{
"cells": [
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"metadata": {},
"source": [
"# CS 237 Spring 2021, HW 09 \n",
"\n",
"#### Due date: Thursday April 8th at Midnight (1 minute after 11:59pm on 4/8) via Gradescope (with a 6 hour grace period)\n",
"\n",
" Late policy: You may submit the homework up to 24 hours late for a 10% penalty. Hence, the late deadline is Friday 4/9 at Midnight (with a 6 hour grace period). \n",
"\n",
"#### General Instructions\n",
"\n",
"Please complete this notebook by filling in solutions where indicated. \n",
"\n",
"For full credit, please take careful note of the following requirements:\n",
"\n",
"- Do NOT use any HTML tags in your notebook, as Gradescope will ignore them;\n",
"\n",
"- Do NOT answer questions by including images, as Gradescope will ignore them; and \n",
"\n",
"- You MUST \"Restart and Run All\" from the Kernel menu before submitting to Gradescope.\n",
"\n",
"**Any assignments which do not follow these requirements will not receive full credit.** \n",
"\n",
"\n",
"\n",
"There are 8 problems on this homework, the last of which is a \"lab\" problem; many will involve using Python to solve, using the functions in the next code cell. Each problem is worth 7.5 points. An introductory video will be posted on YT for\n",
"the analytical problems, and the lab problem will be covered Friday in lab. "
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n"
]
}
],
"source": [
"# Here are some imports which will be used in code that we write for CS 237\n",
"\n",
"import matplotlib.pyplot as plt # normal plotting\n",
"import numpy as np\n",
"\n",
"from math import log, pi, log, floor, ceil, sqrt # import whatever you want from math\n",
"from random import seed, random\n",
"from collections import Counter\n",
"\n",
"%matplotlib inline\n",
"\n",
"from scipy.special import comb\n",
" \n",
"def C(N,K): \n",
" return comb(N,K,True) # just a wrapper around the scipy function\n",
"\n",
"\n",
"# Here are the basic statistical functions we will use from numpy\n",
"\n",
"from numpy import mean, var, std, median\n",
"\n",
"L = [2,4,3,6,4,5]\n",
"\n",
"# mean value\n",
"\n",
"mean(L) \n",
"\n",
"\n",
"# Variance\n",
"# ddof = delta degrees of freedom, default is 0\n",
"\n",
"# population variance\n",
"var(L) \n",
"\n",
"# sample variance\n",
"var(L,ddof=1)\n",
"\n",
"# Standard deviation\n",
"# ddof = delta degrees of freedom, default is 0\n",
"\n",
"# population standard deviation\n",
"std(L) \n",
"\n",
"# sample standard deviation\n",
"std(L,ddof=1) \n",
"\n",
"# Median\n",
"\n",
"median(L) \n",
"\n",
"# Random sampling of `size` elements from list with or without replacement\n",
"\n",
"np.random.choice(L,size=1,replace=True)\n",
" \n",
"# Scipy statistical functions\n",
"\n",
"from scipy.stats import norm, binom, expon, geom, poisson, gamma, nbinom, bernoulli \n",
"\n",
"# https://docs.scipy.org/doc/scipy/reference/stats.html\n",
"\n",
"#### Normal Distribution #####\n",
"\n",
"###### Note that in this library loc = mean and scale = standard deviation #####\n",
"\n",
"# Examples assume random variable X (e.g., housing prices) normally distributed with mu = 60, sigma = 10\n",
"\n",
"# Probability Density Function (really only useful for drawing the curve)\n",
"# f(x) = P(X == x)\n",
"\n",
"norm.pdf(x=50,loc=60, scale= 10) \n",
"\n",
"# Cumulative Density Function\n",
"# F(x) = P(X < x)\n",
"\n",
"# Example: Percentage of houses less than 50K. \n",
"norm.cdf(x=50,loc=60,scale=10) \n",
"\n",
"# Example: Find P(60
(A) \n", " What is the probability that a randomly-selected individual has a height less than 66 inches?
\n", " \n", "(B) What is the probability that a randomly-selected individual has a height more than 72 inches?
\n", "\n", "(C) What is the probability that a randomly-selected individual has a height between 66.5 and 71 inches?
\n", "\n", "(D) What is the maximum height for a person to be in the bottom 1% of the population in terms of height?
\n", "\n", "(E) To characterize the \"middle 50%\" of the population in terms of the standard deviation, give the value $k$ in this formula:\n", " \n", "$$P( | X - \\mu_X | < k\\cdot\\sigma_X ) = 0.5.$$\n", "\n", "Note that this does not depend on the exact values for $\\mu$ and $\\sigma$ given in this problem. \n", "
\n", "\n", "Hint: peruse the functions from the `norm` library given in the first code cell above. \n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Solution:**\n" ] }, { "attachments": { "Screen%20Shot%202020-03-20%20at%205.33.58%20PM.png": { "image/png": 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OLd0+vU8GOENOI1ljfRN7Uw+zYPNoizjLRKsT1sk2KbZpdqfs0xySHGOcfJ3tXPT2aboa7Hc5EHUwx+0WqdW9y6PD875XofdhH0dfaT9KvwX/voCGwPKgguCMkIRQ8iFXslYYd9ha+FDEzcjkKPdo/RjpWP7DnEdYjzLG0RzDHFuOf3e8K+F2Yk5S1In9ySYn9VLMUklpx9OvnXp8euLM54ylsyuZS+e+Zy1mf8pZyP18/ucFmnyVguDC0os9l6Yuz1+Zufqm6GVxf8mTa02ljde7yj7d4K3YX1l482U1wy2L2ynw7rV6X7LGs7agbqAB/UC+8eDDE02lzY0tTY9utJ5tO9oe1RH/OKPz4pPip5e6zjyL6LZ9LtGD6hnrvdOX3u8/YP1Cf1B/yHrYfSRiNOnlybGjr7xf646zjS9M1L85Oen0VuId7t37qbbpizOH3mvNUs4OzhXPH/vg99FzwfdT0OfQL6GLoV/J3yK/x/yIWvJbNlyhXrn7U//ns1WX1U+/+tYpN8a2518MtEOm0CjCC4lBZqDEUL3oWIwUZh57DeeLl8KvErooLlNGEW2oZKmpqJdpXtK20JXTZzEcZfRhsmFWZxFhZWRdZ5tjH+Bo4qziKuYu4Mnlzd6TwZfMHylAEtQX4hH6Kdwtclk0TMxInFcCITEvOSL1RLpB5oZsnly8vJuCiiJGsVcpR9lJhVXlpepFNc+9suoY9QmNGs0MLV9tPR1BXRo9oPddf9Zg2PCBUa6xl4mAyaRpnpmlOda8zSLR0tiKxeqDdZNNlq2vnZo90X7C4abjEScTZ0bnNy5l+0Lg8391/8MD8Qd13XBu/aRC9wCPvZ6UnmNe170P+Sj7rPs2+8X7awWAgJbA40G6wajgjpATodqhPw9VkJ3hM7s83DL8R0Re5N7Iiaj4aM7ohzFusUyxY4crjiQedYoTjls+1hafddwnQS9RNInlBEUySP5xcirleWp12ql00in509jTY2duZaSdDcg0PEd37nHWvqyF7Ngc7Vyd8ykXcPlpBdMXWS/JXla5onJVoUiqWLiE9xprKe11Qhm+nBqOJPVKt5snq25Wv7i1fkf4rsu9c/f7axnqnOsLG0Ya0Q9Fmgyb3VuOPbrU2tT2pn3zMW+n7hOfp6e6bj8b7t7oEend13e+f+KF7ODpoc8jtqP1Y7yvcsal3lC9jZpOn4v5ZPFtedV6a/53vvdtFYwiAFlwnulwGq7zAGTWwnnmAwCYCQBYEQGwUwGIk1UAYVgFoIATf88PCE48cXDOyQS4gQiQhzNNM+ACZ83RIBXOKCtBExgA78E6RAeJQFpwfhgGnYbzwQ5oCgEheBE6CE/ESTjLG0D8QvIhzZGxyDLkCAqHUkUFoYpRL9F0aFM4I2vDQBgtTDymFYvGmmDPYkdxvLhAXD0ei3fEl+F/EcwJVwkrFBYUZZQoSnfKNqIAMZX4mcqOqhHOdDJpAM0hmmlaZ9peOgO6h/TK9DUMqgxtjDaMU0wRzBjmXBZBljpWC9Y5thR2GfYpjsuc7lxiXD+5H/Pk8HrukefD8L3ivyuQIRgoZCosJkIUWRQdEnsgfkkiTtJVSkWaQXpR5rnsDblUeV8FE0VJJUalTeVPKhOqA2pdezvU2zU6NXu0xrTndJb1gD4G3udwRjhjvAmlKYMZr7m8hYVlsFW2daPNjB3RXt7B2fGo0xXndpdZV4r90gccDh5xKyH1uP/05Pey9T7h0+j7y1834ELgarBHyMAhA3JjuHxEdZRE9O3YvYf7joYc44gfTshOMjuxfDI7VTyt45TXGcaMN5nPs8ZzNvN48lUKzS4dvBJTdKVk7LpE+ZVK6arJ21fvHailqK9q3N8s1srdYfCkqJuyV7h/eTBzRPhl/+tLb86/G3jvNr/6ie5L5TfwQ3pZZWVzNe1X3drg+oON4t+hm0rb+we0/c2BDrADQSALNIE5cAVBIA5kghJQD3rBDNiAmCApyATyhhKhIugR9A6BQgghzBBkRD6iDfEFyYE0RR5BViOnUWwoG1Q6qgMNodXRh9EP0OsYTUwi5imWBuuMvYb9htPGZeHe49XwWfgFggE85+sUThT34EyYTDlIVCFeoaKgiqaapXam7qExoGmh1aBtptOl66K3pR+HM9NfjBlMokzPmA+xMLHUsFqzvmeLYSeyl3BocUxzZnKZcFNxj/Pc5T2zx49Ph5+F/6PAQ8GzQt7COiIConRiOHG0BE6SSopOmlYGJ7MqOyc3It+l8EjxkVKX8iuVb2pUe6XVrTX8NMO1yNq+Ok66hnoq+vIGyoaGRgeN40yumnaaLVqwW+pbBcBnWrbtebsc+2yHK47NTl9dFPbFuz4/wHUw3K3Xnc/D2zPH6753j8+075o/U4BcoF1QZHB+SEvoBzJzmEF4ZMT1yLFomhjz2IzDo0cF444emzruk0iT1JUcnoJJPZmOOpVyhj2jLTMhyylH97zaBbUCtYsql0Wuoooel0SWsl9/WO5ewVg5XtVxq/fO0n2Z2iP1zxqpm/RayK2l7fOdOk/vdMv0FPaND/wY/Do8Ozo1Nvf6xxvoLWGKYYZ/1mg+d0HpS9r30pXA1Z61pPW2jR+/V7fnHwGvflrABSSABrAG3uAoyAW3QDf4AOEhMcgcIkN5UAv0AcGE0EOEI0oRY0hapDEyCdmC3ECpoWJRDah1tDY6DT2CEcEcx4xjNbBFOBwuBDeIV8FfJCAI/oQhCj2KB5QqlI+IVsT3VAnUvNQtNK40y7Rn6STontMHMxAZyhh1GF8zxTBzMfewnGF1Z9NhF+Vg4FjjHOeq4z7HE8Rrtkeaj4Ufw78q8FXwi9B34Q1RKjF+cS0JN8l4qYvSdTIvZL/LsykYKyYotalQqrqq3VLHwnfVJu09Oll6TPpVhi7GtCb9ZvkWIVb2NrK2Y/YuDt1ORs4v9nm7/jyQ6AaRQt2HPJW8Cn3wvsf9CQHFQeYhILSWHBLOFdEWFRHjefhzXEl8zPHhhPUkxAlcMs1JuZSw1MF0+1PzZ1LOSma+zErJUcv9mleef6CQcPH6ZaUrD4s0i1uu6ZV2lVmVD1bYVfZVGVTX3xa+c/4e7v7RmvW61AbBB30PE5oVW+ZbC9stH6M6HzwNeybWPd1zqc9pgOHFwFDGiMno5ljla8vxuTcRkxvvEqaRMwmziLnED6iPxxY+fzb4ErN48evpbxHf9b6v/LixZLH0atl3eXklcmX+p+vP3lXd1YpfxF+hvwbWFNby1r6uG68Xra9t2G3c/I387fS7chPatN+8sTX/Yd5ystvHB0SpAwB6YnPzuyAA2HMAbGRubq4VbW5uFMPJxmsAWgJ3/kPaPmtoACh8s4W6RIfi//1fzv8B7B3fj0cqVUcAAAGdaVRYdFhNTDpjb20uYWRvYmUueG1wAAAAAAA8eDp4bXBtZXRhIHhtbG5zOng9ImFkb2JlOm5zOm1ldGEvIiB4OnhtcHRrPSJYTVAgQ29yZSA1LjQuMCI+CiAgIDxyZGY6UkRGIHhtbG5zOnJkZj0iaHR0cDovL3d3dy53My5vcmcvMTk5OS8wMi8yMi1yZGYtc3ludGF4LW5zIyI+CiAgICAgIDxyZGY6RGVzY3JpcHRpb24gcmRmOmFib3V0PSIiCiAgICAgICAgICAgIHhtbG5zOmV4aWY9Imh0dHA6Ly9ucy5hZG9iZS5jb20vZXhpZi8xLjAvIj4KICAgICAgICAgPGV4aWY6UGl4ZWxYRGltZW5zaW9uPjY4ODwvZXhpZjpQaXhlbFhEaW1lbnNpb24+CiAgICAgICAgIDxleGlmOlBpeGVsWURpbWVuc2lvbj4xNTU8L2V4aWY6UGl4ZWxZRGltZW5zaW9uPgogICAgICA8L3JkZjpEZXNjcmlwdGlvbj4KICAgPC9yZGY6UkRGPgo8L3g6eG1wbWV0YT4KyUzMTAAAQABJREFUeAHtnQm8V8P//98pSkmFLH0t2XdCX3sbQrILKVlCKFvIWpYoRFRkX7LLTqkQZd+yJZQ12SX7kpTP/zzn953Pf+6557Pfe/Ppvt6Px71nm5kz85w5c97znvecT50ffvghZRIREAEREAEREAEREAERKBMCi5VJPpVNERABERABERABERABEXAEpMCqIYiACIiACIiACIiACJQVASmwZVVdyqwIiIAIiIAIiIAIiIAUWLUBERABERABERABERCBsiIgBbasqkuZFQEREAEREAEREAERkAKrNiACIiACIiACIiACeRBIpXJ/uCmfMHncSkFyEChZgd1zzz3twQcfzHGb2n35r7/+suOOO67KIHzwwQf21ltvVUhv1KhR9ueff1Y4928/gMstt9xSY9mcNGmSffTRRzV2v3xvdMghh+QbtKRw1X0f6vPYY48tKY/VFTmeN57H3377rbpul1e6X375pZ155pl5hU0K9Ouvv9pjjz1W4VIpbfySSy6x6dOnV0jPH/Tp08d++eUXf6jtv5DA8ccfb3Pnzi06ZzfddJNNmTIlMf5dd92VeD7fk88884x999136eCzZ88uqe2nE/rfTtI7MR6m1GPeufvuu6/tsMMO1qZNG+vZs6d98803FZJ99dVXbe+997a2bdvajjvuaLfddluF6/Q5vXr1sm222caOPPLISn3QPffcY4888kiFOIUeoDxfeuml1rlzZ3vvvfcqRa/uuqh0w2o8UZIC+/bbbxsNMV5J1Zjfskz6n3/+sffff7/K8j5t2jR76aWXKqS3+OKLWzmO+urWrVuhHNV5wL3+jYyqsm1k41fd94FtJgUoW75q4lo8bx9//LEtWLCgJm6d8R4o1Z999lnG67kuoFDeeeedFYKV0sY///zzjIPgDz/8cKHzqlBQHVQiwOB8/vz5lc7ne4J3+c8//5wY/Iorrkg8n+/JRx991L766qt0cPL56aefpo9L3Ul6J5aaZhgftkcddZRdeOGFxiDxueees3322ccpoz7c1KlT7cQTTzRYcZ0yjxs3roKRZuTIkbbpppu69/cGG2xg11xzjY9uc+bMseuuu8522WWX9LlidlCi0c0eeugh4x5xqe66iN+vOo9LUmAffvhhGzBggGv08ZFIdWZaaVcm0L17d2vYsGHlC//iM/Xr17fqtgqGxWdUvPbaa4entC8CixQBtfFFqjpVmH8JgbXWWsuefvrpCgrhHnvsYV9//XXa6n311Vc7y+fqq6/uct2oUSOnkF555ZX2999/u3OTJ0823tUI2xdeeMHt82/w4MHOKt2gQYP0uWJ2sHT/97//tSWWWKKY6GUVp2gFFuvF2LFjnTm9S5cubrQRlvzFF1+0MWPGuFEAZnfM6WeffbbNmzfPmciJgxnen/NxmQYfOHCgderUyZniw6kLRihDhgwxRjqY7zt06GBdu3Y1pg+8fP/993b66ac78zn3vffee41RTzjS8WFpVCNGjDDcIPi7/PLL7YEHHrC+ffu6IDfeeKNheWCam/x4SzMjx379+rlz5GHo0KEVLHtYoQ4//HDbeeed3TZuxj/11FN9FtJbyvXTTz+5Y9gylQAjuFHGGTNmuGvcixHezTffbN26dbOJEye68+eff7798ccfbp98v/vuu3bVVVc5DuSRsoVC3ZE+0wynnHKKS4dpwm+//TYM5va5F3xgwBQx1isvTGNSh5SVfDL68+LbAO3ggAMOcPV1wgknpKciaQsMgLxgJYMxUzDc6+KLLzasVF4y1Ue2/Pm4bGkLjEyRXHlzgYJ/2cpJMDoi6px88zd+/PggtrlROwzgRPuinYZCp8N0MteJP2HChPByen/mzJlu1E8Y6oS2iYXfyyeffOKuk87BBx9sWCZCyXUfykG7ot1RV/GBKVY62gnXST/TlGN4T/aLrdswHcpJG/Bt8bLLLqtgcSo2b9wDq4qvH/qfsN3l6lPI1w033ODyRd7iVtGwDIXuZ2pXtA/q4fnnn3f1xUsSKaWNF5K3bKzzebay9fPkgz4SCzP9Gv0X07fE6d+/f/oZo54yuTXwvNI+6N+IT1v21kX/HsGqBkOuewUjWzsI+WRLnzyH0+X00bQPLzwLJ510kj/M2ndk6vN4V/Ceox/gPRfvb3K1SSygtBn4kAbKV9jmfeZ419Ef0OezPeaYY/wly9YG0oGiHfpF3jf0b6SB64yXbO/yXGXwaWR6J+bT5/D80B/TX/I+9O9Tn3a4bdy4cXjo3re0SQwx8OTdt+2221YI06RJE3fO95P0JUsttZQLQ3q+Tb755pvu3Us+ckm2clGnvOtvvfVWxxoFO5TqrovwXjWyz0/JFvMXKSWpaATh4kadSyoyi1dIJ/KnSTVv3jx1zjnnpKIGm4oqLhW98FLrrrtu6qyzzkp98cUXqegBSEXKSioym6fjtm/fPjVs2LBU1AGkoocnFTWq1KBBg9z1SClLRZWfil40qejF7NKMXuCpyJ/EXY86ptRWW22Vijpxd0z6e+21VyryOUlFnVX6Hr68J598cirqBNy9yF/U8aRat26dojyEiZRkV66os0m98cYb7lzUSFObbbZZKnogU9wverDd/SPF112PlNXUmmuumYo68XT47bffvgIfrvs8+G3UcFOUj+NDDz00FXXgLm3uETVGd0+uRdMwqaiRpqKOPDVr1qxUpGC4OJQbXoQh39wDNnCk7FyPfGvcdfLK/Xz4aErBcY1GmK5MPk9sIyt7KhpppqIHwcWNfO5S0VSK2ydvlC3qZF28qDNKbbjhhqnXXnvNXfdtIFJwXV5Jo3fv3qkzzjjDXacsYbshHG2EeqNc1Ptuu+3mwvpyET6sj2z5C8vBPnUdDQzyylsYN1c5ab/kM+qkXNpsaaeRMumOo6kc10aigY07pj6pj2jKzh23bNkyFflVpaLO0x3Dj/jR9LI7DvNCW3/iiSfcea5HA4pUNKp3x9Egx9U79Ugc2iDtwLerXPfhmaZtR0q+q0/yTXyfD9o6x9G0mLtOOalvn+94fYb5LqZuw/jsn3baaamjjz7atcVooJWKlJJUNGXnylpo3sLnhXLSjuFHnUSWkHTfRt0TNlufQruiHmjf9HWRQpGKBswuX/EyhMfw23XXXTOGy9aueD4iNyLXbugHYE/axbZx4kbKRSpSvl3/Rx8Y/lHPMCZcLta5nnvSyNbPc522Sl8cKVbp+1K2SGl1bY9+bfjw4aloMF+JH2xox9dee62rE+qFtkJ/T9o8D6RPX0Jf6Pu2bO2AeP4vV/qRouby7cPzDuO58cfR9LJ7L3GcrY65nvQO4l0FmzvuuMOxoD4ixYSVRa6fJV6uNslzEyluKZ4jyhP5TLr49913XzqfpMPzQPuCF1v6Zs7nagOE8X/EoW3xniEN0sz1LidurjL49DO9E/PpcyiX70/JE+2GftCnHd/yLn322WfdO5m+ODISubDEpU3Hw3N87rnnpqIBjLvG8+7762jQ4XQZeNDHvP76644P+fHvjqT0spULFrR72ME6Hr+66yJ+v+o+LtoCy8ItRn7Iqquuapi9GdGGgpWUkeaSSy5piy22mLPaRBXoRtdMd2NijxTMtC8M1oZlllnGTSvXq1fPGL1EyqyzoGKtQ6KO1FlTW7Ro4dLcfffd035kUYVZs2bNbKeddnJhST+qSDcaJt244CzNSJ97kT8WdjBCojxeNt54Y4uUcIsaujvFVAILJxhp1alTx90PXxjv+8fIB+vseuutlw6PVZH08xWmEiIl36XNPRghRwq/iw5nePLHSC7TNAHWB9hSNsrOftTpuDSijtoiJdLx5UT08nbMGElyv1B+/PFHW3HFFd0ok/M4n7PYA2H0utpqq7l2QLyVV17ZWWOxCnphxIeFl7yS/v77759m5cOw/f33353lCudz6o1yYe1lZMvo1Eu8PrLlz8fJtM03b7nKidXt9ttvtzXWWMPdii0WypmRtRTBkow1fPnll3fHTD1Fg5S0vyF+i7SbzTff3F2PXnZuEUBoqXAXon9Ydmj7CCP4SMm3TTbZxB1jiYZ1q1at3DFtkHbgFyvlug/1iiVmlVVWce2gXbt2znpC2RCsQTwjW2+9tbtOOSMlws2KuAAZ/hVbt2FylIHZEaxutCN8vrHGkVek2LwRl9kPZmKiAbfBCCsTlmv6glx9CmW7//77naWQfPFc+vom7VIkW7vi+fDPP9tM0475tnGfTyyFMI7/hb66+bDOdt98+nnywyIXZnXo05HoZZhum/RrPXr0cM+Ruxj8gw0WPyzq1Invd8KZMJ7N6EXvrK9cR7K1gyB51zdlSx8fxscff9xFof+KlAaLFE5jdgR56qmnLBrwuv1sdewCRP/ifR7+lTzbpOHfQVghI4XcRcnVJnmWvEWU5wheRxxxhLNS+3v6Lc8D7ctv6ZuRfNqAT4M4MCYdnxbXsr3Lc5XBp8026Z2Yb59Df0fdICuttJKzXvrZDHcy9o+2Szvh+WgZ6QToH0ikhKb791gU16/QbyPRANz5yUaDD6d70Mbvvvtu1w653rFjRzdrzTZSijlVQXKVy7NgC+u4VHddxO9X3cf1irkBUw3RSM222GIL91IhDTp/FCOUNy9xkzudztJLL+0vuy1AMYkjVBgVFwqK7pZbbumUVCoEpTZUsniweGkgbP00uk+DY//Q+XN+SyUzdUQaSLjvw9ARx4V4kfXEMaBjp/F6ZZ4yoKSF4jvI8Fy2fcrB1BgvxsmRzwxTKUxVFCJxztSFX6EK03h6cPIcw/vQGePrzNQGihcDEO9HyqIgpkDoBLzAwivznIvngzr09e3jsEW53m677VxHF57n/igT0cjYnY7XR7b8hekk7eebt1zlpH5x+4hGzs49huk93FqoN8qKW4b3i/L54MUcSryNUl9Ji4wuuugi12ni60hdoGT6envnnXcqtT2uh5LpPuQzskRZNEMSBncdq1/AgfsFixhCQekOXXjCa36/2Lr18dny8qcf4IXrhf6EQTJSbN4oN9xYbBEX7slLKlufQtnIx/XXX18hOv0CygvXipVs7SrfNPNt4z49XHr8s+bPsQ2nNvNhne2+ufp5+hf6ZBTQUHj5o2jx7mFQT5547yQJzwSDD1yxotkz9yyGRgTihm09VztYbrnlKtwmW/oonPRZvCdpWwz41l9/fYssd26Qi3LrB4X51HG8z8OtjTTjwnsJydUmUd55luJt08ePp5t0nE8bSIoXnsv2Ls9Vhnjew3TZz7fPib+bqbts/RnvQP4QVvPjdkC/37RpUzfAchdi/3hH+kEY/TEKMvz46gPtF52J/ue8885zLnUMTGjfGAfi/Uq+5YplIedhddZFzpuXEKCo3hU/ISyQvGB95x6Zz51lFItmqGAWkjfSWmGFFSpFobNA4UoaUYSBsXDRUGggNCxGPTQOLJpJcthhhzmLEtZO8swollF9NsESjIUGKy0dKlYoFPfIdO+ioSQyoi1FsPgxwsN6jUWEhwyn7KqSAw880I3+sHZizWNVIsoW1tS40KlhUUW5wXJAnrxlj/paZ5113EAmjIdFulCBW9IiNMruLYhJaWbLX7HtMH6fXOWEDYoUbY62hsWb5wDhGfEDpHi6xRwzu/DKK6+4P/y1UDjoCLHCkk+vzBaadpKyTBq0ZdJF2GZ6yaEAZJJi6zZMjzSyla3YvFFu0mUwHgrHKFL0J9n6FPKFFTgeHyWrVMnWrkpNu5T4xbL29yR+tn7eh4tv6WtZSIMllS0vevwX8auMCzMeL7/8suuveBYZRBI2k+RqB/F42dKn30FBxieSr8XgY4uyzOwIFjsGYX5GsJg65l3oFaJ4vjjO1Sa5Xuo7KlcbKLXvzVWGpHKH54hfzPskHOSE6SXto4yOGjXKWdhpz/EZaB+HgVT4NYCNNtrI+EOYIY5co1wfhD8wuggSuRRUMAa6k9G/Ysvl4xezLbUuirlnvnGKUmCxDEb+RG4UF96IhQWR31TiCD4Ml2mf6Xksm0x3e0GxoiNgWi6bIuPDY7miwfBiZ3SDQ7OfWvFh/BYrAZWD4oqSgTXPTwn4MPEtLyaUBRS5JGH6lwVXTKdnkkzKAuFRBFC6GaXHrRiZ0iv0PEoIfyyQgykvX9wcsnU6TK+waIeVk7w4Iv9Zo6zUNw9bKJkWVoRh4vtYKKnnuDBSxdKYS5LyxwuvKiRXORlssHADq0ZcsBTwh1WWUboXrNSkG1oU/bVcW+Lg9sEfL8fIj8652fCSxLoFCy8MrKhr/8L05+Nb8ki4yOfTll122fRlLEneHQYrEp0sLiVeIv859zLN1nZKrVvuRRqhK4m/P/nheSw2b5SbgS/swvqhDfvnL1ufQr5glvQMkHYpkq1dlZJuqXGLZe3vm6uf9+GStrQzpp754wsmtP+4AosiwcwVfXW2dhmmn0878OHzSZ93CUp25NfopowZiNNO6NfDd0wxdcysAP3ufvvt57NUYZurTWKo4LkpRUptA7nunasM+cQv5n3CQCdpcEV/TZ7iFltfrwxied9QL96Fizwyq0ud4+4UF95tzNRgbfXCrA2CjkB/HBfyUEy54ukUclxqXRRyr0LDLlZoBFZfMiXj/UbC+FigSvlRA6xLVHboq4RvIC9qXiL5CCNeGhNT+lgCvb9gUlwaAo2V0TJWSaYPcgmj37ARozDgE+N9dHEfwJfQK9s0SPwUGbF6QVlmKgBBYWXVMtMQCA2XqSd/Dx4A0ic8yjzC6JnOsFhhigQlCIXroIMOcl+DyDTyHD16dIUPK5M3plaZiqa+sN6GI0+UYu8jW0j+GGxg8WLKzwsPeLQQydW/PxffZstfPGyxx7nKSd2GiihfXWA1OHWH8P1Apv59/THA4py/nm++aHt8rNyvXCUe7P3MBAMM7sMzilBX3Mf7T7uTWf7xge0LLrjAtUGC0cbwofWffWF2grr1X8ugbZ8XTXtFC/OypPp/7kXF1G2YKO2DWQ9mO7zwzDD4RIrNG3GZouUZ9fVD+eg7sI4h2foUn6+w36NPoC/0Vmn85sI6c4nm8S9Xu6If4IVb01IKa/JabD+PUcJ/jYV0aNdJsxu0e9h45ZV2jKXL99HETZJc7cDHySd9pvjxM2VQ5PtyvrqDwhq6yeWqY3/PcIvSznPgfWq5xjEzM/Qpudok1/mj7/ZCm2WmLVOfhILv32nEKbQNoIyxXiFfyVWGeDrxdyLx8+lzeO59f8a7l/6TssUFP1XaR9iGYMY7CmUe4YsWfGkhNOAwI8dXdeKuW/Q1WFu5vxcMSeg/CNskg0i+5fJpJm2ruy6S7lld5wo2ETz55JOuQpIUHkadPKD8cd13ID7zHCfF8+EAy0PEVA9TJDwwWHv8SypTfJ8+1iZGl4RjAQwKKn4q//nPf5zTeTiioRPiRY9vE4sDGGHRAeDDiTWSUQfp+Lz5e/Biww8LDigULaPRMAtbGHkh+ASyQIdOigeIfKBEYA3ghUZ6LArDionPJy8gRuR06ggdBelxHQY8DLgs4JeGSwQ86Byx+GEdw0/M+996tkn5Jm1/nRcz0ys8jFi1GI2Tf6zcKPOhUA6mvljwQH4Iy2jSj1KZvqZ8cOAlzXn/ya6kNkDanqnf+vuhqFP3KLHUFfXDFI1XDpPKlSt/Pu34NlfewvBMMWcrJwoc05RYLnlZwpBOEOskgqUI31HfJngJ81k3P8WVyVLn68vnhXzwKzBYpLGK0maxtmKBRbBK0Ylyf2YduA9tyS/yynUfLFm0Ddoi9YlyHK2gdc8C6XNPZl6wGLA/M/KlY7bEu4zE65M4XoqpWx/Xb1GmKR8vE15YtF/vI1ZM3jzfsH5wiYErbRy2+fQpPl+0W15U1Dv58jxwL2GgFVpmKBPXmbVCIYkLn0XK1a7ou3je+BQSfYmffvRpFdLGwzh+P7715cnFOtd9c/Xz3DeprWJkYADHbAJ9A/02n0iMC88BzyLtFOWRtPiMFv0YQjl83Ydxs7WDMFyu9AlL+8TIE/qqMuVMvYauWrnqmLx67j4PDFhpX7xnMNagGDIDwHNLe6WfztUmWRxN38DCT/JKnWDMSFo4yn3pz2invNMwUuRqAz6vfksb5X5MpfNsodgn1YEPzzZXGcKwSe/EXH0O8TGOYclGR2CxnTdmhWmzz+CJ9xrvd9z5UPTpK3kv+AEKfHhHoweh1GJdpQ2ESqpPl1ls7s0snBf4UAcMhnmPhJ8Q9WHY5ipXpvbt06juuvD3qYltHT5zUBM3KvQeVCAvbP+Szyd+9HkJ95B5ZdDHYeSEFSk8z5cEcFfgBR0KDZKHGCUzm9CBkrckCwDxGGHRseAcndQZo0CzypnpS6+ghffDuoV7g7euhdd8+ii35IEOKF9BQWcBEf6soWD1RjnAvzlJUNaxFtA5JnU8PLh0gn7aNSmNfM+x0hLlhHvlK7nyl286ucJlK2fcTSCeFvVJGOo8iWE8fKZj37aoe56RuGBJIJ+8xAtpGz4dOmeeP5Sj+MuTMAzEGHihQCW1bZ9O0raYuo2nw0CJ5yN0dfBhSsmbr5+wXIX0KeSLdouVJBQUJwYwSXUVhsu0n6tdMdCnPRXSV2a6VyHnS2Ht71NMPw8P2iV9azahPgnnFYxsYcNrSe0gvO73i03fxw+3ueo4DBvuE492lamMmdqkT4M+nf4inxlO+ljad8i9kDZAv0Jb5R2R6b3p8xVuc5XBh6VfTHonZupzMDqgFzCwpB2iVOfqz6hzBgnwij/nYT6YZWMAnKlefNikLXlhkJbU94bhM5UrDJNpv7rrItN9q/p8wRbYqs5ApvSSXk6ZwvrzNCqmnPnUkzfZM81CY4r7Q6IYYv4PfV7oDHCPYEFaLsn1wPNCyVYGGjajvkzCg5RJeSUO6Yc+e5nSiZ9HWUax9r6DXEeZZpozk68wYegks72AUcqqSqg7X3/5ppkrf/mmkytctnLmqg8U/NB/NNe9Ml3P1bZ4OYR+sJnSyXSeNpItn3Ss2a5nSpfzxdRtPL3wBRq/VkrekuqnkD4lU76wlGV7duJliB/nalfZ+ol4WlV5XAprn49sfaQPE9/m4uHDU5/FSFI7SEqn2PST0sq3TPG4ueJlapM+nUIGPUl9bCFtgH6lEKOEz2OuMvhwmd6JufocysCgNR+hzuO6RDwe+WgZzWAVK/k+E7nKle3+1V0X2e5dldf+tRbYYgrJqAILKquzsdDQkGiYfGstyZ8EKyy+ilhTGb3xMOOvEv98SzF5+TfHQXll6ogpYARlmSkYpjCqslN2ieufCJQxgUL7lDIuqrIuArWKAC5zfBILlxBJeRJYpBTY8qwC5VoEREAEREAEREAERKAQAgV/haCQxBVWBERABERABERABERABKqagBTYqiaq9ERABERABERABERABKqVgBTYasWrxEVABERABERABERABKqagBTYqiaq9ERABERABERABERABKqVgBTYasWrxEVABERABERABERABKqagBTYqiaq9ERABERABERABERABKqVgBTYasWrxEVABERABERABERABKqagBTYqiaq9ERABERABERABERABKqVQJUrsK+//rrdeOON1Zrp6kx8zJgx7te4+IWuXMJPsB577LHpYPySFb/1LBEBERABERABERABEag+AvWqOmkUuC+//LKqk62R9ObNm2fnnnuuPfnkk5bP7xGnUimbPn16Om8ff/yxLViwIH2sHREQAREQAREQAREQgaonUOUW2KrPYs2l+PPPP9saa6yRl/Jac7nSnURABERABERABERABEICRSmw//zzj3MT2HPPPa1Tp0522WWX2fz588N00/uffvqp9evXz4Xr0KGDDR061LBcern55pvNp8N0PFZML9mu+TBsf/31V5eHzp07G/c44YQTDGXUy3PPPWcHHHCAy0PXrl3tmWee8ZfS24kTJ9rRRx9tr776qnXr1s0mTZrkrv355582cOBAF3fvvfe2u+66Kx0n187nn39uffr0sR133NEOPvhgmzJliouC6wF5DGXEiBFGPr3MmjXLhg8f7g5nzpxpvXr1cnmA1S233GLUAfLNN9/YIYcc4vb1TwREQAREQAREQARqA4GiFNghQ4Y4RfO+++6zRx991Pl9Dho0qBKvjz76yI488kjbZ599bNy4cfbggw/a008/bZMnT3Zhn332WadMks748eOdInb99dfnvBbeiGl/FMtVV13VpT9hwgRbZpll7Morr3TBfvnlFzv55JPtqquucve45JJL7NZbbzUU01DatWvnlOBWrVoZeWjTpo273L17d2vZsqXhG0s88n7NNdeEURP3f/zxR9t3332tR48ehnKMEty3b1974403rH79+oZSinKPoIyOHDnSHn744XRaTzzxhC211FLuGCUYBRZGd955p8F12rRp7toSSyxhq6++ejqedkRABERABERABERgUSdQsAKLj+sDDzzgFDIUscUXX9z69+9vq6yySiVWa621lj322GO27bbbWp06daxZs2ZOmfV+oyh5K664olPoiLzNNtsYCiaS7ZoL8L9/KHBjx451Flbyw9/+++9v7733ngvxxx9/WIMGDaxp06bueLXVVjMsu0suuWSYjCtH48aNjfRQHOvVq2cvvPCCU4axcHLcpEkTGzZsmFM2UZyzCQvZWNS19dZbu7LjmoBFFeUf2X333dNWXpRRlHyUW2+dRhHfeeedXdjvvvvOWrRo4fbJI4OFTTbZxB2jrJ9//vluX/9EQAREQAREQAREoDYQKFiB/eSTT2zLLbd0Cp8HhHLXs2dPf1hhi/LI1Pnpp59uTN/ffffd6envXXbZxVDOUNSwmH744YfpuNmupQP9bwdllCl3lEPugULnp9hRkLGEbrfddk7pfvnll9PX4unEj999913r2LFjhdMNGzZ05f/ss88qnI8fvP3224ZVN5TNN9/cPvjgA3dqp512MpRUBJcGjjfeeGObMWOGs2ijwPtBwUUXXeQU3pNOOsnFiVuPXSL6JwIiIAIiIAIiIAK1hEDBCuzcuXMrWS8zscJKiWKLhRT/0nvuucdZJX14lFv8OZmaxzqLgnbKKac4K2S2az6+3+IecNZZZ9kOO+zgfFS976i/ztQ9rgsokKNGjbJdd921go+sDxffeutt/DwKcy4lMlNc0sLKikV29uzZRjj8bbE+o8ROjlwU8IXdbbfd0rfl/CuvvGJdunQxFPC2bdva1KlT09e1IwIiIAIiIAIiIAK1iUDBCiz+lm+++WYlRkkKFb6tTHWfd955TmGrFOl/J1ZaaSW3yAlFl6l/7xvK5WzXuI4/KErf7bffbq1bt7bFFksuElPvTNtfe+21TtHFtSGX4AIRLyuWXRZ65fI7XX/99SspmSy4QlHHnQJBkabMWLAbNWpk22+/vVO08X/FAh0KrhpchyWL5q677rrwsvZFQAREQAREQAREoNYQSNb2shS/efPmbsHUQw89lA6FwsXXBeKClRKfVC9MyTPN7/1HR48ebY888oi/bKzOx0UBZS7btXSEaIc4+K16pXDOnDnOXcHfg3sOHjy4wvdZmab3C6TCtOL7WD4ff/zxtD8t17EWo0iiEGcTFm/hz/vTTz+5YHylAeWzd+/e6Wi4TgwYMMBZXjmJP+vvv//uXC423HBDFw6Gxx9/fAWLMUq7zz/Xn3rqqXSa2hEBERABERABERCBRZ1AUT9kgAWQlfH4s6I8oiz6rwd4RRJwLEw64ogj3A8DoGixmp+FTW+99Zbjin8pLgNYRbFMYsVlQdgKK6zgfE8zXQsrBUWPHx3gc14oy1gz+UQVcZH11lvPKcnt27c3LKqvvfaa8bmtcIo+TC+04Ho3BlwQyB8L2PCp9cp6WFafho/Pffn6Aflif2b01YG99trLMfFhN910U7cb+sqSTz4B5tPGXQHXCKy1pMMCOKzS3gKLVZdFaz/88INPVlsREAEREAEREAERWKQJ1IkUn///UdYCi4qihWUx169W8Z1WFj/VrVs38Q4ot/iCoiR6BdAHzHbNh2GLby5KX2jxDa///fffzhrK1wiYji9UsOyiTFKOQgR/12+//daWW245p1wXEjcMi+sCC7u4P/mQiIAIiIAIiIAIiEBtJVCSAltboancIiACIiACIiACIiACC49AwT6wCy+rurMIiIAIiIAIiIAIiIAImEmBVSsQAREQAREQAREQAREoKwJSYMuqupRZERABERABERABERABKbBqAyIgAiIgAiIgAiIgAmVFQApsWVWXMisCIiACIiACIiACIiAFVm1ABERABERABERABESgrAhIgS2r6lJmRUAEREAEREAEREAEpMCqDYiACIiACIiACIiACJQVASmwZVVdyqwIiIAIiIAIiIAIiIAUWLUBERABERABERABERCBsiIgBbasqkuZFQEREAEREAEREAERkAKrNiACIiACIiACIiACIlBWBKTAllV1KbMiIAIiIAIiIAIiIAJSYNUGREAEREAEREAEREAEyoqAFNiyqi5lVgREQAREQAREQAREQAqs2oAIiIAIiIAIiIAIiEBZEZACW1bVpcyKgAiIgAiIgAiIgAhIgVUbEAEREAEREAEREAERKCsCUmDLqrqUWREQAREQAREQAREQASmwagMiIAIiIAIiIAIiIAJlRUAKbFlVlzIrAiIgAiIgAiIgAiIgBVZtQAREQAREQAREQAREoKwISIEtq+pSZkVABERABERABERABKTAqg2IgAiIgAiIgAiIgAiUFQEpsGVVXcqsCIiACIiACIiACIiAFFi1AREQAREQAREQAREQgbIiIAW2rKpLmRUBERABERABERABEZACqzYgAiIgAiIgAiIgAiJQVgSkwJZVdSmzIiACIiACIiACIiACUmDVBkRABERABERABERABMqKgBTYsqouZVYEREAEREAEREAERKBkBTaVSi2yFBflsi2ylaaCiYAIiIAIiIAILPIE6hVTwgULFthVV11l999/v9WrV8/mz59vXbt2tWOPPdYWW6xknbiYLFVpnGeeecauvPJK+/LLL135tt12WzvzzDOtadOmVXqfbIldcsklttdee9l6662XLViVXrvpppts0003tdatW1dpupkSmzJlivXr1y/TZTvggANcm8oYoIgLme556aWXunIzaGF/zJgxttRSS7l2sNZaa6Xv9N5779l9991n5557bvqcdkRABERABERABGqWQFEKLMrrF198YRMnTrT69evb77//bqeeeqpddtlldtppp9VsCar4bg8++KBde+21dvPNN9vKK69s//zzj40aNcoOO+ywtMJexbdMTO7zzz+3P//8M/FadZ2cPXu2/fzzz9WVfKV0UZSfeuqp9PmOHTva6NGjbZlllnHnqmMw9NVXX1mnTp3sxBNPTN+XncUXX9wdP/fcc/bWW28Zg5hXX33VTj75ZHv00UfdNZTbs846yxhcSERABERABERABBYegaLMpY899phTVFFekUaNGjmr1dSpU62cp91RGC+88EJnYUN5RVCievbsacstt5xNnjzZndO/qiMAX/9Hqn6fbXXIjz/+aCussIIbeNF+/Z+/34svvugGKxxvvfXW9vXXX9vff//tsvLQQw/ZZpttZuuuu251ZE1pioAIiIAIiIAI5EmgKC0BZQ5lNRSmW++44w6rU6eOOz1s2DD75ptvwiBuWharFoKiwDQtSsG+++5rO+64o5199tk2b948e+SRR6xLly7Wpk2b9Lli4xDv008/dVPVWN46dOhgQ4cOTVS0x40b5/LSpEkTolWQU045Je1C8MQTTzgLXRjgo48+cpZazs2ZM8eGDBlib775ph166KG288472yGHHOJ4cO7www93+eAaFsFi5Ndff3UW786dO7u0TjjhhLT1dNasWXbNNddUSvaMM85In8PtAzcJ4sPl6quvtr/++it9nZ1PPvnEjjzySFc3uIegzC0MwRrdp08fl4+DDz7YcAPw4lljOd97770da9rRL7/84oNU2KLAYuGlnX377beGO0woP/30ky299NLpU82aNXOWcHjDC4usRAREQAREQAREYOESKEqBRUFgChZrJUpOkqDg/vHHHxUuoVjhV4qgPOB28Nlnn9mdd95pTz75pKEktGvXzj788EO77bbbbMKECU5pQqEtNg6KJUrYPvvsYyioKDpPP/10ojWVsPiAJsn666+f9g2lDL4cPiwK07Rp09whyhFuFtdff72bbkbh3W233WyPPfawkSNH2uDBg115sfCh6BYqpI+ytuqqq7rywAmlDAULwaXD5yVMO5yuHzRokKGsPfzww27AgCVy+PDh6eDff/+9HXjggYZiTLwePXo4n1RvjUwHrOYdFE4GONwfl5WBAwda37597Y033nB3hsXFF19s77zzjmtHsNhggw0MRTdJSO/uu++27bbbzhiUUAe4vuAqgqy22mppdrRfOKDQMug5/vjjrUGDBs7FABcaiQiIgAiIgAiIwMIhUJQCu+GGGzoLKlOxWBGx4GFJLdR9gKn5k046yZZcckk3dYwVdtddd3WKbcOGDZ1rAguZsKB6KTQOC3BweWAhFtZhLGoos9OnT/dJprdY+ihTVQiMsGquuOKKLrn27ds7ReiGG26wlVZayS0OIx8o64XKEkssYWPHjnUKpZ8C33///Y0FRvnIb7/95uKzMA3fT9I74ogjnLLq4+MDzABjk002cafgRxlQImtSbrzxRjvuuOOcokn9rbHGGk7RDhX/tm3bukVVuLIw9d+9e3fHGmt3XCg7dfzSSy+5GYMXXnjBtYV77rnHBUVZpt4of69evdzfjBkznNKKtZqBw+233+7a/V133RVPXsciIAIiIAIiIAI1QKCoRVzkC6vUUUcd5f6wtmIFwyWAF3++0rhx4wpB+aJBOH3LRZSSUDEuJg5WM6adWT2OxZfFSigqcUHZxOJWFYIbgnenID3KFj+Hku4tf4XeE6UfizaKF9ZI0vF+nLnSmjlzpm255ZYuT2FYOHmhTrGIM0XvBasjCjcDlpqSt99+21n6w/ttvvnm9sEHH6RPhfn2J7Gwkld8VkOhnVIv1AeC8t6/f383kOrWrZtTbhnwsIjrmGOOcZba/fbbz1nNse62atXKsF5jcUehP+iggyrUc3gv7YuACIiACIiACFQPgaIV2DA7WOlwA2CaHMXHW+3CMAtrnylmFBGm248++mhnwcNanOR72rJlS6cYUY64fPfdd/buu+86f9P4tYVxjIvCyy+/7BQvLKW4ZDC1no/MnTvXKW7ZwmKp5CsB3oJM2C222KLCcbb4VXWNafwkBZX0w4FN/H7EoZxx8V8bCM+zYI/BgBcs5HwWDsF9BZcE/hig4eKCMNAiHgOe5s2bu3P6JwIiIAIiIAIiUDMEFiv0NnxmCQsYvoShYNXiJR+ejy+QCcPX1D5WVxTq8847zymv2e67yy67ON9blN648OkklHMvC7Ns+OpOjr6IwFQ2SmaS5TWbryp+nmFZfJnCLT6/LMzbaqut0n/4B6Pc1aSQj3heWRyIK0ho4Y7nCRcRBiShYKVOcrOA5zrrrBMGdfv4ErMYMfxWLYvfvMA4SSH217UVAREQAREQARGoHgIFK7BMg2OFGjBgQAULF4u5Jk2a5KZYySp+hv6LAxwzhT9ixAh2a1T4NBZ+ol6wouI/maSkYklj4RIL1PyKfJQeFjE9/vjj6YVBfIWBryh4YXU+C9tqSsgbU99egWOa//TTT0+Xadlll3VT4N49AQZ8gcAr3ZSTP/99U/INl1tuuSX9ySgWQbHYDDcChLSw9LLYriaFxVsMHlhwhqBAMhjp3bt3Ohsskhs/fnz6GJ/VZ5991ine6ZPRDhzw2cY9wAvnzjnnHPfpLH/Oby+//HL3Qwr+qxQMhHAvQHCnIE81+eMWPl/aioAIiIAIiEBtJ1CUCwF+hLz0sVqxgAalAr9SVt37lz2LrVAGeeGjLGIN48cAvGA19AqYP8dxkjXRhysmDgulWKCE4oWyQj5YFMTH6pMERZAvBeDfuPbaazv/0hYtWrjV/iiGCB/c58cO+DwWFkkscXwayyvsSeVIOkdaSeXlPEK+Pc//O2NuNT5syQu+qCjn+HPytQBW1SPLL7+8883EOouvK36//MBE+BUCLItwwGcZZZgpd/w5/dcVWITGp6soI36f+JyyoI6FTNUldevWrZQ0v0TGp6soK/v475IP6tXL9ttv7yzSDJCwzDKtz6+KhQMXwuJPzVco+JoAX1xgkMXACtcSFg+GwoDstddeqzAwod7vvfdexwCXkiuuuCKMon0REAEREAEREIEaIlDnhx9+SBV7LxRCfEnxB0zyA0Sx5UWPEobysDAFSyKLppKUpKR84V+JlY04XnGNh0NpRwHNdD0evqqP8fFEMY4rav4+uHtQRyhqfhDgr/ktPqZYZuOL4/x1ruFfSxkz3ceHrc4t9UE+sH77BVjcD+s3vr8sZqOsWKfzsYpSd7gI4McappdPGbC84l5RaLx80lYYERABERABERCB3ARKUmBzJ68QIlC9BEIFtnrvpNRFQAREQAREQAT+LQQK9oH9t2Rc+RABCGAFxWVCIgIiIAIiIAIiUHsIyAJbe+paJRUBERABERABERCBRYKALLCLRDWqECIgAiIgAiIgAiJQewhIga09da2SioAIiIAIiIAIiMAiQUAK7CJRjSqECIiACIiACIiACNQeAlJga09dq6QiIAIiIAIiIAIisEgQkAK7SFSjCiECIiACIiACIiACtYeAFNjaU9cqqQiIgAiIgAiIgAgsEgSkwC4S1ahCiIAIiIAIiIAIiEDtIVDrFVh+olQiAvkQUFvJh5LCiIAIiIAIiED1EyhKgb3kkkvsyiuvzJi7zz//3Dp06GA///xzxjAL8wKKyI033mg777yztW3b1tq0aWPXXnutLViwoEaz1bVr1xq9Hzc7/vjjbe7cuTV+30w3HD9+vPXs2TOR/aRJk+zee+/NFLWg888884x99913iXGo9zfffNPOP/9869evX6Uwr776qu29996urey444522223VQjz22+/Wa9evWybbbaxI4880jgO5Z577rFHHnkkPKV9ERABERABERCBEggUpcCioJ577rk2b968xFvffffd9vbbbycqJYkRavjkaaedZlOnTrWHHnrInnvuOXv88cdt2rRpdtlll9VoTrhnTctHH31k8+fPr+nbZrzfjz/+aA8//LDddNNNlcL88ssv9u2331Y6X8yJRx991L766qvEqCj0o0ePtpVWWsk+/PDDCmFoJyeeeKJdccUVrq2Qzrhx4+yWW25Jhxs5cqRtuumm9tJLL9kGG2xg11xzTfranDlz7LrrrrNddtklfU47IiACIiACIiACpREoSoHllhtuuKFT/OK3Rzm67777rGXLlvFL/4rjt956yykpI0aMsEaNGrk8NWzY0IYOHeqUGBQqSc0SOPPMM50F/OOPP67ZG//vbrSDiy++2PbZZ59K97/66qvt0ksvtdVXX91dIywKKTMQf//9tzs3efJk6969u9tn+8ILL6TTGTx4sFG+Bg0apM9pRwREQAREQAREoDQCRSuwRxxxhN16662V7v70009bu3btrEmTJhWu8VI//PDDrVOnTu6PqWMvKAIolHvuuaf7u/zyy+2BBx6wvn37uiBM97/77rt21VVXWefOnZ17AmFCyZZ+GI48Y1GLS/369W3IkCH2559/ukvDhg2zb775pkKwMWPGGNPJyIsvvmgcY8Xdd999janls88+21mlmS7u0qWLc03w5yoklOfBp59+6qa0YYZLBkq298N84oknjGnxULCujho1Kn3qp59+stNPP93xJo8hcx+IafoDDjjAuVMMHDjQ/vrrL3+pxrbLLLOMUxKPO+64rFb7X3/91THG9QP3C18XZJS6e/3119N5xn2F9BhQ0e7Gjh3rFMlu3brZl19+mQ6XbYe43GPbbbetEIy2zbkpU6a4899//70ttdRSbr9x48Zp1xncErAgk1+JCIiACIiACIhA1REoWoH973//617OKFmhoED16NEjPOUsskyrDhgwwClRTLkeffTRhoKF4FOL4vjggw+66eTFF1/cWbm8Ajt9+nQ77LDDbJVVVnG+hCi3Tz75pJvSJT4W32zpE8YLaW200Ub+sMJ2p512shYtWrhzTB3/8ccfFa7PmjUrrfygmJx66qn22Wef2Z133unyg4KF8s40NH6SEyZMsK+//roo/0eUUfwpsQoyZQ0bBgdY+xCUsLgixpS7d0v4559/nGJKfojPFP3EiRPtlVdecfH5hwLM1Dj1gXK7/PLLuzKlA9TgDgOAtdde266//vrEu6K4Y93cYostnOUfd49TTjnFvNUWBf2kk05K1xkDB8per149N/Dp2LGjU35Jf8UVV0y8R/zk7Nmz3UzCYotVfkzIq3dJYP+9995z0d955x1bd911nSJ+1lln2QUXXOB8YlF2fXuP30fHIiACIiACIiAChRGo/GYuID4KFgtUvKBQodjhDxgKltXbb7/d1lhjDXeaLQrLzJkz3TEWS5RBlA2UBSxnWLVWXXXVdDIoLHvttZcLg8WOfa+85Eo/nUi0g//usssuG54qep/FRyhNSy65pMs3Zdp1111dWXBLYLqZfMaV/HxuuNZaa9ljjz3mLH116tSxZs2aOWUWBTwfwbd3vfXWs9122818fCy4Yd1gtcTy3bx5c6tbt64dc8wxTgGG/cIQlL0bbrjBUN7j8vzzz9tqq63mrN2UZ+WVV3YKqfdFhRezAliR4YZ/9v777++SoR6wsGMl5Y+y5iMosCj1SQIzvyiMwRhW/TvuuMPVPc8FfuBYzRGUZyz1bJlJkIiACIiACIiACJRGoF4p0bEOMpWK8onVlJc2Sl1cUB5Y6c20N8oqlqgPPvjAsBIi+AfiRuAVi3Dfp7X00kv7Xbdlqtavps+VfhhxhRVWMPxcq0KJJQ+hoIDH84ny5Kf9w7D57MMFyx0WZiy9KFRYGvMRrMBbb711paDeF5M8YS3EOhuXTz75xJZbbrn46Wo/ZmoeJbt3796V8vX++++7qXl8Ur3AI1ToDz30UDvooIPsqaeechZxH67YbdOmTe2HH35IjI6LAoMKBEsvPrEsXMTSjXLL1wxge95557mZBwYSuIIMHz48o5U58UY6KQIiIAIiIAIiUIlASQosyhqrq5nOx8+Pldx+iju8E9PoKLb4hbKoBQsqSq8X3AOwujLlinUNJSbuhuDDJm1zpR/GYboXy22SAssCLxQ8LJcLW7AgYhHFCo2FD6s1Vjw/bZ0rf7hkeAUrKSwDCizHTMmHwjGMFpZgtWSQw0IprKxecOdYZ511KuU3aeFVVX0OjcFOkjWYPOFOwhcHvOCW4l1T8DvmSxfwxRWFdo1stdVWiZ/p8mloKwIiIAIiIAIikB+BkhRYbnHwwQfbRRdd5Kb2d9hhh/TK/vD2TOvyjc0tt9wyPJ3eRxHGmoriihUWpXj33XdPX8+1kyv9MD5KNH6Q8bywYOeoo45y/qA+fFUpQj69QrZYXTfZZBPnopApXrb8tWzZ0lDI99tvv8ToWIuZHsdfE0ujF/xo41Zkf62mttRn+/btnQ8vFmxkzTXXdOVBCQyF/HphgR6uBCzUYoDE4r9SBMs+Awc4tmrVKp0UMwR8eq1///7pc34HKyzWcqytXmhbCPXlLeD+mrYiIAIiIAIiIAKFEyjJB5bbbbbZZm5qG/9F/ymheDawnuFi4IXV+3ygHkUAYaU31i6suAceeKBtvPHGPmhe21zph4ngp4rvIr6WXlCemdrlU0lesSU/4Sp3pvLxF60pwYKKAuUF30l8Vv23d5ni50sIXrBCs3DJC5ZMLLa4A3jhmEVcnjur8wcNGpR25cC1A4smaS1MQYFmMEN5vbDAjm+whhbRu+66yy0AJAznUWBhgE807Y1BgBcUx2I+kdanTx/39YJQUWYWgR828Mq1vwcuMVhbYerFLzrjGKXXty9/XVsREAEREAEREIHCCRRtgQ1XZrNo5eabb3YWQ58Frvsw+DRiEWPang+7o6jiIsBnqvhsE6v3UcjwN8SnESUL/0ZW8qNU4lbAX1zyST8eh3RwdcBHkV/gIn3cHvbYY48KSi0uDyjTfkEQFk1cHbxw73ieOPZ58uHYxsP5ayiSfqGPP8eWBWsokixKwj0DZZb742aBNRBhQRC/HgZLPsBPWiikXulmsRKWZvxC+XoDyhvWSxRB3BBwLzjkkEPswgsvdGkxPQ97rIqkV1MCryRmcKE8XpiOx78UKzks8EFlkMHn1FAcaWN8+oxwCLMCMKKO+eoAn1+DH9P+lDF0E2FAQ10zkJkxY4arEyzXhCcfXGdWYP3113fW1datW1dQUn0e77//ftt+++2dtdifIw38cvmKBG0fpVsiAiIgAiIgAiJQGoE6kdKYKi2J/GNj4Qunq4mJgoh1k1/2CgVlha8anHPOOeHprPtJ6WeLgNL3xRdfOEWIrwbEhalflBcWF8WtbfGw1XWMck/e/AK3+H1Q9FEAk3x6fVi4oNiFFl1/jS2KG2EYROBa8G8X6gSLaqGuDtQ3P/NKvEw8M5UdJRm/V5T7TBwzxeU8yiu+35kGM9ni6poIiIAIiIAIiEBFAjWqrcSVV7KCpRC/QT6/hUUNQZl64403rH3kB1mIJKWfLT7TzFhgMwnKnP8ubKYw1X0+/qWD+P1Y8Z5LcnFBGcz326i57lUT1zN92irXvanvbAvbssVnkIDlt1jJNsAoNk3FEwEREAEREIHaSqBGLbCZIGOFxScWayOWLiyO+BjyC1ESERABERABERABERABEQgJ/CsU2DBD2hcBERABERABERABERCBbARK/gpBtsR1TQREQAREQAREQAREQASqmoAU2KomqvREQAREQAREQAREQASqlYAU2GrFq8RFQAREQAREQAREQASqmoAU2KomqvREQAREQAREQAREQASqlYAU2GrFq8RFQAREQAREQAREQASqmoAU2KomqvREQAREQAREQAREQASqlYAU2GrFq8RFQAREQAREQAREQASqmkCVKLCpVI39Gm1Vl1/piYAIiIAIiIAIiIAIlBmBohXYP/74w84++2xr06aNtW3b1jp16mRPPfVUjRb/yy+/tDPPPLNG7/nXX3/ZcccdV6P3XJRv1qVLF3vmmWcSi3j44Ycnni/0JL/wxq+9ZRJ+xnjs2LHu19+mTZuWDkZdd+jQodLfjTfemA4zfvx4d53nYNy4cenz7Pz555926KGH2vz58yuc14EIiIAIiIAIiEBpBOoVE50X8x577GGHHHKInX/++VavXj1DmeSY/Xbt2hWTbMFxUDA+++yzguOVEoGfun3//fdLSUJxAwLvvPOO9e3b1yZPnmxLL710cMUsVCYrXCjw4JdffrE777zTOnfunBjz2Wefde2oQYMG7ueMfaCffvrJmjRpYqNHj/an3LZu3bpuy/VzzjnHnnjiCVuwYIHtvPPOtv3226fLMWLECHeOZ0IiAiIgAiIgAiJQdQSKssCOGjXKWVyxLvmX83/+8x+7+uqrbeDAgVWXO6W0yBNAaT3qqKPs3HPPXWhl3X///e3UU0+11VdfvUIeUFCXW245q1+/foU/3+bffvttpxQ3a9bMhevYsaO9++67Lo1PP/3UKeVdu3atkKYOREAEREAEREAESidQlAJ7880325FHHlnp7uuuu6717NnT/v77b3cNpSAuQ4YMMRQDhKlYXvhXXHGFUwSwYN1+++02d+5cw3qFxYwpXBTmYuWFF14wpqJxceCPKV8vw4YNs2+++cYfuu2YMWPs1VdfTZ+bPn26i0/eSOe9995LX2MHi+wNN9xge+65p/vD0icpjAAKLJwnTZqUNSLXDzjgAGfVZKCEBR75+OOPnTtL6It91113ubqeMEDe4lAAAAhlSURBVGGC9enTx55//nnr1q2bXXnllVnvEV78+eefnWJKHX/33Xfp+/kwWHZDqzHW2t9//91dxr1m8ODB5q21Po62IiACIiACIiACpRMoeG4T9wEsUE2bNk28e/fu3dPnk3wb33jjDecbSHyUluuuu85Nw55wwglOcd1pp50M5eOYY46xRx991GbPnm277bab7bDDDrbqqqum085n57777rNHHnnEWYXXWGMN++STT6x9+/Y2depUl3+2KJ6hzJo1K+2ziHLbo0cPp1Svt9569tFHH9nJJ5/slFYf59JLLzUUGe6FonP88cc7PgceeKAPom0OArQnFEuUU5RUFMG40JYY6Nx00022zDLLuEEDAyTirbnmmk5xpN3Q/j744AN3ncHKYost5iyrKJTXX399esYgnn7S8Y8//mhYWbfbbjuXBr6y3ItBGO135ZVXdvXu406ZMsWVAZeClVZayTbbbDP78MMP3YCO9kNeJCIgAiIgAiIgAqUTKFiBRanDXaCq5LLLLkv7zDZq1MgtCGMqFkUWWXHFFW3HHXc0FMtCFViUUxYJ1alTx6WFEktaM2fOtFatWrlz2f7deuut1q9fP0P5QNZaay277bbbbL/99nPHWNvuv/9+e+mll9KK0cUXX2z77LOPSYF1iPL+B1sssQMGDHDW93hElMaRI0da8+bN3SUGOFjnv//+e2clvfDCC52FfauttnKL7K666irDpxVZaqmlbIkllnBbdyLPf9TvvHnz3AKvZZdd1sVCCUYZJi+0oTlz5tgll1ziBl8NGzZ0Si3loF3gH46/NPdGKS/E+ptnFhVMBERABERABGolgYIVWBQIFmxVlYRTsKSJNa5x48YVkkcBwbpZqOC7yOIaLGJYYnFdwDqXb1q4N+AfGQppemHqmvyi1ITCwjJWnnNNkj+BXr162e67724TJ05MD2CIjWsAi73iq/y5hlUdP1XaCBbaLbfc0gYNGmQbbrghl0uSfffd11n/vSJMYiinW2yxhVNsUUyxvD/55JPOunrGGWc4JfWwww5z1ydHC9P4MgeWVwZTtL111lmnpDwpsgiIgAiIgAiIQKQvFgoBRYHPEuGnGr7YfTooi61bt3bTvP7cwtp+/fXXzicXKyz+iEw9J/nlZsofZURJySRcX2WVVZxCE4ZBqZEUTgB/USynDBqefvrpdAIMQpZccslKnFEk11577XQ4v0P4qpJ4G8eaz0wAlt8WLVoYVte99trL3Y6BCworftT4XreP3FW82wCfmpMCW1W1onREQAREQARqO4GCFViAoWDwaSG+QhAKL3AWd82YMcOdrkpFIrxPvvss9GEaF6tcJsmWR/wdKQu+jknCqnWmkJm2DgWfWFlfQyL578McS2z//v3TkWC5/PLLG4sEQ9/rcBHVb7/95j7H9dprr7n4uBeUaoXFAr/BBhukXVDIEAsU8YVeYYUV0vnzO7g/XHDBBa7uUXRxP/BCO1t88cX9obYiIAIiIAIiIAIlEChqVcmxxx5rw4cPd76f/t5YpPANxGcUaxmCRY1pdoRpYFboY6GtKeHHFkKlAcvYvffem/5KAkpI+MUBFuHw9QMvKOr4N6IcIbgFMD1NugjuFFjjHnzwQXfMP5QeLL7hivj0Re3kRYBpetqNbztE4gsQsPfuH7iD4GuMlR0566yznO8rCjBWXH5sAgs5ghWdBViFytChQ42/sC5xU+C+8a8LYHlFuWb2AVl//fVdW+dLCd6PduONNy40CwovAiIgAiIgAiKQQKAoCyzWsIceesituMcihc8qfot81D38lSqO+YIAq7hRIPBv9IuzyAtWKr/AKsxb0jk/FRsPx2eSsLbFhRXovXv3di4DLMDBUsqnsPiqgP90Fp/8YrEVv9KEktGyZUvDf9HL5ptv7qzMLCpjqhrfX5QrXARQasgni9D4TNM999xjLEIjbXxik8rg09X2/xNIslSjHLJIyiuDhOZHMlioRV3gR8oXLLDSstqfQRGfvPIL51Ae+aIBgw++L4uPLIMVPstGW0TZDYU6pA2gMDPIYWBC+yYP3IMvYGDNZXBCmyAfoTCw4RyDIy+kQfuivVNG8oPLgUQEREAEREAERKB0AnV++OGHVCnJYJ3E+sqXCUJrp08TCxTXUXqTrvtw1bnFWhdOPYf3QvngG5+sEkcBTRKsfnxSiTBJChdxUKBQglFcJNVHAKsq9YlSmqkuMt2dtspACL/VQgSfbz7nhrLsZxfyjc9n55BC4+WbvsKJgAiIgAiIQG0kULICWxuhqcwiIAIiIAIiIAIiIAILj0BRPrALL7u6swiIgAiIgAiIgAiIQG0nIAW2trcAlV8EREAEREAEREAEyoyAFNgyqzBlVwREQAREQAREQARqOwEpsLW9Baj8IiACIiACIiACIlBmBKTAllmFKbsiIAIiIAIiIAIiUNsJSIGt7S1A5RcBERABERABERCBMiMgBbbMKkzZFQEREAEREAEREIHaTkAKbG1vASq/CIiACIiACIiACJQZASmwZVZhyq4IiIAIiIAIiIAI1HYCUmBrewtQ+UVABERABERABESgzAhIgS2zClN2RUAEREAEREAERKC2E5ACW9tbgMovAiIgAiIgAiIgAmVGQApsmVWYsisCIiACIiACIiACtZ2AFNja3gJUfhEQAREQAREQAREoMwJSYMuswpRdERABERABERABEajtBKTA1vYWoPKLgAiIgAiIgAiIQJkRkAJbZhWm7IqACIiACIiACIhAbScgBba2twCVXwREQAREQAREQATKjIAU2DKrMGVXBERABERABERABGo7ASmwtb0FqPwiIAIiIAIiIAIiUGYEpMCWWYUpuyIgAiIgAiIgAiJQ2wn8P7rrG+ZfNov6AAAAAElFTkSuQmCC" } }, "cell_type": "markdown", "metadata": {}, "source": [ "## Problem Six (Truncated Normal Distribution)\n", "\n", "The problem with grades is that they are usually normally distributed, but\n", "of course grades can not be any real number, but have upper and lower bounds. Here is a chart of GPAs of 4897 students at a modern university currently on lockdown:\n", "\n", "\n", "\n", "The problem with this, of course, is that a normal distribution seems to fit, but it is truncated at the highest value of 4.0. How do we deal with this kind of distribution? Hm... it looks like we need to *condition* the problem so that we are only looking at that part of the distribution in the range [0..4], that is\n", "\n", "$$P( \\,\\, \\ldots X \\ldots \\,\\,|\\,\\, 0\\le X \\le 4 \\,\\,)$$ \n", "\n", "(realistically you can ignore $X<0$). \n", "\n", "Let us suppose that a normal distribution with mean $mu=3.3$ and variance $\\sigma^2=0.4$ describes the overall curve before it was truncated at 4.0 (and 0.0). \n", "\n", "Browse the functions fromscipy.stats.norm
given in the first code cell above to see which one will solve each problem. \n",
"\n",
"(A) The BA/MS program requires a 3.0 GPA to apply. What percentage of this group\n",
"would be eligible to apply?\n",
"\n",
"(B) Approximately how many students are below 2.0? (Hint: I mean the actual number of students, not the percentage; figure out the percentage of the total, and round to the nearest integer). \n",
"\n",
"(C) Latin Honors at this school are calculated as follows:\n",
"\n",
"\n",
"\n",
"What are the GPA cutoffs for each of these honors?\n",
"\n",
"Hint for (C): You must reduce the percentages appropriately, since you are looking for\n",
"a percentage of the values below 4.0. For example, for Summa, you are looking\n",
"for $k$ such that\n",
"\n",
"$$P(\\,kscipy.stats
function \n",
"\n", " X = norm.rvs(loc=0,scale=1,size=num_trials)\n", "\n", "\n", "(Note that in this case, the normal is defined in terms of the standard devation, and not the variance.)\n", "\n", "Run the next cell several times to get a sense for how this function works" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "From N(0,1):\n", "-2.4221520417392313\n", "\n", "From N(10,2^2):\n", "11.779694860358964\n", "\n", "Ten variates from N(66,3^2):\n", "[67.86317916 62.81627429 71.02267807 67.92493406 69.01923287 64.30318126\n", " 69.81129266 65.78251048 71.17414328 63.83041032]\n" ] } ], "source": [ "print(\"From N(0,1):\")\n", "X = norm.rvs() # default is a standard normal with mean 0 and standard deviation 1\n", "print(X)\n", "print()\n", "print(\"From N(10,2^2):\")\n", "X = norm.rvs(10,2) # defined by mean and standard deviation (NOT the variance)\n", "print(X)\n", "print()\n", "print(\"Ten variates from N(66,3^2):\")\n", "X = norm.rvs(66,3,size=10)\n", "print(X)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Graphing Continuous Variates: A Problem\n", "So generating normal variates is easy! What we are going to concern ourselves with in this next problem is now to graph a collection of such normal numbers. \n", "\n", "Here is the problem: since each value occurs (with high probability) only once, we can't just create a histogram and convert it into a frequency distribution. \n", "\n", "Here is what happens if we do this, and graph it as a scatter plot against the theoretical (continuous) distribution:" ] }, { "cell_type": "code", "execution_count": 95, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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