcBBiInASY2OwE1IxUUBicBJjQ3ATYWHQEzNSMiJgE+AQgIFAgBBAcFCqrICggBCAgI/vgICsiqCgUH/vwIFAj++AgFCq/ICgj++AgIAQgICsivCgUDlgEICAj++AgKyK0KBAf+/AcVB/73BwQKrcgKCP74CAgBCAgKyK0KBAcBCQcVBwEEBwQKrcgKAAEAyAAAA4QETAAZAAATMzIWFREBNhYVERQGJwERFAYrASImNRE0NvpkFR0B0A8VFQ/+MB0VZBUdHQRMHRX+SgHFDggV/BgVCA4Bxf5KFR0dFQPoFR0AAAABAAAAAASwBEwAIwAAEzMyFhURATYWFREBNhYVERQGJwERFAYnAREUBisBIiY1ETQ2MmQVHQHQDxUB0A8VFQ/+MBUP/jAdFWQVHR0ETB0V/koBxQ4IFf5KAcUOCBX8GBUIDgHF/koVCA4Bxf5KFR0dFQPoFR0AAAABAJ0AGQSwBDMAFQAAAREUBicBERQGJwEmNDcBNhYVEQE2FgSwFQ/+MBUP/hQPDwHsDxUB0A8VBBr8GBUIDgHF/koVCA4B4A4qDgHgDggV/koBxQ4IAAAAAQDIABYEMwQ2AAsAABMBFhQHAQYmNRE0NvMDLhIS/NISGRkEMv4OCx4L/g4LDhUD6BUOAAIAyABkA4QD6AAPAB8AABMzMhYVERQGKwEiJjURNDYhMzIWFREUBisBIiY1ETQ2+sgVHR0VyBUdHQGlyBUdHRXIFR0dA+gdFfzgFR0dFQMgFR0dFfzgFR0dFQMgFR0AAAEAyABkBEwD6AAPAAABERQGIyEiJjURNDYzITIWBEwdFfzgFR0dFQMgFR0DtvzgFR0dFQMgFR0dAAAAAAEAAAAZBBMEMwAVAAABETQ2FwEWFAcBBiY1EQEGJjURNDYXAfQVDwHsDw/+FA8V/jAPFRUPAmQBthUIDv4gDioO/iAOCBUBtv47DggVA+gVCA4AAAH//gACBLMETwAjAAABNzIWFRMUBiMHIiY1AwEGJjUDAQYmNQM0NhcBAzQ2FwEDNDYEGGQUHgUdFWQVHQL+MQ4VAv4yDxUFFQ8B0gIVDwHSAh0ETgEdFfwYFR0BHRUBtf46DwkVAbX+OQ4JFAPoFQkP/j4BthQJDv49AbYVHQAAAQEsAAAD6ARMABkAAAEzMhYVERQGKwEiJjURAQYmNRE0NhcBETQ2A1JkFR0dFWQVHf4wDxUVDwHQHQRMHRX8GBUdHRUBtv47DggVA+gVCA7+OwG2FR0AAAIAZADIBLAESAALABsAAAkBFgYjISImNwE2MgEhMhYdARQGIyEiJj0BNDYCrgH1DwkW++4WCQ8B9Q8q/fcD6BUdHRX8GBUdHQQ5/eQPFhYPAhwP/UgdFWQVHR0VZBUdAAEAiP/8A3UESgAFAAAJAgcJAQN1/qABYMX92AIoA4T+n/6fxgIoAiYAAAAAAQE7//wEKARKAAUAAAkBJwkBNwQo/dnGAWH+n8YCI/3ZxgFhAWHGAAIAFwAXBJkEmQAPADMAAAAyHgIUDgIiLgI0PgEFIyIGHQEjIgYdARQWOwEVFBY7ATI2PQEzMjY9ATQmKwE1NCYB4+rWm1tbm9bq1ptbW5sBfWQVHZYVHR0Vlh0VZBUdlhUdHRWWHQSZW5vW6tabW1ub1urWm7odFZYdFWQVHZYVHR0Vlh0VZBUdlhUdAAAAAAIAFwAXBJkEmQAPAB8AAAAyHgIUDgIiLgI0PgEBISIGHQEUFjMhMjY9ATQmAePq1ptbW5vW6tabW1ubAkX+DBUdHRUB9BUdHQSZW5vW6tabW1ub1urWm/5+HRVkFR0dFWQVHQACABcAFwSZBJkADwAzAAAAMh4CFA4CIi4CND4BBCIPAScmIg8BBhQfAQcGFB8BFjI/ARcWMj8BNjQvATc2NC8BAePq1ptbW5vW6tabW1ubAeUZCXh4CRkJjQkJeHgJCY0JGQl4eAkZCY0JCXh4CQmNBJlbm9bq1ptbW5vW6tabrQl4eAkJjQkZCXh4CRkJjQkJeHgJCY0JGQl4eAkZCY0AAgAXABcEmQSZAA8AJAAAADIeAhQOAiIuAjQ+AQEnJiIPAQYUHwEWMjcBNjQvASYiBwHj6tabW1ub1urWm1tbmwEVVAcVCIsHB/IHFQcBdwcHiwcVBwSZW5vW6tabW1ub1urWm/4xVQcHiwgUCPEICAF3BxUIiwcHAAAAAAMAFwAXBJkEmQAPADsASwAAADIeAhQOAiIuAjQ+AQUiDgMVFDsBFjc+ATMyFhUUBgciDgUHBhY7ATI+AzU0LgMTIyIGHQEUFjsBMjY9ATQmAePq1ptbW5vW6tabW1ubAT8dPEIyIRSDHgUGHR8UFw4TARkOGhITDAIBDQ6tBx4oIxgiM0Q8OpYKDw8KlgoPDwSZW5vW6tabW1ub1urWm5ELHi9PMhkFEBQQFRIXFgcIBw4UHCoZCBEQKDhcNi9IKhsJ/eMPCpYKDw8KlgoPAAADABcAFwSZBJkADwAfAD4AAAAyHgIUDgIiLgI0PgEFIyIGHQEUFjsBMjY9ATQmAyMiBh0BFBY7ARUjIgYdARQWMyEyNj0BNCYrARE0JgHj6tabW1ub1urWm1tbmwGWlgoPDwqWCg8PCvoKDw8KS0sKDw8KAV4KDw8KSw8EmVub1urWm1tbm9bq1ptWDwqWCg8PCpYKD/7UDwoyCg/IDwoyCg8PCjIKDwETCg8AAgAAAAAEsASwAC8AXwAAATMyFh0BHgEXMzIWHQEUBisBDgEHFRQGKwEiJj0BLgEnIyImPQE0NjsBPgE3NTQ2ExUUBisBIiY9AQ4BBzMyFh0BFAYrAR4BFzU0NjsBMhYdAT4BNyMiJj0BNDY7AS4BAg2WCg9nlxvCCg8PCsIbl2cPCpYKD2eXG8IKDw8KwhuXZw+5DwqWCg9EZheoCg8PCqgXZkQPCpYKD0RmF6gKDw8KqBdmBLAPCsIbl2cPCpYKD2eXG8IKDw8KwhuXZw8KlgoPZ5cbwgoP/s2oCg8PCqgXZkQPCpYKD0RmF6gKDw8KqBdmRA8KlgoPRGYAAwAXABcEmQSZAA8AGwA/AAAAMh4CFA4CIi4CND4BBCIOARQeATI+ATQmBxcWFA8BFxYUDwEGIi8BBwYiLwEmND8BJyY0PwE2Mh8BNzYyAePq1ptbW5vW6tabW1ubAb/oxXJyxejFcnKaQAcHfHwHB0AHFQd8fAcVB0AHB3x8BwdABxUHfHwHFQSZW5vW6tabW1ub1urWmztyxejFcnLF6MVaQAcVB3x8BxUHQAcHfHwHB0AHFQd8fAcVB0AHB3x8BwAAAAMAFwAXBJkEmQAPABsAMAAAADIeAhQOAiIuAjQ+AQQiDgEUHgEyPgE0JgcXFhQHAQYiLwEmND8BNjIfATc2MgHj6tabW1ub1urWm1tbmwG/6MVycsXoxXJyg2oHB/7ACBQIyggIagcVB0/FBxUEmVub1urWm1tbm9bq1ps7csXoxXJyxejFfWoHFQf+vwcHywcVB2oICE/FBwAAAAMAFwAXBJkEmQAPABgAIQAAADIeAhQOAiIuAjQ+AQUiDgEVFBcBJhcBFjMyPgE1NAHj6tabW1ub1urWm1tbmwFLdMVyQQJLafX9uGhzdMVyBJlbm9bq1ptbW5vW6tabO3LFdHhpAktB0P24PnLFdHMAAAAAAQAXAFMEsAP5ABUAABMBNhYVESEyFh0BFAYjIREUBicBJjQnAgoQFwImFR0dFf3aFxD99hACRgGrDQoV/t0dFcgVHf7dFQoNAasNJgAAAAABAAAAUwSZA/kAFQAACQEWFAcBBiY1ESEiJj0BNDYzIRE0NgJ/AgoQEP32EBf92hUdHRUCJhcD8f5VDSYN/lUNChUBIx0VyBUdASMVCgAAAAEAtwAABF0EmQAVAAAJARYGIyERFAYrASImNREhIiY3ATYyAqoBqw0KFf7dHRXIFR3+3RUKDQGrDSYEif32EBf92hUdHRUCJhcQAgoQAAAAAQC3ABcEXQSwABUAAAEzMhYVESEyFgcBBiInASY2MyERNDYCJsgVHQEjFQoN/lUNJg3+VQ0KFQEjHQSwHRX92hcQ/fYQEAIKEBcCJhUdAAABAAAAtwSZBF0AFwAACQEWFAcBBiY1EQ4DBz4ENxE0NgJ/AgoQEP32EBdesKWBJAUsW4fHfhcEVf5VDSYN/lUNChUBIwIkRHVNabGdcUYHAQYVCgACAAAAAASwBLAAFQArAAABITIWFREUBi8BBwYiLwEmND8BJyY2ASEiJjURNDYfATc2Mh8BFhQPARcWBgNSASwVHRUOXvkIFAhqBwf5Xg4I/iH+1BUdFQ5e+QgUCGoHB/leDggEsB0V/tQVCA5e+QcHaggUCPleDhX7UB0VASwVCA5e+QcHaggUCPleDhUAAAACAEkASQRnBGcAFQArAAABFxYUDwEXFgYjISImNRE0Nh8BNzYyASEyFhURFAYvAQcGIi8BJjQ/AScmNgP2agcH+V4OCBX+1BUdFQ5e+QgU/QwBLBUdFQ5e+QgUCGoHB/leDggEYGoIFAj5Xg4VHRUBLBUIDl75B/3xHRX+1BUIDl75BwdqCBQI+V4OFQAAAAADABcAFwSZBJkADwAfAC8AAAAyHgIUDgIiLgI0PgEFIyIGFxMeATsBMjY3EzYmAyMiBh0BFBY7ATI2PQE0JgHj6tabW1ub1urWm1tbmwGz0BQYBDoEIxQ2FCMEOgQYMZYKDw8KlgoPDwSZW5vW6tabW1ub1urWm7odFP7SFB0dFAEuFB3+DA8KlgoPDwqWCg8AAAAABQAAAAAEsASwAEkAVQBhAGgAbwAAATIWHwEWHwEWFxY3Nj8BNjc2MzIWHwEWHwIeATsBMhYdARQGKwEiBh0BIREjESE1NCYrASImPQE0NjsBMjY1ND8BNjc+BAUHBhY7ATI2LwEuAQUnJgYPAQYWOwEyNhMhIiY1ESkBERQGIyERAQQJFAUFFhbEFQ8dCAsmxBYXERUXMA0NDgQZCAEPCj0KDw8KMgoP/nDI/nAPCjIKDw8KPQsOCRkFDgIGFRYfAp2mBwQK2woKAzMDEP41sQgQAzMDCgrnCwMe/okKDwGQAlgPCv6JBLAEAgIKDXYNCxUJDRZ2DQoHIREQFRh7LAkLDwoyCg8PCq8BLP7UrwoPDwoyCg8GBQQwgBkUAwgWEQ55ogcKDgqVCgSqnQcECo8KDgr8cg8KAXf+iQoPAZAAAAAAAgAAAAwErwSmACsASQAAATYWFQYCDgQuAScmByYOAQ8BBiY1NDc+ATc+AScuAT4BNz4GFyYGBw4BDwEOBAcOARY2Nz4CNz4DNz4BBI0IGgItQmxhi2KORDg9EQQRMxuZGhYqCFUYEyADCQIQOjEnUmFch3vAJQgdHyaiPT44XHRZUhcYDhItIRmKcVtGYWtbKRYEBKYDEwiy/t3IlVgxEQgLCwwBAQIbG5kYEyJAJghKFRE8Hzdff4U/M0o1JSMbL0QJGCYvcSEhHjZST2c1ODwEJygeW0AxJUBff1UyFAABAF0AHgRyBM8ATwAAAQ4BHgQXLgc+ATceAwYHDgQHBicmNzY3PgQuAScWDgMmJy4BJyY+BDcGHgM3PgEuAicmPgMCjScfCic4R0IgBBsKGAoQAwEJEg5gikggBhANPkpTPhZINx8SBgsNJysiCRZOQQoVNU1bYC9QZwICBAUWITsoCAYdJzIYHw8YIiYHDyJJYlkEz0OAZVxEOSQMBzgXOB42IzElKRIqg5Gnl0o3Z0c6IAYWCwYNAwQFIDhHXGF1OWiqb0sdBxUknF0XNTQ8PEUiNWNROBYJDS5AQVUhVZloUSkAAAAAA//cAGoE1ARGABsAPwBRAAAAMh4FFA4FIi4FND4EBSYGFxYVFAYiJjU0NzYmBwYHDgEXHgQyPgM3NiYnJgUHDgEXFhcWNj8BNiYnJicuAQIGpJ17bk85HBw6T257naKde25POhwcOU9uewIPDwYIGbD4sBcIBw5GWg0ECxYyWl+DiINfWjIWCwQMWv3/Iw8JCSU4EC0OIw4DDywtCyIERi1JXGJcSSpJXGJcSS0tSVxiXEkqSVxiXEncDwYTOT58sLB8OzcTBg9FcxAxEiRGXkQxMEVeRSQSMRF1HiQPLxJEMA0EDyIPJQ8sSRIEAAAABP/cAAAE1ASwABQAJwA7AEwAACEjNy4ENTQ+BTMyFzczEzceARUUDgMHNz4BNzYmJyYlBgcOARceBBc3LgE1NDc2JhcHDgEXFhcWNj8CJyYnLgECUJQfW6l2WSwcOU9ue51SPUEglCYvbIknUGqYUi5NdiYLBAw2/VFGWg0ECxIqSExoNSlrjxcIB3wjDwkJJTgQLQ4MFgMsLQsieBRhdHpiGxVJXGJcSS0Pef5StVXWNBpacm5jGq0xiD8SMRFGckVzEDESHjxRQTkNmhKnbjs3EwZwJA8vEkQwDQQPC1YELEkSBAAAAAP/ngAABRIEqwALABgAKAAAJwE2FhcBFgYjISImJSE1NDY7ATIWHQEhAQczMhYPAQ4BKwEiJi8BJjZaAoIUOBQCghUbJfryJRsBCgFZDwqWCg8BWf5DaNAUGAQ6BCMUNhQjBDoEGGQEKh8FIfvgIEdEhEsKDw8KSwLT3x0U/BQdHRT8FB0AAAABAGQAFQSwBLAAKAAAADIWFREBHgEdARQGJyURFh0BFAYvAQcGJj0BNDcRBQYmPQE0NjcBETQCTHxYAWsPFhgR/plkGhPNzRMaZP6ZERgWDwFrBLBYPv6t/rsOMRQpFA0M+f75XRRAFRAJgIAJEBVAFF0BB/kMDRQpFDEOAUUBUz4AAAARAAAAAARMBLAAHQAnACsALwAzADcAOwA/AEMARwBLAE8AUwBXAFsAXwBjAAABMzIWHQEzMhYdASE1NDY7ATU0NjsBMhYdASE1NDYBERQGIyEiJjURFxUzNTMVMzUzFTM1MxUzNTMVMzUFFTM1MxUzNTMVMzUzFTM1MxUzNQUVMzUzFTM1MxUzNTMVMzUzFTM1A1JkFR0yFR37tB0VMh0VZBUdAfQdAQ8dFfwYFR1kZGRkZGRkZGRk/HxkZGRkZGRkZGT8fGRkZGRkZGRkZASwHRUyHRWWlhUdMhUdHRUyMhUd/nD9EhUdHRUC7shkZGRkZGRkZGRkyGRkZGRkZGRkZGTIZGRkZGRkZGRkZAAAAAMAAAAZBXcElwAZACUANwAAARcWFA8BBiY9ASMBISImPQE0NjsBATM1NDYBBycjIiY9ATQ2MyEBFxYUDwEGJj0BIyc3FzM1NDYEb/kPD/kOFZ/9qP7dFR0dFdECWPEV/amNetEVHR0VASMDGvkPD/kOFfG1jXqfFQSN5g4qDuYOCBWW/agdFWQVHQJYlhUI/piNeh0VZBUd/k3mDioO5g4IFZa1jXqWFQgAAAABAAAAAASwBEwAEgAAEyEyFhURFAYjIQERIyImNRE0NmQD6Ck7Oyn9rP7QZCk7OwRMOyn9qCk7/tQBLDspAlgpOwAAAAMAZAAABEwEsAAJABMAPwAAEzMyFh0BITU0NiEzMhYdASE1NDYBERQOBSIuBTURIRUUFRwBHgYyPgYmNTQ9AZbIFR3+1B0C0cgVHf7UHQEPBhgoTGacwJxmTCgYBgEsAwcNFB8nNkI2Jx8TDwUFAQSwHRX6+hUdHRX6+hUd/nD+1ClJalZcPigoPlxWakkpASz6CRIVKyclIRsWEAgJEBccISUnKhURCPoAAAAB//8A1ARMA8IABQAAAQcJAScBBEzG/p/+n8UCJwGbxwFh/p/HAicAAQAAAO4ETQPcAAUAAAkCNwkBBE392v3ZxgFhAWEDFf3ZAifH/p8BYQAAAAAC/1EAZAVfA+gAFAApAAABITIWFREzMhYPAQYiLwEmNjsBESElFxYGKwERIRchIiY1ESMiJj8BNjIBlALqFR2WFQgO5g4qDuYOCBWW/oP+HOYOCBWWAYHX/RIVHZYVCA7mDioD6B0V/dkVDvkPD/kOFQGRuPkOFf5wyB0VAiYVDvkPAAABAAYAAASeBLAAMAAAEzMyFh8BITIWBwMOASMhFyEyFhQGKwEVFAYiJj0BIRUUBiImPQEjIiYvAQMjIiY0NjheERwEJgOAGB4FZAUsIf2HMAIXFR0dFTIdKh3+1B0qHR8SHQYFyTYUHh4EsBYQoiUY/iUVK8gdKh0yFR0dFTIyFR0dFTIUCQoDwR0qHQAAAAACAAAAAASwBEwACwAPAAABFSE1MzQ2MyEyFhUFIREhBLD7UMg7KQEsKTv9RASw+1AD6GRkKTs7Kcj84AACAAAAAAXcBEwADAAQAAATAxEzNDYzITIWFSEVBQEhAcjIyDspASwqOgH0ASz+1PtQASwDIP5wAlgpOzspyGT9RAK8AAEBRQAAA2sErwAbAAABFxYGKwERMzIWDwEGIi8BJjY7AREjIiY/ATYyAnvmDggVlpYVCA7mDioO5g4IFZaWFQgO5g4qBKD5DhX9pxUO+Q8P+Q4VAlkVDvkPAAAAAQABAUQErwNrABsAAAEXFhQPAQYmPQEhFRQGLwEmND8BNhYdASE1NDYDqPkODvkPFf2oFQ/5Dg75DxUCWBUDYOUPKQ/lDwkUl5cUCQ/lDykP5Q8JFZWVFQkAAAAEAAAAAASwBLAACQAZAB0AIQAAAQMuASMhIgYHAwUhIgYdARQWMyEyNj0BNCYFNTMVMzUzFQSRrAUkFP1gFCQFrAQt/BgpOzspA+gpOzv+q2RkZAGQAtwXLSgV/R1kOylkKTs7KWQpO8hkZGRkAAAAA/+cAGQEsARMAAsAIwAxAAAAMhYVERQGIiY1ETQDJSMTFgYjIisBIiYnAj0BNDU0PgE7ASUBFSIuAz0BND4CNwRpKh0dKh1k/V0mLwMRFQUCVBQdBDcCCwzIAqP8GAQOIhoWFR0dCwRMHRX8rhUdHRUDUhX8mcj+7BAIHBUBUQ76AgQQDw36/tT6AQsTKRwyGigUDAEAAAACAEoAAARmBLAALAA1AAABMzIWDwEeARcTFzMyFhQGBw4EIyIuBC8BLgE0NjsBNxM+ATcnJjYDFjMyNw4BIiYCKV4UEgYSU3oPP3YRExwaEggeZGqfTzl0XFU+LwwLEhocExF2Pw96UxIGEyQyNDUxDDdGOASwFRMlE39N/rmtHSkoBwQLHBYSCg4REg4FBAgoKR2tAUdNfhQgExr7vgYGMT09AAEAFAAUBJwEnAAXAAABNwcXBxcHFycHJwcnBzcnNyc3Jxc3FzcDIOBO6rS06k7gLZubLeBO6rS06k7gLZubA7JO4C2bmy3gTuq0tOpO4C2bmy3gTuq0tAADAAAAZASwBLAAIQAtAD0AAAEzMhYdAQchMhYdARQHAw4BKwEiJi8BIyImNRE0PwI+ARcPAREzFzMTNSE3NQEzMhYVERQGKwEiJjURNDYCijIoPBwBSCg8He4QLBf6B0YfHz0tNxSRYA0xG2SWZIjW+v4+Mv12ZBUdHRVkFR0dBLBRLJZ9USxkLR3+qBghMhkZJCcBkCQbxMYcKGTU1f6JZAF3feGv/tQdFf4MFR0dFQH0FR0AAAAAAwAAAAAEsARMACAAMAA8AAABMzIWFxMWHQEUBiMhFh0BFAYrASImLwImNRE0NjsBNgUzMhYVERQGKwEiJjURNDYhByMRHwEzNSchNQMCWPoXLBDuHTwo/rgcPCgyGzENYJEUNy09fP3pZBUdHRVkFR0dAl+IZJZkMjIBwvoETCEY/qgdLWQsUXYHlixRKBzGxBskAZAnJGRkHRX+DBUdHRUB9BUdZP6J1dSv4X0BdwADAAAAZAUOBE8AGwA3AEcAAAElNh8BHgEPASEyFhQGKwEDDgEjISImNRE0NjcXERchEz4BOwEyNiYjISoDLgQnJj8BJwUzMhYVERQGKwEiJjURNDYBZAFrHxZuDQEMVAEuVGxuVGqDBhsP/qoHphwOOmQBJYMGGw/LFRMSFv44AgoCCQMHAwUDAQwRklb9T2QVHR0VZBUdHQNp5hAWcA0mD3lMkE7+rRUoog0CDRElCkj+CVkBUxUoMjIBAgIDBQIZFrdT5B0V/gwVHR0VAfQVHQAAAAP/nABkBLAETwAdADYARgAAAQUeBBURFAYjISImJwMjIiY0NjMhJyY2PwE2BxcWBw4FKgIjIRUzMhYXEyE3ESUFMzIWFREUBisBIiY1ETQ2AdsBbgIIFBANrAf+qg8bBoNqVW1sVAEuVQsBDW4WSpIRDAIDBQMHAwkDCgH+Jd0PHAaCASZq/qoCUGQVHR0VZBUdHQRP5gEFEBEXC/3zDaIoFQFTTpBMeQ8mDXAWrrcWGQIFAwICAWQoFf6tWQH37OQdFf4MFR0dFQH0FR0AAAADAGEAAARMBQ4AGwA3AEcAAAAyFh0BBR4BFREUBiMhIiYvAQMmPwE+AR8BETQXNTQmBhURHAMOBAcGLwEHEyE3ESUuAQMhMhYdARQGIyEiJj0BNDYB3pBOAVMVKKIN/fMRJQoJ5hAWcA0mD3nGMjIBAgIDBQIZFrdT7AH3Wf6tFSiWAfQVHR0V/gwVHR0FDm5UaoMGGw/+qgemHA4OAWsfFm4NAQxUAS5U1ssVExIW/jgCCgIJAwcDBQMBDBGSVv6tZAElgwYb/QsdFWQVHR0VZBUdAAP//QAGA+gFFAAPAC0ASQAAASEyNj0BNCYjISIGHQEUFgEVFAYiJjURBwYmLwEmNxM+BDMhMhYVERQGBwEDFzc2Fx4FHAIVERQWNj0BNDY3JREnAV4B9BUdHRX+DBUdHQEPTpBMeQ8mDXAWEOYBBRARFwsCDQ2iKBX9iexTtxYZAgUDAgIBMjIoFQFTWQRMHRVkFR0dFWQVHfzmalRubFQBLlQMAQ1uFh8BawIIEw8Mpgf+qg8bBgHP/q1WkhEMAQMFAwcDCQIKAv44FhITFcsPGwaDASVkAAIAFgAWBJoEmgAPACUAAAAyHgIUDgIiLgI0PgEBJSYGHQEhIgYdARQWMyEVFBY3JTY0AeLs1ptbW5vW7NabW1ubAob+7RAX/u0KDw8KARMXEAETEASaW5vW7NabW1ub1uzWm/453w0KFYkPCpYKD4kVCg3fDSYAAAIAFgAWBJoEmgAPACUAAAAyHgIUDgIiLgI0PgENAQYUFwUWNj0BITI2PQE0JiMhNTQmAeLs1ptbW5vW7NabW1ubASX+7RAQARMQFwETCg8PCv7tFwSaW5vW7NabW1ub1uzWm+jfDSYN3w0KFYkPCpYKD4kVCgAAAAIAFgAWBJoEmgAPACUAAAAyHgIUDgIiLgI0PgEBAyYiBwMGFjsBERQWOwEyNjURMzI2AeLs1ptbW5vW7NabW1ubAkvfDSYN3w0KFYkPCpYKD4kVCgSaW5vW7NabW1ub1uzWm/5AARMQEP7tEBf+7QoPDwoBExcAAAIAFgAWBJoEmgAPACUAAAAyHgIUDgIiLgI0PgEFIyIGFREjIgYXExYyNxM2JisBETQmAeLs1ptbW5vW7NabW1ubAZeWCg+JFQoN3w0mDd8NChWJDwSaW5vW7NabW1ub1uzWm7sPCv7tFxD+7RAQARMQFwETCg8AAAMAGAAYBJgEmAAPAJYApgAAADIeAhQOAiIuAjQ+ASUOAwcGJgcOAQcGFgcOAQcGFgcUFgcyHgEXHgIXHgI3Fg4BFx4CFxQGFBcWNz4CNy4BJy4BJyIOAgcGJyY2NS4BJzYuAQYHBicmNzY3HgIXHgMfAT4CJyY+ATc+AzcmNzIWMjY3LgMnND4CJiceAT8BNi4CJwYHFB4BFS4CJz4BNxYyPgEB5OjVm1xcm9Xo1ZtcXJsBZA8rHDoKDz0PFD8DAxMBAzEFCRwGIgEMFhkHECIvCxU/OR0HFBkDDRQjEwcFaHUeISQDDTAMD0UREi4oLBAzDwQBBikEAQMLGhIXExMLBhAGKBsGBxYVEwYFAgsFAwMNFwQGCQcYFgYQCCARFwkKKiFBCwQCAQMDHzcLDAUdLDgNEiEQEgg/KhADGgMKEgoRBJhcm9Xo1ZtcXJvV6NWbEQwRBwkCAwYFBycPCxcHInIWInYcCUcYChQECA4QBAkuHgQPJioRFRscBAcSCgwCch0kPiAIAQcHEAsBAgsLIxcBMQENCQIPHxkCFBkdHB4QBgEBBwoMGBENBAMMJSAQEhYXDQ4qFBkKEhIDCQsXJxQiBgEOCQwHAQ0DBAUcJAwSCwRnETIoAwEJCwsLJQcKDBEAAAAAAQAAAAIErwSFABYAAAE2FwUXNxYGBw4BJwEGIi8BJjQ3ASY2AvSkjv79kfsGUE08hjv9rA8rD28PDwJYIk8EhVxliuh+WYcrIgsW/awQEG4PKxACV2XJAAYAAABgBLAErAAPABMAIwAnADcAOwAAEyEyFh0BFAYjISImPQE0NgUjFTMFITIWHQEUBiMhIiY9ATQ2BSEVIQUhMhYdARQGIyEiJj0BNDYFIRUhZAPoKTs7KfwYKTs7BBHIyPwYA+gpOzsp/BgpOzsEEf4MAfT8GAPoKTs7KfwYKTs7BBH+1AEsBKw7KWQpOzspZCk7ZGTIOylkKTs7KWQpO2RkyDspZCk7OylkKTtkZAAAAAIAZAAABEwEsAALABEAABMhMhYUBiMhIiY0NgERBxEBIZYDhBUdHRX8fBUdHQI7yP6iA4QEsB0qHR0qHf1E/tTIAfQB9AAAAAMAAABkBLAEsAAXABsAJQAAATMyFh0BITIWFREhNSMVIRE0NjMhNTQ2FxUzNQEVFAYjISImPQEB9MgpOwEsKTv+DMj+DDspASw7KcgB9Dsp/BgpOwSwOylkOyn+cGRkAZApO2QpO2RkZP1EyCk7OynIAAAABAAAAAAEsASwABUAKwBBAFcAABMhMhYPARcWFA8BBiIvAQcGJjURNDYpATIWFREUBi8BBwYiLwEmND8BJyY2ARcWFA8BFxYGIyEiJjURNDYfATc2MgU3NhYVERQGIyEiJj8BJyY0PwE2MhcyASwVCA5exwcHaggUCMdeDhUdAzUBLBUdFQ5exwgUCGoHB8deDgj+L2oHB8deDggV/tQVHRUOXscIFALLXg4VHRX+1BUIDl7HBwdqCBQIBLAVDl7HCBQIagcHx14OCBUBLBUdHRX+1BUIDl7HBwdqCBQIx14OFf0maggUCMdeDhUdFQEsFQgOXscHzl4OCBX+1BUdFQ5exwgUCGoHBwAAAAYAAAAABKgEqAAPABsAIwA7AEMASwAAADIeAhQOAiIuAjQ+AQQiDgEUHgEyPgE0JiQyFhQGIiY0JDIWFAYjIicHFhUUBiImNTQ2PwImNTQEMhYUBiImNCQyFhQGIiY0Advy3Z9fX5/d8t2gXl6gAcbgv29vv+C/b2/+LS0gIC0gAUwtICAWDg83ETNIMykfegEJ/octICAtIAIdLSAgLSAEqF+f3fLdoF5eoN3y3Z9Xb7/gv29vv+C/BiAtISEtICAtIQqRFxwkMzMkIDEFfgEODhekIC0gIC0gIC0gIC0AAf/YAFoEuQS8AFsAACUBNjc2JicmIyIOAwcABw4EFx4BMzI3ATYnLgEjIgcGBwEOASY0NwA3PgEzMhceARcWBgcOBgcGIyImJyY2NwE2NzYzMhceARcWBgcBDgEnLgECIgHVWwgHdl8WGSJBMD8hIP6IDx4eLRMNBQlZN0ozAiQkEAcdEhoYDRr+qw8pHA4BRyIjQS4ODyw9DQ4YIwwod26La1YOOEBGdiIwGkQB/0coW2tQSE5nDxE4Qv4eDyoQEAOtAdZbZWKbEQQUGjIhH/6JDxsdNSg3HT5CMwIkJCcQFBcMGv6uDwEcKQ4BTSIjIQEINykvYyMLKnhuiWZMBxtAOU6+RAH/SBg3ISSGV121Qv4kDwIPDyYAAAACAGQAWASvBEQAGQBEAAABPgIeAhUUDgMHLgQ1ND4CHgEFIg4DIi4DIyIGFRQeAhcWFx4EMj4DNzY3PgQ1NCYCiTB7eHVYNkN5hKg+PqeFeEM4WnZ4eQEjIT8yLSohJyktPyJDbxtBMjMPBw86KzEhDSIzKUAMBAgrKT8dF2oDtURIBS1TdkA5eYB/slVVsn+AeTlAdlMtBUgtJjY1JiY1NiZvTRc4SjQxDwcOPCouGBgwKEALBAkpKkQqMhNPbQACADn/8gR3BL4AFwAuAAAAMh8BFhUUBg8BJi8BNycBFwcvASY0NwEDNxYfARYUBwEGIi8BJjQ/ARYfAQcXAQKru0KNQjgiHR8uEl/3/nvUaRONQkIBGxJpCgmNQkL+5UK6Qo1CQjcdLhJf9wGFBL5CjUJeKmsiHTUuEl/4/nvUahKNQrpCARv+RmkICY1CukL+5UJCjUK7Qjc3LxFf+AGFAAAAAAMAyAAAA+gEsAARABUAHQAAADIeAhURFAYjISImNRE0PgEHESERACIGFBYyNjQCBqqaZDo7Kf2oKTs8Zj4CWP7/Vj09Vj0EsB4uMhX8Ryk7OykDuRUzLar9RAK8/RY9Vj09VgABAAAAAASwBLAAFgAACQEWFAYiLwEBEScBBRMBJyEBJyY0NjIDhgEbDx0qDiT+6dT+zP7oywEz0gEsAQsjDx0qBKH+5g8qHQ8j/vX+1NL+zcsBGAE01AEXJA4qHQAAAAADAScAEQQJBOAAMgBAAEsAAAEVHgQXIy4DJxEXHgQVFAYHFSM1JicuASczHgEXEScuBDU0PgI3NRkBDgMVFB4DFxYXET4ENC4CArwmRVI8LAKfBA0dMydAIjxQNyiym2SWVygZA4sFV0obLkJOMCAyVWg6HSoqFQ4TJhkZCWgWKTEiGBkzNwTgTgUTLD9pQiQuLBsH/s0NBxMtPGQ+i6oMTU8QVyhrVk1iEAFPCA4ZLzlYNkZwSCoGTf4SARIEDh02Jh0rGRQIBgPQ/soCCRYgNEM0JRkAAAABAGQAZgOUBK0ASgAAATIeARUjNC4CIyIGBwYVFB4BFxYXMxUjFgYHBgc+ATM2FjMyNxcOAyMiLgEHDgEPASc+BTc+AScjNTMmJy4CPgE3NgIxVJlemSc8OxolVBQpGxoYBgPxxQgVFS02ImIWIIwiUzUyHzY4HCAXanQmJ1YYFzcEGAcTDBEJMAwk3aYXFQcKAg4tJGEErVCLTig/IhIdFSw5GkowKgkFZDKCHj4yCg8BIh6TExcIASIfBAMaDAuRAxAFDQsRCjePR2QvORQrREFMIVgAAAACABn//wSXBLAADwAfAAABMzIWDwEGIi8BJjY7AREzBRcWBisBESMRIyImPwE2MgGQlhUIDuYOKg7mDggVlsgCF+YOCBWWyJYVCA7mDioBLBYO+g8P+g4WA4QQ+Q4V/HwDhBUO+Q8AAAQAGf//A+gEsAAHABcAGwAlAAABIzUjFSMRIQEzMhYPAQYiLwEmNjsBETMFFTM1EwczFSE1NyM1IQPoZGRkASz9qJYVCA7mDioO5g4IFZbIAZFkY8jI/tTIyAEsArxkZAH0/HwWDvoPD/oOFgOEZMjI/RL6ZJb6ZAAAAAAEABn//wPoBLAADwAZACEAJQAAATMyFg8BBiIvASY2OwERMwUHMxUhNTcjNSERIzUjFSMRIQcVMzUBkJYVCA7mDioO5g4IFZbIAljIyP7UyMgBLGRkZAEsx2QBLBYO+g8P+g4WA4SW+mSW+mT7UGRkAfRkyMgAAAAEABn//wRMBLAADwAVABsAHwAAATMyFg8BBiIvASY2OwERMwEjESM1MxMjNSMRIQcVMzUBkJYVCA7mDioO5g4IFZbIAlhkZMhkZMgBLMdkASwWDvoPD/oOFgOE/gwBkGT7UGQBkGTIyAAAAAAEABn//wRMBLAADwAVABkAHwAAATMyFg8BBiIvASY2OwERMwEjNSMRIQcVMzUDIxEjNTMBkJYVCA7mDioO5g4IFZbIArxkyAEsx2QBZGTIASwWDvoPD/oOFgOE/gxkAZBkyMj7tAGQZAAAAAAFABn//wSwBLAADwATABcAGwAfAAABMzIWDwEGIi8BJjY7AREzBSM1MxMhNSETITUhEyE1IQGQlhUIDuYOKg7mDggVlsgB9MjIZP7UASxk/nABkGT+DAH0ASwWDvoPD/oOFgOEyMj+DMj+DMj+DMgABQAZ//8EsASwAA8AEwAXABsAHwAAATMyFg8BBiIvASY2OwERMwUhNSEDITUhAyE1IQMjNTMBkJYVCA7mDioO5g4IFZbIAyD+DAH0ZP5wAZBk/tQBLGTIyAEsFg76Dw/6DhYDhMjI/gzI/gzI/gzIAAIAAAAABEwETAAPAB8AAAEhMhYVERQGIyEiJjURNDYFISIGFREUFjMhMjY1ETQmAV4BkKK8u6P+cKW5uQJn/gwpOzspAfQpOzsETLuj/nClubmlAZClucg7Kf4MKTs7KQH0KTsAAAAAAwAAAAAETARMAA8AHwArAAABITIWFREUBiMhIiY1ETQ2BSEiBhURFBYzITI2NRE0JgUXFhQPAQYmNRE0NgFeAZClubml/nCju7wCZP4MKTs7KQH0KTs7/m/9ERH9EBgYBEy5pf5wpbm5pQGQo7vIOyn+DCk7OykB9Ck7gr4MJAy+DAsVAZAVCwAAAAADAAAAAARMBEwADwAfACsAAAEhMhYVERQGIyEiJjURNDYFISIGFREUFjMhMjY1ETQmBSEyFg8BBiIvASY2AV4BkKO7uaX+cKW5uQJn/gwpOzspAfQpOzv+FQGQFQsMvgwkDL4MCwRMvKL+cKW5uaUBkKO7yDsp/gwpOzspAfQpO8gYEP0REf0QGAAAAAMAAAAABEwETAAPAB8AKwAAASEyFhURFAYjISImNRE0NgUhIgYVERQWMyEyNjURNCYFFxYGIyEiJj8BNjIBXgGQpbm5pf5wo7u5Amf+DCk7OykB9Ck7O/77vgwLFf5wFQsMvgwkBEy5pf5wo7u8ogGQpbnIOyn+DCk7OykB9Ck7z/0QGBgQ/REAAAAAAgAAAAAFFARMAB8ANQAAASEyFhURFAYjISImPQE0NjMhMjY1ETQmIyEiJj0BNDYHARYUBwEGJj0BIyImPQE0NjsBNTQ2AiYBkKW5uaX+cBUdHRUBwik7Oyn+PhUdHb8BRBAQ/rwQFvoVHR0V+hYETLml/nCluR0VZBUdOykB9Ck7HRVkFR3p/uQOJg7+5A4KFZYdFcgVHZYVCgAAAQDZAAID1wSeACMAAAEXFgcGAgclMhYHIggBBwYrAScmNz4BPwEhIicmNzYANjc2MwMZCQgDA5gCASwYEQ4B/vf+8wQMDgkJCQUCUCcn/tIXCAoQSwENuwUJEASeCQoRC/5TBwEjEv7K/sUFDwgLFQnlbm4TFRRWAS/TBhAAAAACAAAAAAT+BEwAHwA1AAABITIWHQEUBiMhIgYVERQWMyEyFh0BFAYjISImNRE0NgUBFhQHAQYmPQEjIiY9ATQ2OwE1NDYBXgGQFR0dFf4+KTs7KQHCFR0dFf5wpbm5AvEBRBAQ/rwQFvoVHR0V+hYETB0VZBUdOyn+DCk7HRVkFR25pQGQpbnp/uQOJg7+5A4KFZYdFcgVHZYVCgACAAAAAASwBLAAFQAxAAABITIWFREUBi8BAQYiLwEmNDcBJyY2ASMiBhURFBYzITI2PQE3ERQGIyEiJjURNDYzIQLuAZAVHRUObf7IDykPjQ8PAThtDgj+75wpOzspAfQpO8i7o/5wpbm5pQEsBLAdFf5wFQgObf7IDw+NDykPAThtDhX+1Dsp/gwpOzsplMj+1qW5uaUBkKW5AAADAA4ADgSiBKIADwAbACMAAAAyHgIUDgIiLgI0PgEEIg4BFB4BMj4BNCYEMhYUBiImNAHh7tmdXV2d2e7ZnV1dnQHD5sJxccLmwnFx/nugcnKgcgSiXZ3Z7tmdXV2d2e7ZnUdxwubCcXHC5sJzcqBycqAAAAMAAAAABEwEsAAVAB8AIwAAATMyFhURMzIWBwEGIicBJjY7ARE0NgEhMhYdASE1NDYFFTM1AcLIFR31FAoO/oEOJw3+hQ0JFfod/oUD6BUd+7QdA2dkBLAdFf6iFg/+Vg8PAaoPFgFeFR38fB0V+voVHWQyMgAAAAMAAAAABEwErAAVAB8AIwAACQEWBisBFRQGKwEiJj0BIyImNwE+AQEhMhYdASE1NDYFFTM1AkcBeg4KFfQiFsgUGPoUCw4Bfw4n/fkD6BUd+7QdA2dkBJ7+TQ8g+hQeHRX6IQ8BrxAC/H8dFfr6FR1kMjIAAwAAAAAETARLABQAHgAiAAAJATYyHwEWFAcBBiInASY0PwE2MhcDITIWHQEhNTQ2BRUzNQGMAXEHFQeLBwf98wcVB/7cBweLCBUH1APoFR37tB0DZ2QC0wFxBweLCBUH/fMICAEjCBQIiwcH/dIdFfr6FR1kMjIABAAAAAAETASbAAkAGQAjACcAABM3NjIfAQcnJjQFNzYWFQMOASMFIiY/ASc3ASEyFh0BITU0NgUVMzWHjg4qDk3UTQ4CFtIOFQIBHRX9qxUIDtCa1P49A+gVHfu0HQNnZAP/jg4OTdRMDyqa0g4IFf2pFB4BFQ7Qm9T9Oh0V+voVHWQyMgAAAAQAAAAABEwEsAAPABkAIwAnAAABBR4BFRMUBi8BByc3JyY2EwcGIi8BJjQ/AQEhMhYdASE1NDYFFTM1AV4CVxQeARUO0JvUm9IOCMNMDyoOjg4OTf76A+gVHfu0HQNnZASwAgEdFf2rFQgO0JrUmtIOFf1QTQ4Ojg4qDk3+WB0V+voVHWQyMgACAAT/7ASwBK8ABQAIAAAlCQERIQkBFQEEsP4d/sb+cQSs/TMCq2cBFP5xAacDHPz55gO5AAAAAAIAAABkBEwEsAAVABkAAAERFAYrAREhESMiJjURNDY7AREhETMHIzUzBEwdFZb9RJYVHR0V+gH0ZMhkZAPo/K4VHQGQ/nAdFQPoFB7+1AEsyMgAAAMAAABFBN0EsAAWABoALwAAAQcBJyYiDwEhESMiJjURNDY7AREhETMHIzUzARcWFAcBBiIvASY0PwE2Mh8BATYyBEwC/tVfCRkJlf7IlhUdHRX6AfRkyGRkAbBqBwf+XAgUCMoICGoHFQdPASkHFQPolf7VXwkJk/5wHRUD6BQe/tQBLMjI/c5qBxUH/lsHB8sHFQdqCAhPASkHAAMAAAANBQcEsAAWABoAPgAAAREHJy4BBwEhESMiJjURNDY7AREhETMHIzUzARcWFA8BFxYUDwEGIi8BBwYiLwEmND8BJyY0PwE2Mh8BNzYyBExnhg8lEP72/reWFR0dFfoB9GTIZGQB9kYPD4ODDw9GDykPg4MPKQ9GDw+Dgw8PRg8pD4ODDykD6P7zZ4YPAw7+9v5wHRUD6BQe/tQBLMjI/YxGDykPg4MPKQ9GDw+Dgw8PRg8pD4ODDykPRg8Pg4MPAAADAAAAFQSXBLAAFQAZAC8AAAERISIGHQEhESMiJjURNDY7AREhETMHIzUzEzMyFh0BMzIWDwEGIi8BJjY7ATU0NgRM/qIVHf4MlhUdHRX6AfRkyGRklmQVHZYVCA7mDioO5g4IFZYdA+j+1B0Vlv5wHRUD6BQe/tQBLMjI/agdFfoVDuYODuYOFfoVHQAAAAADAAAAAASXBLAAFQAZAC8AAAERJyYiBwEhESMiJjURNDY7AREhETMHIzUzExcWBisBFRQGKwEiJj0BIyImPwE2MgRMpQ4qDv75/m6WFR0dFfoB9GTIZGTr5g4IFZYdFWQVHZYVCA7mDioD6P5wpQ8P/vf+cB0VA+gUHv7UASzIyP2F5Q8V+hQeHhT6FQ/lDwADAAAAyASwBEwACQATABcAABMhMhYdASE1NDYBERQGIyEiJjURExUhNTIETBUd+1AdBJMdFfu0FR1kAZAETB0VlpYVHf7U/doVHR0VAib+1MjIAAAGAAMAfQStBJcADwAZAB0ALQAxADsAAAEXFhQPAQYmPQEhNSE1NDYBIyImPQE0NjsBFyM1MwE3NhYdASEVIRUUBi8BJjQFIzU7AjIWHQEUBisBA6f4Dg74DhX+cAGQFf0vMhUdHRUyyGRk/oL3DhUBkP5wFQ73DwOBZGRkMxQdHRQzBI3mDioO5g4IFZbIlhUI/oUdFWQVHcjI/cvmDggVlsiWFQgO5g4qecgdFWQVHQAAAAACAGQAAASwBLAAFgBRAAABJTYWFREUBisBIiY1ES4ENRE0NiUyFh8BERQOAg8BERQGKwEiJjURLgQ1ETQ+AzMyFh8BETMRPAE+AjMyFh8BETMRND4DA14BFBklHRXIFR0EDiIaFiX+4RYZAgEVHR0LCh0VyBUdBA4iGhYBBwoTDRQZAgNkBQkVDxcZAQFkAQUJFQQxdBIUH/uuFR0dFQGNAQgbHzUeAWcfRJEZDA3+Phw/MSkLC/5BFR0dFQG/BA8uLkAcAcICBxENCxkMDf6iAV4CBxENCxkMDf6iAV4CBxENCwABAGQAAASwBEwAMwAAARUiDgMVERQWHwEVITUyNjURIREUFjMVITUyPgM1ETQmLwE1IRUiBhURIRE0JiM1BLAEDiIaFjIZGf5wSxn+DBlL/nAEDiIaFjIZGQGQSxkB9BlLBEw4AQUKFA78iBYZAQI4OA0lAYr+diUNODgBBQoUDgN4FhkBAjg4DSX+dgGKJQ04AAAABgAAAAAETARMAAwAHAAgACQAKAA0AAABITIWHQEjBTUnITchBSEyFhURFAYjISImNRE0NhcVITUBBTUlBRUhNQUVFAYjIQchJyE3MwKjAXcVHWn+2cj+cGQBd/4lASwpOzsp/tQpOzspASwCvP5wAZD8GAEsArwdFf6JZP6JZAGQyGkD6B0VlmJiyGTIOyn+DCk7OykB9Ck7ZMjI/veFo4XGyMhm+BUdZGTIAAEAEAAQBJ8EnwAmAAATNzYWHwEWBg8BHgEXNz4BHwEeAQ8BBiIuBicuBTcRohEuDosOBhF3ZvyNdxEzE8ATBxGjAw0uMUxPZWZ4O0p3RjITCwED76IRBhPCFDERdo78ZXYRBA6IDi8RogEECBUgNUNjO0qZfHNVQBAAAAACAAAAAASwBEwAIwBBAAAAMh4EHwEVFAYvAS4BPQEmIAcVFAYPAQYmPQE+BRIyHgIfARUBHgEdARQGIyEiJj0BNDY3ATU0PgIB/LimdWQ/LAkJHRTKFB2N/sKNHRTKFB0DDTE7ZnTKcFImFgEBAW0OFR0V+7QVHRUOAW0CFiYETBUhKCgiCgrIFRgDIgMiFZIYGJIVIgMiAxgVyAQNJyQrIP7kExwcCgoy/tEPMhTUFR0dFdQUMg8BLzIEDSEZAAADAAAAAASwBLAADQAdACcAAAEHIScRMxUzNTMVMzUzASEyFhQGKwEXITcjIiY0NgMhMhYdASE1NDYETMj9qMjIyMjIyPyuArwVHR0VDIn8SokMFR0dswRMFR37UB0CvMjIAfTIyMjI/OAdKh1kZB0qHf7UHRUyMhUdAAAAAwBkAAAEsARMAAkAEwAdAAABIyIGFREhETQmASMiBhURIRE0JgEhETQ2OwEyFhUCvGQpOwEsOwFnZCk7ASw7/Rv+1DspZCk7BEw7KfwYA+gpO/7UOyn9RAK8KTv84AGQKTs7KQAAAAAF/5wAAASwBEwADwATAB8AJQApAAATITIWFREUBiMhIiY1ETQ2FxEhEQUjFTMRITUzNSMRIQURByMRMwcRMxHIArx8sLB8/UR8sLAYA4T+DMjI/tTIyAEsAZBkyMhkZARMsHz+DHywsHwB9HywyP1EArzIZP7UZGQBLGT+1GQB9GT+1AEsAAAABf+cAAAEsARMAA8AEwAfACUAKQAAEyEyFhURFAYjISImNRE0NhcRIREBIzUjFSMRMxUzNTMFEQcjETMHETMRyAK8fLCwfP1EfLCwGAOE/gxkZGRkZGQBkGTIyGRkBEywfP4MfLCwfAH0fLDI/UQCvP2oyMgB9MjIZP7UZAH0ZP7UASwABP+cAAAEsARMAA8AEwAbACMAABMhMhYVERQGIyEiJjURNDYXESERBSMRMxUhESEFIxEzFSERIcgCvHywsHz9RHywsBgDhP4MyMj+1AEsAZDIyP7UASwETLB8/gx8sLB8AfR8sMj9RAK8yP7UZAH0ZP7UZAH0AAAABP+cAAAEsARMAA8AEwAWABkAABMhMhYVERQGIyEiJjURNDYXESERAS0BDQERyAK8fLCwfP1EfLCwGAOE/gz+1AEsAZD+1ARMsHz+DHywsHwB9HywyP1EArz+DJaWlpYBLAAAAAX/nAAABLAETAAPABMAFwAgACkAABMhMhYVERQGIyEiJjURNDYXESERAyERIQcjIgYVFBY7AQERMzI2NTQmI8gCvHywsHz9RHywsBgDhGT9RAK8ZIImOTYpgv4Mgik2OSYETLB8/gx8sLB8AfR8sMj9RAK8/agB9GRWQUFUASz+1FRBQVYAAAAF/5wAAASwBEwADwATAB8AJQApAAATITIWFREUBiMhIiY1ETQ2FxEhEQUjFTMRITUzNSMRIQEjESM1MwMjNTPIArx8sLB8/UR8sLAYA4T+DMjI/tTIyAEsAZBkZMjIZGQETLB8/gx8sLB8AfR8sMj9RAK8yGT+1GRkASz+DAGQZP4MZAAG/5wAAASwBEwADwATABkAHwAjACcAABMhMhYVERQGIyEiJjURNDYXESERBTMRIREzASMRIzUzBRUzNQEjNTPIArx8sLB8/UR8sLAYA4T9RMj+1GQCWGRkyP2oZAEsZGQETLB8/gx8sLB8AfR8sMj9RAK8yP5wAfT+DAGQZMjIyP7UZAAF/5wAAASwBEwADwATABwAIgAmAAATITIWFREUBiMhIiY1ETQ2FxEhEQEHIzU3NSM1IQEjESM1MwMjNTPIArx8sLB8/UR8sLAYA4T+DMdkx8gBLAGQZGTIx2RkBEywfP4MfLCwfAH0fLDI/UQCvP5wyDLIlmT+DAGQZP4MZAAAAAMACQAJBKcEpwAPABsAJQAAADIeAhQOAiIuAjQ+AQQiDgEUHgEyPgE0JgchFSEVISc1NyEB4PDbnl5entvw255eXp4BxeTCcXHC5MJxcWz+1AEs/tRkZAEsBKdentvw255eXp7b8NueTHHC5MJxccLkwtDIZGTIZAAAAAAEAAkACQSnBKcADwAbACcAKwAAADIeAhQOAiIuAjQ+AQQiDgEUHgEyPgE0JgcVBxcVIycjFSMRIQcVMzUB4PDbnl5entvw255eXp4BxeTCcXHC5MJxcWwyZGRklmQBLMjIBKdentvw255eXp7b8NueTHHC5MJxccLkwtBkMmQyZGQBkGRkZAAAAv/y/50EwgRBACAANgAAATIWFzYzMhYUBisBNTQmIyEiBh0BIyImNTQ2NyY1ND4BEzMyFhURMzIWDwEGIi8BJjY7ARE0NgH3brUsLC54qqp4gB0V/tQVHd5QcFZBAmKqepYKD4kVCg3fDSYN3w0KFYkPBEF3YQ6t8a36FR0dFfpzT0VrDhMSZKpi/bMPCv7tFxD0EBD0EBcBEwoPAAAAAAL/8v+cBMMEQQAcADMAAAEyFhc2MzIWFxQGBwEmIgcBIyImNTQ2NyY1ND4BExcWBisBERQGKwEiJjURIyImNzY3NjIB9m62LCsueaoBeFr+hg0lDf6DCU9xVkECYqnm3w0KFYkPCpYKD4kVCg3HGBMZBEF3YQ+teGOkHAFoEBD+k3NPRWsOExNkqWP9kuQQF/7tCg8PCgETFxDMGBMAAAABAGQAAARMBG0AGAAAJTUhATMBMwkBMwEzASEVIyIGHQEhNTQmIwK8AZD+8qr+8qr+1P7Uqv7yqv7yAZAyFR0BkB0VZGQBLAEsAU3+s/7U/tRkHRUyMhUdAAAAAAEAeQAABDcEmwAvAAABMhYXHgEVFAYHFhUUBiMiJxUyFh0BITU0NjM1BiMiJjU0Ny4BNTQ2MzIXNCY1NDYCWF6TGll7OzIJaUo3LRUd/tQdFS03SmkELzlpSgUSAqMEm3FZBoNaPWcfHRpKaR77HRUyMhUd+x5pShIUFVg1SmkCAhAFdKMAAAAGACcAFASJBJwAEQAqAEIASgBiAHsAAAEWEgIHDgEiJicmAhI3PgEyFgUiBw4BBwYWHwEWMzI3Njc2Nz4BLwEmJyYXIgcOAQcGFh8BFjMyNz4BNz4BLwEmJyYWJiIGFBYyNjciBw4BBw4BHwEWFxYzMjc+ATc2Ji8BJhciBwYHBgcOAR8BFhcWMzI3PgE3NiYvASYD8m9PT29T2dzZU29PT29T2dzZ/j0EBHmxIgQNDCQDBBcGG0dGYAsNAwkDCwccBAVQdRgEDA0iBAQWBhJROQwMAwkDCwf5Y4xjY4xjVhYGElE6CwwDCQMLBwgEBVB1GAQNDCIEjRcGG0dGYAsNAwkDCwcIBAR5sSIEDQwkAwPyb/7V/tVvU1dXU28BKwErb1NXVxwBIrF5DBYDCQEWYEZHGwMVDCMNBgSRAhh1UA0WAwkBFTpREgMVCyMMBwT6Y2OMY2MVFTpREQQVCyMMBwQCGHVQDRYDCQEkFmBGRxsDFQwjDQYEASKxeQwWAwkBAAAABQBkAAAD6ASwAAwADwAWABwAIgAAASERIzUhFSERNDYzIQEjNQMzByczNTMDISImNREFFRQGKwECvAEstP6s/oQPCgI/ASzIZKLU1KJktP51Cg8DhA8KwwMg/oTIyALzCg/+1Mj84NTUyP4MDwoBi8jDCg8AAAAABQBkAAAD6ASwAAkADAATABoAIQAAASERCQERNDYzIQEjNRMjFSM1IzcDISImPQEpARUUBisBNQK8ASz+ov3aDwoCPwEsyD6iZKLUqv6dCg8BfAIIDwqbAyD9+AFe/doERwoP/tTI/HzIyNT+ZA8KNzcKD1AAAAAAAwAAAAAEsAP0AAgAGQAfAAABIxUzFyERIzcFMzIeAhUhFSEDETM0PgIBMwMhASEEiqJkZP7UotT9EsgbGiEOASz9qMhkDiEaAnPw8PzgASwB9AMgyGQBLNTUBBErJGT+ogHCJCsRBP5w/nAB9AAAAAMAAAAABEwETAAZADIAOQAAATMyFh0BMzIWHQEUBiMhIiY9ATQ2OwE1NDYFNTIWFREUBiMhIic3ARE0NjMVFBYzITI2AQc1IzUzNQKKZBUdMhUdHRX+1BUdHRUyHQFzKTs7Kf2oARP2/ro7KVg+ASw+WP201MjIBEwdFTIdFWQVHR0VZBUdMhUd+pY7KfzgKTsE9gFGAUQpO5Y+WFj95tSiZKIAAwBkAAAEvARMABkANgA9AAABMzIWHQEzMhYdARQGIyEiJj0BNDY7ATU0NgU1MhYVESMRMxQOAiMhIiY1ETQ2MxUUFjMhMjYBBzUjNTM1AcJkFR0yFR0dFf7UFR0dFTIdAXMpO8jIDiEaG/2oKTs7KVg+ASw+WAGc1MjIBEwdFTIdFWQVHR0VZBUdMhUd+pY7Kf4M/tQkKxEEOykDICk7lj5YWP3m1KJkogAAAAP/ogAABRYE1AALABsAHwAACQEWBiMhIiY3ATYyEyMiBhcTHgE7ATI2NxM2JgMVMzUCkgJ9FyAs+wQsIBcCfRZARNAUGAQ6BCMUNhQjBDoEGODIBK37sCY3NyYEUCf+TB0U/tIUHR0UAS4UHf4MZGQAAAAACQAAAAAETARMAA8AHwAvAD8ATwBfAG8AfwCPAAABMzIWHQEUBisBIiY9ATQ2EzMyFh0BFAYrASImPQE0NiEzMhYdARQGKwEiJj0BNDYBMzIWHQEUBisBIiY9ATQ2ITMyFh0BFAYrASImPQE0NiEzMhYdARQGKwEiJj0BNDYBMzIWHQEUBisBIiY9ATQ2ITMyFh0BFAYrASImPQE0NiEzMhYdARQGKwEiJj0BNDYBqfoKDw8K+goPDwr6Cg8PCvoKDw8BmvoKDw8K+goPD/zq+goPDwr6Cg8PAZr6Cg8PCvoKDw8BmvoKDw8K+goPD/zq+goPDwr6Cg8PAZr6Cg8PCvoKDw8BmvoKDw8K+goPDwRMDwqWCg8PCpYKD/7UDwqWCg8PCpYKDw8KlgoPDwqWCg/+1A8KlgoPDwqWCg8PCpYKDw8KlgoPDwqWCg8PCpYKD/7UDwqWCg8PCpYKDw8KlgoPDwqWCg8PCpYKDw8KlgoPAAAAAwAAAAAEsAUUABkAKQAzAAABMxUjFSEyFg8BBgchJi8BJjYzITUjNTM1MwEhMhYUBisBFyE3IyImNDYDITIWHQEhNTQ2ArxkZAFePjEcQiko/PwoKUIcMT4BXmRkyP4+ArwVHR0VDIn8SooNFR0dswRMFR37UB0EsMhkTzeEUzMzU4Q3T2TIZPx8HSodZGQdKh3+1B0VMjIVHQAABAAAAAAEsAUUAAUAGQArADUAAAAyFhUjNAchFhUUByEyFg8BIScmNjMhJjU0AyEyFhQGKwEVBSElNSMiJjQ2AyEyFh0BITU0NgIwUDnCPAE6EgMBSCkHIq/9WrIiCikBSAOvArwVHR0VlgET/EoBE5YVHR2zBEwVHftQHQUUOykpjSUmCBEhFpGRFiERCCb+lR0qHcjIyMgdKh39qB0VMjIVHQAEAAAAAASwBJ0ABwAUACQALgAAADIWFAYiJjQTMzIWFRQXITY1NDYzASEyFhQGKwEXITcjIiY0NgMhMhYdASE1NDYCDZZqapZqty4iKyf+vCcrI/7NArwVHR0VDYr8SokMFR0dswRMFR37UB0EnWqWamqW/us5Okxra0w6Of5yHSodZGQdKh3+1B0VMjIVHQAEAAAAAASwBRQADwAcACwANgAAATIeARUUBiImNTQ3FzcnNhMzMhYVFBchNjU0NjMBITIWFAYrARchNyMiJjQ2AyEyFh0BITU0NgJYL1szb5xvIpBvoyIfLiIrJ/68Jysj/s0CvBUdHRUNivxKiQwVHR2zBEwVHftQHQUUa4s2Tm9vTj5Rj2+jGv4KOTpMa2tMOjn+ch0qHWRkHSod/tQdFTIyFR0AAAADAAAAAASwBRIAEgAiACwAAAEFFSEUHgMXIS4BNTQ+AjcBITIWFAYrARchNyMiJjQ2AyEyFh0BITU0NgJYASz+1CU/P00T/e48PUJtj0r+ogK8FR0dFQ2K/EqJDBUdHbMETBUd+1AdBLChizlmUT9IGVO9VFShdksE/H4dKh1kZB0qHf7UHRUyMhUdAAIAyAAAA+gFFAAPACkAAAAyFh0BHgEdASE1NDY3NTQDITIWFyMVMxUjFTMVIxUzFAYjISImNRE0NgIvUjsuNv5wNi5kAZA2XBqsyMjIyMh1U/5wU3V1BRQ7KU4aXDYyMjZcGk4p/kc2LmRkZGRkU3V1UwGQU3UAAAMAZP//BEwETAAPAC8AMwAAEyEyFhURFAYjISImNRE0NgMhMhYdARQGIyEXFhQGIi8BIQcGIiY0PwEhIiY9ATQ2BQchJ5YDhBUdHRX8fBUdHQQDtgoPDwr+5eANGiUNWP30Vw0mGg3g/t8KDw8BqmQBRGQETB0V/gwVHR0VAfQVHf1EDwoyCg/gDSUbDVhYDRslDeAPCjIKD2RkZAAAAAAEAAAAAASwBEwAGQAjAC0ANwAAEyEyFh0BIzQmKwEiBhUjNCYrASIGFSM1NDYDITIWFREhETQ2ExUUBisBIiY9ASEVFAYrASImPQHIAyBTdWQ7KfopO2Q7KfopO2R1EQPoKTv7UDvxHRVkFR0D6B0VZBUdBEx1U8gpOzspKTs7KchTdf4MOyn+1AEsKTv+DDIVHR0VMjIVHR0VMgADAAEAAASpBKwADQARABsAAAkBFhQPASEBJjQ3ATYyCQMDITIWHQEhNTQ2AeACqh8fg/4f/fsgIAEnH1n+rAFWAS/+q6IDIBUd/HwdBI39VR9ZH4MCBh9ZHwEoH/5u/qoBMAFV/BsdFTIyFR0AAAAAAgCPAAAEIQSwABcALwAAAQMuASMhIgYHAwYWMyEVFBYyNj0BMzI2AyE1NDY7ATU0NjsBETMRMzIWHQEzMhYVBCG9CCcV/nAVJwi9CBMVAnEdKh19FROo/a0dFTIdFTDILxUdMhUdAocB+hMcHBP+BhMclhUdHRWWHP2MMhUdMhUdASz+1B0VMh0VAAAEAAAAAASwBLAADQAQAB8AIgAAASERFAYjIREBNTQ2MyEBIzUBIREUBiMhIiY1ETQ2MyEBIzUDhAEsDwr+if7UDwoBdwEsyP2oASwPCv12Cg8PCgF3ASzIAyD9wQoPAk8BLFQKD/7UyP4M/cEKDw8KA7YKD/7UyAAC/5wAZAUUBEcARgBWAAABMzIeAhcWFxY2NzYnJjc+ARYXFgcOASsBDgEPAQ4BKwEiJj8BBisBIicHDgErASImPwEmLwEuAT0BNDY7ATY3JyY2OwE2BSMiBh0BFBY7ATI2PQE0JgHkw0uOakkMEhEfQwoKGRMKBQ8XDCkCA1Y9Pgc4HCcDIhVkFRgDDDEqwxgpCwMiFWQVGAMaVCyfExwdFXwLLW8QBxXLdAFF+goPDwr6Cg8PBEdBa4pJDgYKISAiJRsQCAYIDCw9P1c3fCbqFB0dFEYOCEAUHR0UnUplNQcmFTIVHVdPXw4TZV8PCjIKDw8KMgoPAAb/nP/mBRQEfgAJACQANAA8AFIAYgAAASU2Fh8BFgYPASUzMhYfASEyFh0BFAYHBQYmJyYjISImPQE0NhcjIgYdARQ7ATI2NTQmJyYEIgYUFjI2NAE3PgEeARceAT8BFxYGDwEGJi8BJjYlBwYfAR4BPwE2Jy4BJy4BAoEBpxMuDiAOAxCL/CtqQ0geZgM3FR0cE/0fFyIJKjr+1D5YWLlQExIqhhALIAsSAYBALS1ALf4PmBIgHhMQHC0aPzANITNQL3wpgigJASlmHyElDR0RPRMFAhQHCxADhPcICxAmDyoNeMgiNtQdFTIVJgeEBBQPQ1g+yD5YrBwVODMQEAtEERzJLUAtLUD+24ITChESEyMgAwWzPUkrRSgJL5cvfRxYGyYrDwkLNRAhFEgJDAQAAAAAAwBkAAAEOQSwAFEAYABvAAABMzIWHQEeARcWDgIPATIeBRUUDgUjFRQGKwEiJj0BIxUUBisBIiY9ASMiJj0BNDY7AREjIiY9ATQ2OwE1NDY7ATIWHQEzNTQ2AxUhMj4CNTc0LgMjARUhMj4CNTc0LgMjAnGWCg9PaAEBIC4uEBEGEjQwOiodFyI2LUAjGg8KlgoPZA8KlgoPrwoPDwpLSwoPDwqvDwqWCg9kD9cBBxwpEwsBAQsTKRz++QFrHCkTCwEBCxMpHASwDwptIW1KLk0tHwYGAw8UKDJOLTtdPCoVCwJLCg8PCktLCg8PCksPCpYKDwJYDwqWCg9LCg8PCktLCg/+1MgVHR0LCgQOIhoW/nDIFR0dCwoEDiIaFgAAAwAEAAIEsASuABcAKQAsAAATITIWFREUBg8BDgEjISImJy4CNRE0NgQiDgQPARchNy4FAyMT1AMMVnokEhIdgVL9xFKCHAgYKHoCIIx9VkcrHQYGnAIwnAIIIClJVSGdwwSuelb+YDO3QkJXd3ZYHFrFMwGgVnqZFyYtLSUMDPPzBQ8sKDEj/sIBBQACAMgAAAOEBRQADwAZAAABMzIWFREUBiMhIiY1ETQ2ARUUBisBIiY9AQHblmesVCn+PilUrAFINhWWFTYFFKxn/gwpVFQpAfRnrPwY4RU2NhXhAAACAMgAAAOEBRQADwAZAAABMxQWMxEUBiMhIiY1ETQ2ARUUBisBIiY9AQHbYLOWVCn+PilUrAFINhWWFTYFFJaz/kIpVFQpAfRnrPwY4RU2NhXhAAACAAAAFAUOBBoAFAAaAAAJASUHFRcVJwc1NzU0Jj4CPwEnCQEFJTUFJQUO/YL+hk5klpZkAQEBBQQvkwKCAVz+ov6iAV4BXgL//uWqPOCWx5SVyJb6BA0GCgYDKEEBG/1ipqaTpaUAAAMAZAH0BLADIAAHAA8AFwAAEjIWFAYiJjQkMhYUBiImNCQyFhQGIiY0vHxYWHxYAeh8WFh8WAHofFhYfFgDIFh8WFh8WFh8WFh8WFh8WFh8AAAAAAMBkAAAArwETAAHAA8AFwAAADIWFAYiJjQSMhYUBiImNBIyFhQGIiY0Aeh8WFh8WFh8WFh8WFh8WFh8WARMWHxYWHz+yFh8WFh8/shYfFhYfAAAAAMAZABkBEwETAAPAB8ALwAAEyEyFh0BFAYjISImPQE0NhMhMhYdARQGIyEiJj0BNDYTITIWHQEUBiMhIiY9ATQ2fQO2Cg8PCvxKCg8PCgO2Cg8PCvxKCg8PCgO2Cg8PCvxKCg8PBEwPCpYKDw8KlgoP/nAPCpYKDw8KlgoP/nAPCpYKDw8KlgoPAAAABAAAAAAEsASwAA8AHwAvADMAAAEhMhYVERQGIyEiJjURNDYFISIGFREUFjMhMjY1ETQmBSEyFhURFAYjISImNRE0NhcVITUBXgH0ory7o/4Mpbm5Asv9qCk7OykCWCk7O/2xAfQVHR0V/gwVHR1HAZAEsLuj/gylubmlAfSlucg7Kf2oKTs7KQJYKTtkHRX+1BUdHRUBLBUdZMjIAAAAAAEAZABkBLAETAA7AAATITIWFAYrARUzMhYUBisBFTMyFhQGKwEVMzIWFAYjISImNDY7ATUjIiY0NjsBNSMiJjQ2OwE1IyImNDaWA+gVHR0VMjIVHR0VMjIVHR0VMjIVHR0V/BgVHR0VMjIVHR0VMjIVHR0VMjIVHR0ETB0qHcgdKh3IHSodyB0qHR0qHcgdKh3IHSodyB0qHQAAAAYBLAAFA+gEowAHAA0AEwAZAB8AKgAAAR4BBgcuATYBMhYVIiYlFAYjNDYBMhYVIiYlFAYjNDYDFRQGIiY9ARYzMgKKVz8/V1c/P/75fLB8sAK8sHyw/cB8sHywArywfLCwHSodKAMRBKNDsrJCQrKy/sCwfLB8fLB8sP7UsHywfHywfLD+05AVHR0VjgQAAAH/tQDIBJQDgQBCAAABNzYXAR4BBw4BKwEyFRQOBCsBIhE0NyYiBxYVECsBIi4DNTQzIyImJyY2NwE2HwEeAQ4BLwEHIScHBi4BNgLpRRk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<div id="header">
<h1 class="title toc-ignore">Introduction to R demos</h1>
<h3 class="subtitle">Probability density function review</h3>
<h4 class="author">Dr. Joseph P. Yurko</h4>
</div>
<div id="overview" class="section level2">
<h2>Overview</h2>
<p>This markdown quickly reviews important concepts related to working
with probability density functions (pdfs) and cumulative distribution
functions (CDFs). Just a single library is loaded in,
<code>tidyverse</code>, which brings in multiple packages as shown in
the code chunk display below.</p>
<pre class="r"><code>library(tidyverse)</code></pre>
<pre><code>## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.1 ──</code></pre>
<pre><code>## ✔ ggplot2 3.3.6 ✔ purrr 0.3.4
## ✔ tibble 3.1.7 ✔ dplyr 1.0.9
## ✔ tidyr 1.2.0 ✔ stringr 1.4.0
## ✔ readr 2.1.2 ✔ forcats 0.5.1</code></pre>
<pre><code>## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()</code></pre>
<p>This markdown uses functions from the <code>dplyr</code> and
<code>tibble</code> packages introduced in previous examples. However,
it also makes use of functions from <code>tidyr</code> and
<code>purrr</code>. Both of these packages are part of the wider
<code>tidyverse</code> and are imported with <code>dplyr</code>.</p>
</div>
<div id="gaussian-distribution" class="section level2">
<h2>Gaussian distribution</h2>
<p>We will start with the Gaussian or normal distribution. The density
of a Gaussian variable <span class="math inline">\(x\)</span> with
hyperparameters <span class="math inline">\(\mu\)</span> and <span class="math inline">\(\sigma\)</span> is:</p>
<p><span class="math display">\[
p\left( x|\mu,\sigma \right) = \frac{1}{\sigma \sqrt{2\pi}}
\mathrm{exp}\left(-\frac{1}{2} \left(\frac{x-\mu}{\sigma} \right)^2
\right)
\]</span></p>
<p>The <strong>standard</strong> normal density corresponds to a
Gaussian distributed variable with <span class="math inline">\(\mu =
0\)</span> and <span class="math inline">\(\sigma = 1\)</span>:</p>
<p><span class="math display">\[
p\left(x|\mu=0,\sigma=1\right) = \frac{1}{\sqrt{2\pi}} \mathrm{exp}
\left( -\frac{1}{2}x^2 \right)
\]</span></p>
<p>As we will discuss in lecture, if we define a variable <span class="math inline">\(z = \sigma \times x + \mu\)</span>, and <span class="math inline">\(x\)</span> has a Gaussian distribution, the
variable <span class="math inline">\(z\)</span> will have a standard
normal distribution. In this document we will focus on the standard
normal, but because of this transformation we can apply our learning to
a general Gaussian distribution.</p>
<div id="r-functions" class="section level3">
<h3>R functions</h3>
<p>We do not need to code the Gaussian distribution in order to evaluate
it. The <code>*norm()</code> family of functions provides us several
functions for evaluating and working with Gaussian random variables. If
you type <code>?dnorm()</code> into the <code>R</code> console the help
page displays 4 functions, <code>dnorm()</code>, <code>pnorm()</code>,
<code>qnorm()</code>, and <code>rnorm()</code>. The last of these,
<code>rnorm()</code> is the random number generator for Gaussian random
variables. We will use <code>rnorm()</code> extensively throughout this
course. However, within this markdown, we will focus on the other three
functions.</p>
<p>The first of those functions, <code>dnorm()</code>, evaluates the
density function of a Gaussian distribution with <span class="math inline">\(\mu\)</span> equal to the <code>mean</code>
argument and <span class="math inline">\(\sigma\)</span> equal to the
<code>sd</code> argument. By default, all of the <code>*norm()</code>
family functions have <code>mean = 0</code> and <code>sd = 1</code>. So
to evaluate the density of a standard normal variable at
<code>x = 1.15</code> we only need to specify the first argument
<code>x =</code> in the <code>dnorm()</code> function call. The code to
do so is shown in the code chunk below.</p>
<pre class="r"><code>dnorm(x = 1.15)</code></pre>
<pre><code>## [1] 0.2059363</code></pre>
<p>We get the same result if we explicitly set the <code>mean = 0</code>
and <code>sd = 1</code>:</p>
<pre class="r"><code>dnorm(x = 1.15, mean = 0, sd = 1)</code></pre>
<pre><code>## [1] 0.2059363</code></pre>
<p>In the previous code chunks, we passed in scalars to the
<code>x</code> argument of the <code>dnorm()</code> function. We can
also pass in vectors in order to evaluate the density function at many
different <code>x</code> variable values. For example, evaluate the
standard normal density function at -2, -1, 0, 1, and 2:</p>
<pre class="r"><code>dnorm(x = -2:2, mean = 0, sd = 1)</code></pre>
<pre><code>## [1] 0.05399097 0.24197072 0.39894228 0.24197072 0.05399097</code></pre>
</div>
<div id="visualize" class="section level3">
<h3>Visualize</h3>
<p>Using this notation we will evaluate the standard normal density
function over the interval -4.5 to 4.5. The code chunk below creates a
<code>tibble</code> with the variable <code>x</code> which has 1001
elements from -4.5 to 4.5. That <code>tibble</code> is passted into the
<code>mutate()</code> function where the variable
<code>normal_pdf</code> is created by passing the variable
<code>x</code> to the <code>dnorm()</code> function.</p>
<pre class="r"><code>df_gauss <- tibble::tibble(
x = seq(-4.5, 4.5, length.out = 1001)
) %>%
mutate(normal_pdf = dnorm(x))</code></pre>
<p>The standard normal density function is visualized in the code chunk
below using the <code>geom_line()</code> geometric object in
<code>ggplot2</code>.</p>
<pre class="r"><code>df_gauss %>%
ggplot(mapping = aes(x = x, y = normal_pdf)) +
geom_line(mapping = aes(group = 1), size = 1.25) +
scale_x_continuous(breaks = -4:4) +
theme_bw() +
theme(axis.text = element_text(size = 12),
axis.title = element_text(size = 12))</code></pre>
<p><img 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" width="672" /></p>
<p>Looking at the distribution’s shape reveals some important properties
of the Gaussian. First, it is symmetric. Second, it is unimodal, since
there is just one local maximum density value. The center of the
distribution is located at <code>x = 0</code>, which corresponds to the
mean or expected value of the standard normal, <span class="math inline">\(\mathbb{E}\left[x\right]=\mu\)</span>. As shown in
the figure, the maximum density value (the mode) is also located at the
<code>x = 0</code>. Thus, the <strong>mode and mean are the same for a
Gaussian</strong>.</p>
<p>Although it may not be obvious from just look at the figure,
<strong>the mode and mean also correspond to the median for a
Gaussian</strong>. This property occurs for any symmetric unimodal
distribution, not just the Gaussian (as long as the distribution has a
mean). The median is the 0.5 quantile and corresponds to the <span class="math inline">\(x\)</span> value where the probability
<em>mass</em> up to and including that value is 50%. That also means
that 50% of the probability mass is located above (or greater) than the
median. Notice the language used to the describe the median. The median
does not correspond to the value that has 50% chance of occurring.
Remember that the Gaussian distribution is continuous, and thus the
probability that <span class="math inline">\(x\)</span> exactly equals a
specific value is 0. In fact, the density function does not give the
probability, it gives (as the name states) the <em>density</em>. In
order to calculate the probability we must <em>integrate</em> the
density function. Hence why the term <em>mass</em> was used. The
interval we integrate over is the “volume” that contains the probability
mass. The higher the density is within an interval, the more the mass in
concentrated within that interval relative to other intervals.</p>
<p>Let’s make this clear by visualizing the Cumulative Distribution
Function (CDF). In the code chunk below, we pipe <code>df_gauss</code>
into <code>mutate()</code> and call the <code>pnorm()</code> function.
The result is piped into a <code>ggplot()</code> to visualize the CDF
with respect to the <code>x</code> variable.</p>
<pre class="r"><code>df_gauss %>%
mutate(normal_cdf = pnorm(q = x)) %>%
ggplot(mapping = aes(x = x, y = normal_cdf)) +
geom_line(mapping = aes(group = 1), size = 1.25) +
scale_x_continuous(breaks = -4:4) +
theme_bw() +
theme(axis.text = element_text(size = 12),
axis.title = element_text(size = 12))</code></pre>
<p><img 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" width="672" /></p>
<p>What’s going on here? The x-axis is still the standard normal random
variable, <code>x</code>. The y-axis is now between 0 and 1, because the
y-axis gives the probability that the variable will take on a value less
than or equal to the corresponding value on the x-axis. By integrating,
we are “accumulating” the density to calculate the probability mass
“contained” up to that point. That is why on the far left side of the
x-axis (around <code>x = -4</code>) the CDF value displayed on the
y-axis is essentially zero. At the extreme values of <span class="math inline">\(x \leq -4\)</span>, the density is very low, so
integrating over the interval yields a low probability. Why then does
the right hand side of the figure, with <span class="math inline">\(x
\geq 4\)</span>, have CDF values all near 1? The density, as shown in
the PDF figure, is also very low in that interval as well?</p>
<p>Let’s put the PDF and CDF together into a single graphic with
separate facets. In the figure below the CDF is displayed by the plot
shown in the top row, while the PDF is shown by the plot in the bottom
row. The dataset needed to be reformatted or <em>reshaped</em> to a
<strong>long</strong> or <strong>tall</strong> format in order to create
the figure below. The reshaping or <em>pivoting</em> operation is
controlled by the <code>pivot_longer()</code> function. We will discuss
<code>pivot_longer()</code> in more detail another time, but notice that
the <code>starts_with()</code> helper function is used to identify the
columns of interest. The syntax “reads” as “gather all columns that have
names starting with” the pattern <code>'normal_'</code>. The reshaped
long-format data are then passed to <code>ggplot()</code>. The
<code>facet_grid()</code> function is used to create separated subplots
for the CDF and PDF curves.</p>
<pre class="r"><code>df_gauss %>%
mutate(normal_cdf = pnorm(q = x)) %>%
tibble::rowid_to_column() %>%
pivot_longer(starts_with('normal_')) %>%
ggplot(mapping = aes(x = x, y = value)) +
geom_line(mapping = aes(group = name), size = 1.15) +
facet_grid(name ~ ., scales = "free_y") +
scale_x_continuous(breaks = -4:4) +
theme_bw()</code></pre>
<p><img 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" width="672" /></p>
<p>Let’s walk through the figure above. The CDF is calculated by
integrating the PDF over the entire range of the <code>x</code> variable
(known as the <strong>support</strong>). A Gaussian random variable is
unbounded, spanning the whole real line. Thus, we must integrate from
<span class="math inline">\(-\infty\)</span> to <span class="math inline">\(+\infty\)</span>. The PDF shows that for <span class="math inline">\(\left| x\right|>3\)</span> the density is very
low. Thus integrating from <span class="math inline">\(-\infty\)</span>
up to -3 yields very little “accumulated density” or <em>mass</em>. As
we continue to move from -3 to -2, the density increases, yielding an
increasing slope in the CDF, though it is still rather small. Continuing
to from -2 to -1 however, we that the slope of the CDF increases
sharply. The slope from -1 to 0 appears roughly constant in the CDF.
Moving from 0 to +1 reveals that the CDF continues to increase, even
though the PDF reaches its maximum at <span class="math inline">\(x=0\)</span>. As mentioned already, the CDF is
“accumulating” or building up mass via integration. The probability mass
continues to increase at a slower rate than previously because the
density is decreasing, especially between +1 and +2. At approximately
<span class="math inline">\(x=2.5\)</span>, the probability mass
essentially saturates. Continuing to integrate over <span class="math inline">\(x\)</span> yields only a small increase in the
cumulative probably. Thus, even though the Gaussian random variable
exists over the entire real line almost all of the probability mass is
contained within the interval of -3 to +3. This statement carries over
to a general Gaussian variable in the form of -3<span class="math inline">\(\sigma\)</span> to +3<span class="math inline">\(\sigma\)</span>.</p>
</div>
<div id="quantiles" class="section level3">
<h3>Quantiles</h3>
<p>Let’s calculate various quantiles to quantify the statements we made
from visually studying the PDF and CDF. The <code>qnorm()</code>
function allows us to calculate a quantile based on a desired
probability as specified by the <code>p =</code> argument. For example,
the median or 0.5 quantile of the standard normal distribution is:</p>
<pre class="r"><code>qnorm(p = 0.5)</code></pre>
<pre><code>## [1] 0</code></pre>
<p>The result is 0 because, as mentioned already the mean, mode, median
are the same for the Gaussian. The code chunk below adds a horizontal
line on the y-axis of the normal CDF subplot at a probability value of
0.5. Both subplots have a vertical blue line located at median. Notice
that the horizontal line and vertical lines intersect. Hopefully this
makes it clear what the 50th quantile (the median) represents. After
integrating from <span class="math inline">\(-\infty\)</span> to
<code>x = 0</code>, the accumulating probability mass is 50% of the
total probability mass.</p>
<pre class="r"><code>df_gauss %>%
mutate(normal_cdf = pnorm(q = x)) %>%
tibble::rowid_to_column() %>%
pivot_longer(starts_with('normal_')) %>%
ggplot(mapping = aes(x = x, y = value)) +
geom_line(mapping = aes(group = name), size = 1.15) +
geom_hline(data = data.frame(prob_val = 0.5, name = c("normal_cdf")),
mapping = aes(yintercept = prob_val),
color = "red") +
geom_vline(xintercept = qnorm(0.5), color = "navyblue") +
facet_grid(name ~ ., scales = "free_y") +
scale_x_continuous(breaks = -4:4) +
theme_bw()</code></pre>
<p><img src="data:image/png;base64,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" width="672" /></p>
<p>We can make a similar figure to show the 0.95 quantile. The
horizontal red line on the CDF plot is now placed at the y-axis value of
0.95. Likewise, the vertical blue line is located at
<code>qnorm(0.95)</code> on the x-axis in both subplots. For the 95th
quantile, we integrate from <span class="math inline">\(-\infty\)</span>
to 1.645.</p>
<pre class="r"><code>df_gauss %>%
mutate(normal_cdf = pnorm(q = x)) %>%
tibble::rowid_to_column() %>%
pivot_longer(starts_with('normal_')) %>%
ggplot(mapping = aes(x = x, y = value)) +
geom_line(mapping = aes(group = name), size = 1.15) +
geom_hline(data = data.frame(prob_val = 0.95, name = c("normal_cdf")),
mapping = aes(yintercept = prob_val),
color = "red") +
geom_vline(xintercept = qnorm(0.95), color = "navyblue") +
facet_grid(name ~ ., scales = "free_y") +
scale_x_continuous(breaks = -4:4) +
theme_bw()</code></pre>
<p><img 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" width="672" /></p>
</div>
<div id="intervals" class="section level3">
<h3>Intervals</h3>
<p>You have probably heard of the “2-sigma” rule which states
approximately 95% of the probability is contained between <span class="math inline">\(-2\sigma\)</span> and <span class="math inline">\(+2\sigma\)</span>. Notice that in the previous
figure, the 0.95 quantile is not located at 2…it is located at 5.64485.
That is because the 0.95 quantile is calculated by integrating starting
from <span class="math inline">\(-\infty\)</span>. The “2-sigma” rule
however, defines an interval <strong>centered around</strong> the mean.
The left hand side of the integral used to calculate the probability
starts at the 0.025 quantile and the integration ends at the 0.975
quantile. The interval therefore spans 95% of the probability. We could
use a different interval which captures 95% of the probability mass. For
example, the 0.01 quantile to the 0.96 quantile would also cover 95% of
the probability mass. Spanning the 0.025 through 0.975 quantiles though
encompasses a central interval, with the median/mean/mode at its center.
The central 95% interval therefore represents the uncertainty around the
most likely value.</p>
<p>Let’s first calculate the probability mass contained between -2 and
+2 (for the standard normal). We already know that the CDF is evaluated
by the <code>pnorm()</code> function, but since the left hand side
starts at <span class="math inline">\(`-\infty\)</span>, we need to
setup the calculation slightly different. We need to integrate from
<span class="math inline">\(-\infty\)</span> to +2, and then subtract
out the integral from <span class="math inline">\(-\infty\)</span> to
-2. We can perform the calculation quite simply in <code>R</code>, as
shown in the code chunk below:</p>
<pre class="r"><code>pnorm(2) - pnorm(-2)</code></pre>
<pre><code>## [1] 0.9544997</code></pre>
<p>The result 0.9545 is pretty close to 95%. This shows that the
“2-sigma” is an approximation, a pretty good approximation, but still an
approximation. The actual 0.025 and 0.975 quantile values are:</p>
<pre class="r"><code>qnorm(p = c(0.025, 0.975))</code></pre>
<pre><code>## [1] -1.959964 1.959964</code></pre>
<p>If we plug in the actual quantiles to the integral calculation, we
obtain 95% exactly:</p>
<pre class="r"><code>pnorm(qnorm(0.975)) - pnorm(qnorm(0.025))</code></pre>
<pre><code>## [1] 0.95</code></pre>
<p>To visualize the relationship between the integral of the PDF to the
central 95% probability interval, the figure below shades in the area
under the PDF curve between the two quantiles.</p>
<pre class="r"><code>df_gauss %>%
mutate(normal_cdf = pnorm(q = x)) %>%
tibble::rowid_to_column() %>%
pivot_longer(starts_with('normal_')) %>%
mutate(show_area = ifelse(name == "normal_cdf",
NA,
between(x, qnorm(0.025), qnorm(0.975)))) %>%
ggplot(mapping = aes(x = x, y = value)) +
geom_area(mapping = aes(fill = show_area)) +
geom_line(mapping = aes(group = name), size = 1.15) +
geom_hline(data = data.frame(prob_val = c(0.025, 0.975), name = c("normal_cdf")),
mapping = aes(yintercept = prob_val),
color = "red") +
geom_vline(xintercept = qnorm(c(0.025, 0.975)), color = "navyblue") +
facet_grid(name ~ ., scales = "free_y") +
scale_fill_manual("Area under the density curve for probability interval",
values = c("TRUE" = "red",
"FALSE" = "grey",
"NA" = NA),
labels = c("TRUE" = "included in integral",
"FALSE" = "outside integral",
"NA" = NA),
na.value = NA) +
scale_x_continuous(breaks = -4:4) +
theme_bw() +
theme(legend.position = "top")</code></pre>
<p><img src="data:image/png;base64,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" width="672" /></p>
</div>
</div>
<div id="beta-distribution" class="section level2">
<h2>Beta distribution</h2>
<p>Many of the concepts described for the Gaussian can be carried over
to other distributions. Especially how to interpret the CDF and relate
the PDF to the CDF through integration. We will now apply those
understandings to the Beta distribution.</p>
<p>The Beta distribution is a continuous distribution, but unlike the
Gaussian it is bounded between 0 and 1. Also, the Beta distribution can
take a wide variety of shapes based upon its hyperparameters. The Bishop
book denotes these hyperparameters as <span class="math inline">\(a\)</span> and <span class="math inline">\(b\)</span>, but in <code>R</code> they are
referred to as <code>shape1</code> and <code>shape2</code>,
respectively.</p>
<p>As you will see in lecture, the Beta distribution can be used as the
prior distribution for an unknown event probability, <span class="math inline">\(\mu\)</span>. Within this markdown we will denote
that variable simply as <code>x</code>. Doing so allows us to be
consistent with the input arguments to the <code>*beta</code> family of
functions. This document therefore represents a more general notation
consistent with many references discussing probability distributions.
The Beta density function on the variable <span class="math inline">\(x\)</span> given the hyperparameters <span class="math inline">\(a\)</span> and <span class="math inline">\(b\)</span> is proportional to:</p>
<p><span class="math display">\[
p\left( x|a,b \right) \propto x^{a-1}\left( 1 - x\right)^{b-1}
\]</span></p>
<div id="r-functions-1" class="section level3">
<h3>R functions</h3>
<p>The <code>*beta()</code> family of functions are
<code>dbeta()</code>, <code>pbeta()</code>, <code>qbeta()</code>, and
<code>rbeta()</code>. The <code>rbeta()</code> is the random number
generation function for beta distribution values bounded between 0 and
1. Compared with the <code>*norm()</code> family of functions, the
hyperparameters, <code>shape1</code> and <code>shape2</code> do not have
default argument values. The user <strong>must</strong> supply the
hyperparameters for the functions to execute.</p>
</div>
<div id="visualize-1" class="section level3">
<h3>Visualize</h3>
<p>Let’s start out evaluating the density function <code>dbeta()</code>
using the <span class="math inline">\(a\)</span> and <span class="math inline">\(b\)</span> hyperparameters set to 2 and 3,
respectively. We will discuss how to interpret these hyperparameters in
lecture. The mean for this Beta is 0.4 since the expected value of the
Beta distribution has the following formula:</p>
<p><span class="math display">\[
\mathbb{E}\left[x|a,b\right] = \frac{a}{a+b}
\]</span></p>
<p>The code chunk below stores a vector of values between 0 and 1 and
then calculates the Beta density function at each element.</p>
<pre class="r"><code>df_beta_01 <- tibble::tibble(
x = seq(0, 1, length.out = 201)
) %>%
mutate(beta_pdf = dbeta(x, shape1 = 2, shape2 = 3))</code></pre>
<p>Plot the Beta density function using are given hyperparameters.</p>
<pre class="r"><code>df_beta_01 %>%
ggplot(mapping = aes(x = x, y = beta_pdf)) +
geom_line(mapping = aes(group = 1), size = 1.25) +
scale_x_continuous(breaks = seq(0, 1, by = 0.2)) +
theme_bw()</code></pre>
<p><img 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" width="672" /></p>
<p>Notice how in the figure above, the particular Beta distribution is
<strong>not</strong> symmetric, but it is unimodal. Because of this, the
mean will not correspond to the mode. To make this clear the code chunk
below plots the same Beta distribution, but marks the mean value with a
vertical blue line. The figure below also displays the median value with
a dashed vertical orange line. The median is calculated using the
<code>qbeta()</code> function (which has similar behavior as the
<code>qnorm()</code> function, except for hyperparameter changes).</p>
<pre class="r"><code>df_beta_01 %>%
ggplot(mapping = aes(x = x, y = beta_pdf)) +
geom_line(mapping = aes(group = 1), size = 1.25) +
geom_vline(data = tibble::tibble(stat_val = c((2 / (2+3)),
qbeta(0.5, shape1 = 2, shape2 = 3)),
stat_name = c("mean", "median")),
mapping = aes(xintercept = stat_val,
color = stat_name,
linetype = stat_name),
size = 1.15) +
scale_color_manual("Statistic",
values = c("mean" = "navyblue",
"median" = "darkorange")) +
scale_linetype_manual("Statistic",
values = c("mean" = "solid",
"median" = "dashed")) +
theme_bw() +
theme(legend.position = "top")</code></pre>
<p><img 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" width="672" /></p>
<p>Let’s demonstrate the impact of the hyperparameters on the Beta
distribution shape. The code chunk below sets the hyperparameters to be
<span class="math inline">\(a = 1.5\)</span> and <span class="math inline">\(b = 4.5\)</span> and then plots the Beta density
function. Colored vertical lines give the mean and median, as in the
previous figure. Try out a different set of hyperparameters and include
the mean and median as colored vertical lines.</p>
<pre class="r"><code>tibble::tibble(
x = seq(0, 1, length.out = 201)
) %>%
mutate(beta_pdf = dbeta(x, shape1 = 1.5, shape2 = 4.5)) %>%
ggplot(mapping = aes(x = x, y = beta_pdf)) +
geom_line(mapping = aes(group = 1), size = 1.25) +
geom_vline(data = tibble::tibble(stat_val = c((1.5 / (1.5+4.5)),
qbeta(0.5, shape1 = 1.5, shape2 = 4.5)),
stat_name = c("mean", "median")),
mapping = aes(xintercept = stat_val,
color = stat_name,
linetype = stat_name),
size = 1.15) +
scale_color_manual("Statistic",
values = c("mean" = "navyblue",
"median" = "darkorange")) +
scale_linetype_manual("Statistic",
values = c("mean" = "solid",
"median" = "dashed")) +
theme_bw() +
theme(legend.position = "top")</code></pre>
<p><img 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" width="672" /></p>
<p>Rather than plotting the distributions in separate figues, let’s use
a separate subplot for each. To accomplish this, we will need to combine
the two datasets used to create the two previous figures. That is an
easy operation to do, but let’s generalize our setup such that we can
easily try out arbitrary hyperparameter values. We will first define a
function, <code>make_beta_pdf()</code>, which creates a
<code>tibble</code> consisting of the beta density evaluated at specific
<code>x</code> values, based on the user supplied hyperparameter values.
Notice that in <code>make_beta_pdf()</code> I did not use the
<code>return()</code> function. By default, <code>R</code> will
therefore return the last object within the function, which in this case
is a <code>tibble</code> consisting of <code>x</code>, the Beta density
function value, <code>beta_pdf</code>, and the two hyperparameters which
defined the distribution.</p>
<pre class="r"><code>make_beta_pdf <- function(shape_1, shape_2, vector_length)
{
tibble::tibble(
x = seq(0, 1, length.out = vector_length),
beta_pdf = dbeta(x = x,
shape1 = shape_1,
shape2 = shape_2)
) %>%
mutate(a = shape_1,
b = shape_2)
}</code></pre>
<p>The <code>make_beta_pdf()</code> function can be called just like any
function in <code>R</code>. We just pass in the arguments we wish to
use. To demonstrate, call <code>make_beta_pdf()</code> with the
following arguments <code>shape_1 = 2</code>, <code>shape_2 = 3</code>,
and <code>vector_length = 3</code>. Pipe the result of the function call
to the <code>glimpse()</code> function. As shown below, the resulting
dataset consists of 3 observations of 4 variables. The values of those
variables are printed below. The hyperparameters are simply repeated
over all of the rows.</p>
<pre class="r"><code>make_beta_pdf(shape_1 = 2, shape_2 = 3, vector_length = 3) %>%
glimpse()</code></pre>
<pre><code>## Rows: 3
## Columns: 4
## $ x <dbl> 0.0, 0.5, 1.0
## $ beta_pdf <dbl> 0.0, 1.5, 0.0
## $ a <dbl> 2, 2, 2
## $ b <dbl> 3, 3, 3</code></pre>
<p>Next, we will evaluate the Beta density function for several sets of
hyperparameters. We could use a for-loop to accomplish this task, but
instead I use the use the <code>purrr</code> package to perform the
iterations for me. You may not be familar with <code>purrr</code> or
functional programming in general. We will cover <code>purrr</code>
later in this course. For now, it’s ok to view the use of
<code>purrr</code> as managing the for-loop for us.</p>
<p>Before iterating though, we have to specify what we will iterate
over. The code chunk below creates a <code>tibble</code> which stores
three sets of hyperparameters, named <code>hyper_params</code>.</p>
<pre class="r"><code>hyper_params <- tibble::tibble(
a = c(2, 1.5, 8),
b = c(3, 4.5, 4)
)</code></pre>
<p>Now iterate over the three different hyperparameter sets using the
<code>purrr::map2_dfr()</code> function. Store the result as
<code>beta_results</code>.</p>
<pre class="r"><code>beta_results <- purrr::map2_dfr(hyper_params$a,
hyper_params$b,
make_beta_pdf,
vector_length = 201)</code></pre>
<p>Pipe <code>beta_results</code> into the <code>glimpse()</code>
function to get an idea about the structure of the dataset. As shown
below, there are 603 rows, which equals three times the specified value
of the <code>vector_length</code> argument. Thus, the
<code>purrr::map2_dfr()</code> function “stacked” the three generated
<code>tibble</code>s on top of each other.</p>
<pre class="r"><code>beta_results %>% glimpse()</code></pre>
<pre><code>## Rows: 603
## Columns: 4
## $ x <dbl> 0.000, 0.005, 0.010, 0.015, 0.020, 0.025, 0.030, 0.035, 0.040…
## $ beta_pdf <dbl> 0.0000000, 0.0594015, 0.1176120, 0.1746405, 0.2304960, 0.2851…
## $ a <dbl> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2…
## $ b <dbl> 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3…</code></pre>
<p>We can now plot each of the three separate Beta distributions by
specifying the facets based on the combination of the <code>a</code> and
<code>b</code> variables in the <code>beta_results</code> object.</p>
<pre class="r"><code>beta_results %>%
ggplot(mapping = aes(x = x, y = beta_pdf)) +
geom_line(mapping = aes(group = interaction(a, b)),
size = 1.15) +
facet_grid(. ~ a + b, labeller = "label_both") +
theme_bw()</code></pre>
<p><img 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" width="672" /></p>
</div>
<div id="cdf" class="section level3">
<h3>CDF</h3>
<p>As we did with the Gaussian distribution, let’s now relate the Beta
density function with its Cumulative Distribution Function (CDF). We
will evaluate the Beta CDF with the <code>pbeta()</code> function in
much the same way that we evaluated the <code>pnorm()</code> function.
To facilitate comparing the three different sets of hyperparameters, we
will create a function <code>make_beta_cdf()</code> which calls
<code>pbeta()</code> at the same conditions we evaluated
<code>dbeta()</code> with. First, create the function:</p>
<pre class="r"><code>make_beta_cdf <- function(shape_1, shape_2, vector_length)
{
tibble::tibble(
x = seq(0, 1, length.out = vector_length),
beta_cdf = pbeta(q = x,
shape1 = shape_1,
shape2 = shape_2)
) %>%
mutate(a = shape_1,
b = shape_2)
}</code></pre>
<p>Next, iterate over the same set of Beta hyperparameters we used
before and save the results to <code>beta_integrate</code>.</p>
<pre class="r"><code>beta_integrate <- purrr::map2_dfr(hyper_params$a,
hyper_params$b,
make_beta_cdf,
vector_length = 201)</code></pre>
<p>We need to merge or join the <code>beta_results</code> and
<code>beta_integrate</code> datasets in order to plot the Beta density
functions and CDFs as subplots of a single graphic. Although we have not
walked through joining datasets before, the operation is straightforward
to do in this case. We will use the <code>left_join()</code> function
from <code>dplyr</code> and instruct the function to join
<code>by</code>: <code>x</code>, <code>a</code>, and <code>b</code>. The
merged dataset is then reshaped to long-format using
<code>pivot_longer()</code>. Finally the reshaped dataset is passed into
<code>ggplot()</code> to give the CDF on the top row of subplots, and
the density functions on the bottom row.</p>
<pre class="r"><code>beta_results %>%
left_join(beta_integrate,
by = c("x", "a", "b")) %>%
pivot_longer(starts_with('beta_')) %>%
ggplot(mapping = aes(x = x, y = value)) +
geom_line(mapping = aes(group = interaction(name, a, b)),
size = 1.15) +
facet_grid(name ~ a + b,
labeller = "label_both",
scales = "free_y") +
theme_bw()</code></pre>
<p><img 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" width="672" /></p>
<p>We can walk through the figure above, just as we walked through the
Gaussian CDFs and PDFs. A key difference between the Beta and Gaussian
though is the Beta is bounded between 0 and 1. Thus, the integration of
the Beta density function <strong>starts</strong> at <span class="math inline">\(x = 0\)</span>, not at <span class="math inline">\(-\infty\)</span>. The Beta density is integrated
to <span class="math inline">\(x = 1\)</span> and not <span class="math inline">\(+\infty\)</span> because by definition the Beta
distribution “stops” at <span class="math inline">\(x = 1\)</span>.
Thus, at <span class="math inline">\(x=0\)</span> the Beta CDF equals 0
and at <span class="math inline">\(x=1\)</span> the Beta CDF equals
1.</p>
<p>Comparing the horizontal subplots allows us to compare how the rate
of increase in the accumulated probability mass based on the density
shape. In the right column of subplots, the density is roughly at zero
until <span class="math inline">\(x \approx 0.25\)</span>. The CDF
therefore remains at essentially zero since there is so little mass
being accumulated integrating over <span class="math inline">\(x=0\)</span> up to <span class="math inline">\(x
\approx 0.25\)</span>. Moving to the middle and then finally the left
column of subplots, the density increases closer and closer to zero.
This causes the probability mass to accumulate at a faster rate
integrating from <span class="math inline">\(x=0\)</span> to <span class="math inline">\(x \approx 0.25\)</span>. That is why the slope of
the CDF of the left most distribution is higher than the slope of the
middle and right distributions.</p>
</div>
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