{ "cells": [ { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "# Distributions\n", "\n", "This notebook summarizes the distributions we will study in CS 237:\n", " - Discrete:\n", " - Uniform\n", " - Bernoulli\n", " - Binomial\n", " - Geometric\n", " - Poisson\n", " - Continuous\n", " - Exponential\n", " - Normal\n", " \n", "For each we will present:\n", "\n", " - Basic motivation and definition\n", " - Formula for calculating P(X=k) and relevant statistics (mean, variance, standard deviation), plus useful formulae.\n", " - The canonical problem with an example\n", " - Interactive code to display the distribution function and the cumulative distribution function (CDF)\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.15865525393145707" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Jupyter notebook specific \n", "from IPython.display import Image\n", "from IPython.core.display import HTML \n", "from IPython.display import display_html\n", "from IPython.display import display\n", "from IPython.display import Math\n", "from IPython.display import Latex\n", "from IPython.display import HTML \n", "\n", "# General useful imports\n", "import numpy as np\n", "from numpy import arange,linspace, mean, var, std\n", "import matplotlib.pyplot as plt \n", "from numpy.random import random, randint,uniform, choice, binomial, geometric, poisson \n", "import math\n", "from collections import Counter\n", "import pandas as pd\n", "%matplotlib inline\n", "\n", "\n", "# Number of K-permutations from N objects\n", "def P(N,K):\n", " count = 1\n", " for i in range(N,N-K,-1):\n", " count *= i\n", " return count\n", "\n", "# N choose K, calculated efficiently using dynamic programming\n", "def C(N,K):\n", " if(K > N):\n", " return 0\n", " if(K < N/2):\n", " K = N - K\n", " X = [1]*(K+1)\n", " for row in range(1,N-K+1):\n", " X[row] *= 2\n", " for col in range(row+1,K+1):\n", " X[col] = X[col]+X[col-1]\n", " return X[K]\n", "\n", "def round4(x):\n", " return round(float(x)+0.00000000001,4)\n", "\n", "def roundList(S):\n", " return [round4(s) for s in S]\n", "\n", "\n", "# Numpy basic stats functions\n", "\n", "# https://docs.scipy.org/doc/numpy-1.13.0/reference/routines.statistics.html\n", "\n", "\n", "X = [1,2,3]\n", "\n", "# mean of a list\n", "mean(X)\n", "\n", "# population variance\n", "var(X)\n", "\n", "# sample variance\n", "var(X,ddof=1)\n", "\n", "# population standard deviation\n", "std(X)\n", "\n", "# sample standard deviation\n", "std(X,ddof=1)\n", "\n", "\n", "# Scipy statistical functions for the normal distribution\n", "\n", "from scipy.stats import norm \n", "\n", "# https://docs.scipy.org/doc/scipy/reference/stats.html\n", "\n", "# given random variable X (e.g., housing prices) normally distributed with mu = 60, sigma = 10\n", "\n", "#a. Find P(X<50)\n", "norm.cdf(x=50,loc=60,scale=10) # 0.4012936743170763\n", "\n", "#b. Find P(X>50)\n", "norm.sf(x=50,loc=60,scale=40) # 0.5987063256829237\n", "\n", "#c. Find P(60x) = 0.05\n", "norm.isf(q=0.05,loc=60,scale=40)\n", "\n", "#e. how much top most 5% cheapest house cost at least? or find x where P(XMotivation: The uniform distribution describes the equiprobable case where X takes on sequential integer values from a (inclusive) to b (exclusive).\n", "\n", "Definition: X ~ Unif(a,b) when\n", " \n", "
\n", "$\\begin{aligned}\n", " Rng(X) & = \\{ a, ..., b-1 \\} &\\\\\n", " f(X) &= 1/(b-a) &\\\\\n", " & &\\\\\n", " E(X) &= \\frac{a+b-1}{2} &\\\\\n", " Var(X) &= \\frac{(b-a)^2 - 1}{12} &\\\\\n", "\\end{aligned}$\n", "
\n", " \n", "Canonical Problem and Example: Throw a single die. What is the probability that 4 shows?\n", " \n", "
\n", "$\\begin{aligned}\n", " Rng(X) &= \\{ 1,2,3,4,5,6 \\} &\\\\\n", " P &= \\{ \\mbox{$\\frac{1}{6}$}, \\ldots, \\mbox{$\\frac{1}{6}$} \\} &\\\\\n", "\\end{aligned}$\n", "
\n", "and $P(X=4)$ = $\\frac{1}{6}$.\n", "\n", " \n", "\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Distribution Function and Cumulative Distribution Function of Unif(a,b):" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def display_uniform(a,b):\n", " X = list(range(a,b))\n", " probs = [a/(b-a) for k in X]\n", " fig, (ax,ax1) = plt.subplots(2,1,figsize=(12,12), sharex=True) \n", " plt.tight_layout(pad=0.4, w_pad=4, h_pad=6.0)\n", " plt.setp(ax.get_xticklabels(), visible=True)\n", " \n", " ax.bar(X,probs,tick_label=X, width=1.0,edgecolor='black')\n", " ax.set_title('Probability Distribution for U('+str(a)+',' +str(b)+')')\n", " ax.set_ylabel(\"P(X=k)\")\n", " ax.set_xlabel(\"k in Range(X)\")\n", "\n", " \n", " cum_probs = np.zeros(len(probs))\n", " for i in range(len(probs)):\n", " for j in range(i+1):\n", " cum_probs[i] += probs[j]\n", " ax1.bar(X,cum_probs,tick_label=X, width=1.0,edgecolor='black')\n", " ax1.set_title('CDF for U('+str(a)+',' +str(b)+')')\n", " ax1.set_ylabel(\"P(X<=k)\")\n", " ax1.set_xlabel(\"k in Range(X)\")\n", " plt.show()\n", "\n", " \n", "\n", "# Modify the parameters in this next line to see different examples\n", "display_uniform(1,7)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bernoulli Distribution: Bernoulli(p)\n", "\n", "Motivation: The Bernoulli distribution describes the outcomes of a single trial with two outcomes, success or failure, where p = probability of success.\n", "\n", "Definition: If 1 = success and 0 = failure, then X ~ Bern(p) when\n", "\n", "
\n", "$\\begin{aligned}\n", " R_X & = \\{ 0, 1 \\} &\\\\\n", " f_X &= \\{ 1-p, p \\} &\\\\\n", " & &\\\\\n", " E(X) &= p &\\\\\n", " Var(X) &= p - p^2 = (1-p) p &\\\\\n", " \\sigma_X &= \\sqrt{(1-p) p} &\\\\\n", "\\end{aligned}$\n", "
\n", " \n", "Canonical Problem and Example: Flip a (possibly unfair) coin, where the probability of a head is p. Count the number of heads which appear. Suppose that p = 0.6, then:\n", " \n", "
\n", "$\\begin{aligned}\n", " S &= \\{ 0,1 \\} &\\\\\n", " P &= \\{ 0.4, 0.6 \\} &\\\\\n", "\\end{aligned}$\n", "
" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Rng(X) = [0, 1]\n", " f(X) = [0.5, 0.5]\n" ] }, { "data": { "image/png": "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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Rng(X) = [0, 1]\n", " F(X) = [0.5 1. ]\n" ] } ], "source": [ "def display_bernoulli(p):\n", " X = [0,1]\n", " probs = [1-p,p]\n", " plt.bar(X,probs,tick_label=X, width=1.0,edgecolor='black')\n", " plt.title('Probability Distribution for Bern('+str(p)+')')\n", " plt.ylabel(\"P(X=k)\")\n", " plt.xlabel(\"k in Range(X)\")\n", " plt.show()\n", " print(\"Rng(X) = \" + str(X))\n", " print(\" f(X) = \" + str(probs))\n", " \n", " cum_probs = np.zeros(len(probs))\n", " for i in range(len(probs)):\n", " for j in range(i+1):\n", " cum_probs[i] += probs[j]\n", " plt.bar(X,cum_probs, tick_label=X,width=1.0,edgecolor='black')\n", " plt.title('CDF for Bernoulli('+str(p)+')')\n", " plt.ylabel(\"P(X<=k)\")\n", " plt.xlabel(\"k in Range(X)\")\n", " plt.show()\n", " print(\"Rng(X) = \" + str(X))\n", " print(\" F(X) = \" + str(cum_probs))\n", " \n", "\n", "# Modify the parameters in this next line to see different examples\n", "display_bernoulli(0.5) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Binomial Distribution: B(N,p)\n", "\n", "Motivation: The binomial distribution describes the number of successes which occur among N independent and identically-distributed Bernoulli trials.\n", "\n", "Definition: $X \\sim B(N,p)$ when\n", "\n", " \n", "
\n", "$\\begin{aligned}\n", " R_X & = \\{\\, 0, ..., N\\, \\} &\\\\\n", " f_X(k) &= {N \\choose k} \\,p^k \\,(1-p)^{ n-k} &\\\\\n", " E(X) &= N\\, p &\\\\\n", " Var(X) &= N\\, (1-p)\\, p &\\\\\n", " \\sigma_X &= \\sqrt{N (1-p) p} &\\\\\n", "\\end{aligned}$\n", "
\n", " \n", "Canonical Problem and Example: Throw a (possibly unfair) coin N times, where the probability of heads is p. What is the probability that k heads appear? For N = 5 and p = 0.5 we have:\n", "\n", "
\n", "$\\begin{aligned}\n", " S &= \\{ 0,1,2,3,4,5 \\} &\\\\\n", " f_X &= \\{ \\mbox{$\\frac{1}{32}$}, \\mbox{$\\frac{5}{32}$},\\mbox{$\\frac{10}{32}$},\\mbox{$\\frac{10}{32}$},\\mbox{$\\frac{5}{32}$},\\mbox{$\\frac{1}{32}$} \\} &\\\\\n", "\\end{aligned}$\n", "
\n", "\n", "\n", "and $P(X=3)$ is $\\frac{10}{32}$. \n", "\n", " " ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def f_binomial(N,p,k):\n", " return C(N,k) * (1-p)**(N-k) * (p**k)\n", " \n", "def display_binomial(N,p):\n", " X = list(range(N+1))\n", " probs = [ f_binomial(N,p,k) for k in range(N+1)]\n", " # print(probs)\n", " fig, (ax,ax1) = plt.subplots(2,1,figsize=(12,8), sharex=True) \n", " plt.tight_layout(pad=0.4, w_pad=4, h_pad=6.0)\n", " plt.setp(ax.get_xticklabels(), visible=True)\n", " \n", " ax.bar(X,probs,tick_label=X, width=1.0,edgecolor='black')\n", "\n", " ax.set_title('Probability Distribution for B('+str(N)+','+str(p)+')')\n", " ax.set_ylabel(\"P(X=k)\")\n", " ax.set_xlabel(\"k in Range(X)\")\n", "\n", " \n", " cum_probs = np.zeros(len(probs))\n", "\n", " for i in range(len(probs)):\n", " for j in range(i+1):\n", " cum_probs[i] += probs[j]\n", " ax1.bar(X,cum_probs, tick_label=X,width=1.0,edgecolor='black')\n", " ax1.set_title('CDF for B('+str(N)+','+str(p)+')')\n", " ax1.set_ylabel(\"P(X\\le k)\")\n", " ax1.set_xlabel(\"k in Range(X)\")\n", " plt.show()\n", "# print(cum_probs)\n", "\n", "\n", "# Modify the parameters in this next line to see different examples\n", "display_binomial(10,0.5)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\\binom{10,000}{5,000}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Geometrical Distribution: G(p)\n", "\n", "Motivation: This counts the number of i.i.d. Bernoulli trials until the first success occurs. \n", "\n", "Definition and Example: X ~ G(p) if\n", " \n", "
\n", "$\\begin{aligned}\n", " R_X & = \\{ 1, 2, \\ldots \\} &\\\\\n", " f_X &= (1-p)^{k-1}p &\\\\\n", " & &\\\\\n", " E(X) &= \\frac{1}{p} &\\\\\n", " Var(X) &= \\frac{1-p}{p^2} &\\\\\n", " & & \\\\\n", " P(X\\gt k) &= {(1-p)^k} &\\\\\n", " P(X\\le k) &= 1 - {(1-p)^k} &\\\\\n", "\\end{aligned}$\n", "
\n", "                  \n", "What is the probability when flipping a fair coin that it takes exactly 4 flips to get the first head?\n", "\n", "
\n", "\n", "$ P(X=4) \\; = \\; (\\mbox{$\\frac{1}{2}$})^3(\\mbox{$\\frac{1}{2}$})\\; =\\; \\mbox{$\\frac{1}{32}$}$\n", "\n", "
\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def f_geometric(k,p):\n", " return (1-p)**(k-1)*p\n", "\n", "def display_geometric(p,limit=10):\n", " X = list(range(1,limit+1))\n", " probs = [ f_geometric(k,p) for k in range(1,limit+1)]\n", " fig, (ax,ax1) = plt.subplots(2,1,figsize=(12,12), sharex=True) \n", " plt.tight_layout(pad=0.4, w_pad=4, h_pad=6.0)\n", " plt.setp(ax.get_xticklabels(), visible=True)\n", " \n", " ax.bar(X,probs, tick_label=X,width=1.0,edgecolor='black')\n", "\n", " ax.set_title('Probability Distribution for G('+str(p)+')')\n", " ax.set_ylabel(\"P(X=k)\")\n", " ax.set_xlabel(\"k in Range(X)\")\n", "\n", " \n", " cum_probs = np.zeros(len(probs))\n", " for i in range(len(probs)):\n", " for j in range(i+1):\n", " cum_probs[i] += probs[j]\n", " ax1.bar(X,cum_probs, tick_label=X,width=1.0,edgecolor='black')\n", " ax1.set_title('CDF for G('+str(p)+')')\n", " ax1.set_ylabel(\"P(X<=k)\")\n", " ax1.set_xlabel(\"k in Range(X)\")\n", " plt.show()\n", "\n", "\n", "# Modify the parameters in this next line to see different examples\n", "display_geometric(0.8)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Poisson Distribution: Poi(λ)\n", "\n", "Motivation: If we have a process in which events arrive (hence, called arrivals) independently through time, with some mean rate λ = # arrivals/unit time, then the Poisson characterizes how many arrivals will occur in a randomly chosen time unit.\n", "\n", "Definition: X ~ Poi(λ) if\n", " \n", "
\n", "$\\begin{aligned}\n", " Rng(X) & = \\{ 0, 1, 2, \\ldots \\} &\\\\\n", " f(k) &= \\frac{\\lambda^k \\, e^{-\\lambda}}{k\\,!} &\\\\\n", " & &\\\\\n", " E(X) &= \\lambda &\\\\\n", " Var(X) &= \\lambda &\\\\\n", "\\end{aligned}$\n", "
\n", "\n", "where $e = 2.71828183\\ldots$ (Euler's constant). \n", "\n", "Canonial Example: If emails arrive in my inbox on average 5 times an hour, what is the probability that in the next hour, only 4 emails will arrive?\n", "\n", " time unit = 1 hour, λ = 5, k = 4\n", "\n", "
\n", "$\\begin{aligned}\n", "\\text{Solution:} & \\frac{5^4 e^{-5}}{4!} = 0.1755.\\\\\n", "\\end{aligned}$\n", "
" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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rRhcAAKxg353ZvuPyZZt2XXT2OhcDwGZiRg4AAGAwghwAAMBgBDkANpVtC4sr3hcGAEy4Rw6ATeX6vbvdFwYAB2FGDgAAYDCCHAAAwGAEOQAAgMEIcgAAAIMR5AAAAAYjyAEAAAxGkAMAABiMIAcAADAYQQ4AAGAwghwAAMBgBDkAAIDBCHIAAACDEeQAAAAGI8gBAAAMRpADAAAYjCAHAAAwGEEOAABgMIIcAADAYAQ5AACAwQhyAAAAgxHkAAAABiPIAQAADEaQA4ARbTkuVbXitm1hcaMrBGCOtm50AQDAYdh3Z7bvuHzF5l0Xnb2OxQCw3szIAQAADEaQAwAAGIwgBwAAMBhBDgAAYDCCHADrbtvC4oqrLQIAB2fVSgDW3fV7d6+44qLVFgHg4MzIAQAADEaQAwAAGMxcg1xVnVVVV1fVNVX14mXaj6+qN03b31dVpy9pX6yq26rqJ+dZJwAAwEjmFuSqakuS1yZ5apIzkjy3qs5Y0u38JDd390OSvCbJRUvaX5PkT+ZVIwAAwIjmOSP32CTXdPe13X1HkjcmOWdJn3OSXDJ9/ZYkT6rpkmVV9cwk1ya5ao41AgAADGeeQe7UJLtn9vdMjy3bp7vvSnJLkgdU1dcn2ZHkFXOsDwAAYEjzDHLLPQyoV9nnFUle0923HfANqi6oqp1VtfOGG244zDIBAADGMs/nyO1JctrM/kKS61bos6eqtia5b5KbkjwuyblV9YtJ7pfkK1V1e3f/6uzJ3X1xkouT5Mwzz1waEgEAAI5K8wxyH0jy0Kp6UJK9Sc5L8gNL+lyW5IVJ3pvk3CTv6u5O8vj9Harq5UluWxriAAAAjlVzC3LdfVdVXZjkHUm2JHlDd19VVa9MsrO7L0vy+iSXVtU1mczEnTevegAAAI4W85yRS3dfkeSKJcdeOvP69iTPPsgYL59LcQAAAIOa6wPBAQAAWHuCHAAAwGAEOQAAgMEIcgAAAIMR5AAAAAYjyAEAAAxGkAMAABiMIAcAADAYQQ4AAGAwghwAAMBgBDkAOBptOS5Vtey2bWFxo6sD4Aht3egCAIA52Hdntu+4fNmmXRedvc7FALDWzMgBAAAMRpADAAAYjCAHAAAwGEEOAABgMIIcAADAYAQ5AACAwQhyAAAAgxHkAFhz2xYWV3wYdVVtdHkAMDwPBAdgzV2/d/eKD6NOPJAaAI6UGTkAAIDBCHIAAACDEeQAAAAGI8gBAAAMRpADAAAYjCAHAAAwGEEOAABgMIIcAADAYAQ5AACAwQhyAAAAgxHkAAAABiPIAQAADEaQAwAAGIwgBwAAMBhBDgAAYDCCHAAAwGAEOQAAgMEIcgAAAIMR5AAAAAYjyAHAsWbLcamqFbdtC4sbXSEAB7F1owsAANbZvjuzfcflKzbvuujsdSwGgMNhRg4AAGAwghwAAMBgBDkAAIDBCHIAAACDEeQAAAAGI8gBAAAMZlWPH6iqv5/k+Uken2Rbki8l+XiSP07yO919y9wqBAAA4G4OOiNXVX+S5J8leUeSszIJcmckeUmSE5L8UVU9Y55FAgAA8DWrmZF7QXffuOTYbUk+ON1+qapOXvPKAAAAWNZBZ+T2h7iqeurStqp60WwfAI4d2xYWU1XLbgDAfK3qHrmpn62qL3f3u5KkqnYkeUKSX59HYQBsbtfv3Z3tOy5ftm3XRWevczUAcGw5lCD3jCSXV9VPZXKv3DdPjwEAALCOVh3kuvvG6aIm/zXJlUnO7e6eW2UAAAAs66BBrqpuTTIb2O6V5MFJzq2q7u6T5lUcAAAA97SaxU7u090nzWwndPeJ+48f6NyqOquqrq6qa6rqxcu0H19Vb5q2v6+qTp8ef2xVfXi6faSqnnW4HxAAAOBoc9AgN6uqTpr98yB9tyR5bZKnZvLcuedW1RlLup2f5ObufkiS1yS5aHr840nO7O5HZXI/3m9U1aHczwcAAHDUOqQgl+TdS/48kMcmuaa7r+3uO5K8Mck5S/qck+SS6eu3JHlSTa7X/Jvuvmt6/ITc/dJOAACAY9qhBrn9VvOQoFOT7J7Z3zM9tmyfaXC7JckDkqSqHldVVyX5WJIXzQS7rxVRdUFV7ayqnTfccMOhfwoAAIABHW6QW43lwt7SmbUV+3T3+7r7kUm+I8lPV9UJ9+jYfXF3n9ndZ55yyilHXDAAAMAI5hnk9iQ5bWZ/Icl1K/WZ3gN33yQ3zXbo7r9M8sUk3zK3SgEAAAZyuEFuNfesfSDJQ6vqQVV1ryTnJblsSZ/Lkrxw+vrcJO/q7p6eszVJqmp7kocn+fRh1goAAHBUOdSVIGvJnyvq7ruq6sIk70iyJckbuvuqqnplkp3dfVmS1ye5tKquyWQm7rzp6d+Z5MVVdWeSryT5ke6+8RBrBQAAOCodapB7zpI/D6i7r0hyxZJjL515fXuSZy9z3qVJLj3E2gAAAI4JB720sqpO3P+6uz85+2dVfdP8SgMAAGA5q7lH7iNV9f2zB6rqhKr6+SR/Op+yAAAAWMlqgtxTkvxwVb2zqh5SVedk8my345P83blWBwAAwD0c9B657v5UkqdW1U8l+d9Jrk/y3d191byLAwAA4J5Wc4/c1qr66ST/T5IfSbIzyS9X1cPnXRwAsAG2HJeqWnbbtrC40dUBkNWtWvmhJP8jyWO6+5YkF1fV2Un+qKre2t3/Zq4VAgDra9+d2b7j8mWbdl109joXA8ByVnOP3A9194XTEJck6e7LM7k/bjUPBgcAAGANrSbIfXC5g939pe7+mSSpqoM+IBwAAIC1sZog99+r6ker6m4XxVfVvarqH1fVJUleOJ/yAAAAWGo198idleSfJvm9qnpQki8kOSHJliT/JclruvvD8ysRAACAWat5/MDtSV6X5HVVdVySk5N8qbu/MO/iAAAAuKeDBrmqOiHJi5I8JMlHk7yhu++ad2EAAAAsbzX3yF2S5MwkH0vytCS/NNeKAAAAOKDV3CN3Rnd/a5JU1euTvH++JQEAAHAgq5mRu3P/C5dUAgAAbLzVzMh9e1X99fR1Jbn3dL+SdHefNLfqAAAAuIfVrFq5ZT0KAQAAYHVWc2klAAAAm4ggBwAAMBhBDoBlbVtYTFWtuAEAG2c1i50AcAy6fu/ubN9x+Yrtuy46ex2rAQBmmZEDAAAYjCAHAAAwGEEOAABgMIIcAADAYAQ5AACAwQhyAAAAgxHkAAAABiPIAQAADEaQAwAAGIwgBwAAMBhBDgAAYDCCHACweluOS1Utu21bWNzo6gCOGVs3ugAAYCD77sz2HZcv27TrorPXuRiAY5cZOQAAgMEIcgAAAIMR5AAAAAYjyAEAAAxGkAMAABiMIAcAADAYQQ4AAGAwghwAAMBgBDkAAIDBCHIAAACDEeQAAAAGI8gBAAAMRpADAAAYjCAHAAAwGEEOAABgMIIcwDFs28JiqmrZDQDYvLZudAEAbJzr9+7O9h2XL9u266Kz17kaAGC1zMgBAAAMRpADAAAYjCAHAAAwGEEOAABgMHMNclV1VlVdXVXXVNWLl2k/vqreNG1/X1WdPj3+5Kq6sqo+Nv3zH8+zTgAAgJHMLchV1ZYkr03y1CRnJHluVZ2xpNv5SW7u7ockeU2Si6bHb0zy9O7+1iQvTHLpvOoEAAAYzTxn5B6b5Jruvra770jyxiTnLOlzTpJLpq/fkuRJVVXd/aHuvm56/KokJ1TV8XOsFQAAYBjzDHKnJtk9s79nemzZPt19V5JbkjxgSZ/vS/Kh7v7ynOoEANbCluNWfMB8VWXbwuJGVwhw1JjnA8FrmWN9KH2q6pGZXG75lGXfoOqCJBckyeKivxwAYEPtu3PFB8wnHjIPsJbmOSO3J8lpM/sLSa5bqU9VbU1y3yQ3TfcXkvxhkh/s7k8t9wbdfXF3n9ndZ55yyilrXD4AAMDmNM8g94EkD62qB1XVvZKcl+SyJX0uy2QxkyQ5N8m7urur6n5J/jjJT3f3n8+xRgAAgOHMLchN73m7MMk7kvxlkjd391VV9cqqesa02+uTPKCqrkny40n2P6LgwiQPSfKzVfXh6fZ35lUrAADASOZ5j1y6+4okVyw59tKZ17cnefYy5/18kp+fZ20AAACjmusDwQEAAFh7ghwAAMBgBDkAAIDBCHIAAACDEeQAAAAGI8gBAAAMRpADAAAYjCAHAAAwGEEOAABgMIIcAADAYAQ5AACAwQhyAAAAgxHkAAAABiPIARzlti0spqqW3QCAMW3d6AIAmK/r9+7O9h2XL9u266Kz17kaAGAtmJEDAAAYjCAHAAAwGEEOAABgMIIcALA+thy34sI72xYWN7o6gKFY7AQAWB/77rTwDsAaMSMHAAAwGEEOAABgMIIcAADAYAQ5AACAwQhyAAAAgxHkAAAABiPIAQAADEaQAwAAGIwgBwAAMBhBDgAAYDCCHAAAwGAEOQAAgMEIcgAAAIMR5AAAAAYjyAEAAAxGkAMAABiMIAcAADAYQQ4AAGAwghzA4LYtLKaqVtxgCFuOO+DP8baFxY2uEGBT2brRBQBwZK7fuzvbd1y+Yvuui85ex2rgMO27088xwCEwIwcAADAYQQ4AAGAwghwAAMBgBDkAAIDBCHIAAACDEeQAAAAGI8gBAAAMRpADAAAYjCAHAAAwGEEOAABgMIIcAADAYAQ5AACAwQhyAAAAgxHkAAAABiPIAQAADEaQAwAAGMxcg1xVnVVVV1fVNVX14mXaj6+qN03b31dVp0+PP6Cq/ntV3VZVvzrPGgGAAWw5LlW17LZtYXGjqwNYd1vnNXBVbUny2iRPTrInyQeq6rLu/sRMt/OT3NzdD6mq85JclOQ5SW5P8rNJvmW6AQDHsn13ZvuOy5dt2nXR2etcDMDGm+eM3GOTXNPd13b3HUnemOScJX3OSXLJ9PVbkjypqqq7v9jdf5ZJoAM45m1bWFxxNgIAOPbMbUYuyalJds/s70nyuJX6dPddVXVLkgckuXGOdQEM5/q9u81GAABfNc8ZueX+mbgPo8/Kb1B1QVXtrKqdN9xwwyEVBwAAMKp5Brk9SU6b2V9Ict1Kfapqa5L7JrlptW/Q3Rd395ndfeYpp5xyhOUCAACMYZ5B7gNJHlpVD6qqeyU5L8llS/pcluSF09fnJnlXd696Rg4AAOBYNLd75Kb3vF2Y5B1JtiR5Q3dfVVWvTLKzuy9L8vokl1bVNZnMxJ23//yq+nSSk5Lcq6qemeQpS1a8BAAAOCbNc7GTdPcVSa5YcuylM69vT/LsFc49fZ61AQAAjGquDwQHAABg7QlyAAAAgxHkAAAABiPIAQAADEaQAwAAGIwgBwAAMBhBDgAY25bjUlUrbtsWFje6QoA1N9fnyAEAzN2+O7N9x+UrNu+66Ox1LAZgfZiRAwAAGIwgBwAAMBhBDgAAYDCCHMAmsG1h8YCLNQAAzLLYCcAmcP3e3RZrAABWzYwcAADAYAQ5AACAwQhyAAAAgxHkAAAABiPIAQAADEaQAwCObluOW/HRHtsWFje6OoDD4vEDAMDRbd+dKz7ew6M9gFGZkQMAABiMIAcAADAYQQ4AAGAwghwAAMBgBDmAdbJtYXHFlfMAAA6FVSsB1sn1e3dbOQ8AWBNm5AAAAAYjyAEAAAxGkAMAjl1bjlvx3tVtC4sbXR3AitwjBwAcu/bd6d5VYEhm5AAAAAYjyAEAAAxGkAMAABiMIAcAADAYQQ4AAGAwghzAGtm2sLjiMuZVtdHlAQBHEY8fAFgj1+/dveIy5omlzGE402fMreQbTz0tn93zmXUsCOBrBDkAgOUc4BlziX+cATaWSysBAAAGI8gBAAAMRpADAAAYjCAHAAAwGEEOAOBwTFe1XG7btrC40dUBRzmrVgIcgm0Li7l+7+6NLgPYDA6wqqUVLYF5E+QADsGBnhXnFzcAYL24tBIAAGAwghwAAMBgBDkAgLV2gIVQLIYCrAX3yAEsYUET4IgdYCGUxD21wJET5ACWsKAJALDZubQSAGC9eQYdcITMyAEArDfPoAOOkBk54JizbWHxgIsQAABsdmbkgGPOge6BS/xrOLDBppddruQbTz0tn93zmXUsCNiMBDkAgM3EipfAKri0EjgqHejySYChWSgFyJxn5KrqrCT/b5ItSf5Td7bZ0vkAACAASURBVP/Ckvbjk/x2ksck+askz+nuT0/bfjrJ+Un2JfmX3f2OedYKHF08QgA4ah1ooZRXPWvFf7BySSYcXeYW5KpqS5LXJnlykj1JPlBVl3X3J2a6nZ/k5u5+SFWdl+SiJM+pqjOSnJfkkUkemOS/VtXDunvfvOoFxuKh3QDLOMyQlwh6MJp5zsg9Nsk13X1tklTVG5Ock2Q2yJ2T5OXT129J8qs1+T/MOUne2N1fTvJ/q+qa6XjvnWO9wDo7WBjbcq8Tsu+O21dsdw8JwCE42L13Bwh6B/v/sRAI66+6ez4DV52b5Kzu/mfT/RckeVx3XzjT5+PTPnum+59K8rhMwt3/6u7fmR5/fZI/6e63LHmPC5JcMN19eJKr5/Jh1tbJSW5c47YRz92MNR3JuZuxpiM5dzPWdCTnbsaajuRcNc3/3M1Y05GcuxlrOpJzN2NNR3LuZqzpSM7djDUdybmbsaYjOXcz1nQk586zps1ie3efco+j3T2XLcmzM7kvbv/+C5L8ypI+VyVZmNn/VJIHZHJJ5vNnjr8+yffNq9b13JLsXOu2Ec/djDX5PJu7Jp9HTT6Pz7OZa/J5NndNPs/mrmmzfp7Nvs1z1co9SU6b2V9Ict1Kfapqa5L7JrlplecCAAAck+YZ5D6Q5KFV9aCqulcmi5dctqTPZUleOH19bpJ39SQeX5bkvKo6vqoelOShSd4/x1oBAACGMbfFTrr7rqq6MMk7Mnn8wBu6+6qqemUm05iXZXLJ5KXTxUxuyiTsZdrvzZksjHJXkn/RR8+KlRfPoW3EczdjTUdy7mas6UjO3Yw1Hcm5m7GmIzlXTfM/dzPWdCTnbsaajuTczVjTkZy7GWs6knM3Y01Hcu5mrOlIzt2MNR3JufOsaVOb22InALDWqur0JJd397ccoM8Dk/xyd597COO+O8m2JLcnuSPJP+/uDx9RsYdgumLzf0vyzExuM3hPksd0901V9beTfDDJE5L8TZJLu/us9aoNgM1pnpdWAsC66+7rDiXEzXhed397ktcl+Q9rXNbBPC3JR7r7r7t7d5JfS/IL07ZfSHJxd+/q7huSfLaq/uE61wfAJiPIATCkqnpwVX2oqr5jyfHTp4+3SVX9UFW9tar+tKr+T1X94iqGfm+SU2fG+7Wq2llVV1XVK2aOf7qqXlFVH6yqj1XVN0+Pn1JV75we/42q2lVVJ0/bnl9V76+qD0/btkyHe16SP5qp4TVJ/l5V/ViS70zySzNtb5v2B+AYJsgBMJyqeniSP0jyw939gYN0f1SS5yT51iTPqarTDtL/rEzC0n4/091nJvm2JN9VVd8203Zjdz86kxm0n5wee1kmi3c9OskfJlmc1vyIaR3/sLsflWRfvhbI/mGSK/cP2t13JvmpTALdj3X3HTPvuTPJ4w/yGQA4ys1tsRMAmJNTMpm9+r7uvmoV/f9bd9+SJFX1iSTbk+xept/vVtXXZ7JA16Nnjn9/VV2Qyd+Z25KckeSj07a3Tv+8Msn3Tl9/Z5JnJUl3/2lV3Tw9/qQkj0nygcktcbl3ks9P2+7f3bcuqeepST6b5FuSvHPm+OeTPPDgHxuAo5kZOQBGc0smQWy194l9eeb1vqz8j5jPS/KgJP85yWuTZPoInJ9M8qTu/rYkf5zkhGXGnh23Vhi/klzS3Y+abg/v7pdP2+6qqq/+nVxVj0ry5CR/L8m/qqptM+OckORLK7wHAMcIQQ6A0dyRyeqOP1hVP7CWA08vaXxJJvenPSLJSUm+mOSWqvqGTGbJDubPknx/klTVU5L87enx/5bk3Kr6O9O2+1fV9mnb1UkePD1emVyq+WPd/ZlMFl551cz4D0vy8cP+kAAcFQQ5AIbT3V9McnYms1XnrPHYX8pkcZGf7O6PJPlQkquSvCHJn69iiFckeUpVfTBfuzzy1u7+RCYh8b9U1UczuVxy/0zbH2fyeIEk+edJPtPd+y+nfF2Sb66q75ruP3HaH4BjmOfIAcAaqqrjk+zr7ruq6u8n+bXp4iYHOmdbkt/u7ievYvz3JDmnu28+WF8Ajl4WOwGAtbWY5M3Te97uyGSG7YC6+7NV9ZtVdVJ3//VK/arqlCSvFuIAMCMHAAAwGPfIAQAADEaQAwAAGIwgBwAAMBhBDgAAYDCCHAAAwGAEOQAAgMEIcgAAAIMR5AAAAAYjyAEAAAxGkAMAABiMIAcAADAYQQ4AAGAwghwAAMBgBDkAAIDBCHIAAACDEeQAAAAGI8gBAAAMRpADAAAYjCAHAAAwGEEOAABgMIIcAADAYAQ5AACAwQhyAAAAgxHkAAAABiPIAQAADEaQAwAAGIwgBwAAMBhBDgAAYDCCHAAAwGAEOQAAgMEIcgAAAIMR5AAAAAYjyAEAAAxGkAMAABiMIAcAADAYQQ4AAGAwghwAAMBgBDkAAIDBCHIAAACDEeQAOOZU1b2r6u1VdUtV/f4G13JVVT1hZv+Mqtq5RmO/v6oeuRZjAbC5CHIAbApV9QNVtbOqbquqz1bVn1TVd07bXl5Vd1bVrdPtk1X1q1W1beb8J1TVV6bn79/evsLbnZvkG5I8oLufvQa1z773rVV1dVX98GrO7e5Hdve7Zw79XJJXzYz97qq6feYzXb3kvX+gqnZV1Rer6m1Vdf+Z5lcleeURfDQANilBDoANV1U/nuQ/Jvl3mQSsxSSvS3LOTLc3dfd9ktw/ybOSfGOSK2fDXJLruvvEme3pK7zl9iSf7O67DqPWrSs0XdfdJyY5KcmOJL9ZVWcc4tjbkjwxyduWNF0485kePtP/kUl+I8kLMvne/iaT722/y5I8ccl3BMBRQJADYENV1X0zmTX6F9391u7+Ynff2d1v7+6fWtp/2nZVkuckuSHJTxzi+70iyUuTPGc6w3V+VX1dVb1kOrP1+ar67WldqarTq6qn/T6T5F0HGr8n3pbk5iRnTMd4xvQSyi9MZ9geMVPPp6vqn0x3n5zkg919+yo/zvOSvL2739PdtyX52STfW1X3mdZye5IrkzxlleMBMAhBDoCN9veTnJDkDw/lpO7el+SPkjz+EM97WSYzf2+aznC9PskPTbcnJnlwkhOT/OqSU78rySOSfPeBxp+GwmcluV+Sj1XVw5L8XpIfS3JKkiuSvL2q7rXM6d+a5Opljv/7qrqxqv589n66JI9M8pGZz/apJHckedhMn79M8u0HqhmA8QhyAGy0ByS58XAuc0xyXSaXWu73wOms1/7t+1c5zvOSvLq7r53ObP10kvOWXEb58uls4ZdWGOOBVfWFJDcmeVmSF3T31ZnMHP5xd7+zu+/M5L61eyf5B8uMcb8kty45tiOTcHlqkoszCYHfNG07McktS/rfkuQ+M/u3TscF4Ciy0nX+ALBe/irJyVW19TDC3KlJbprZv667Fw6jhgcm2TWzvyuTvyO/YebY7oOMsdJ7323s7v5KVe3OpPalbs7dQ1i6+30zu5dU1XOTPC3JryS5LZN78madlLuHwfsk+cJBagdgMGbkANho701ye5JnHspJVfV1SZ6e5H+uQQ3XZbIAyn6LSe5K8rmZY70WY1dVJTktyd5l+n40d78scjmdpKavr8rMZZNV9eAkxyf55Ez/R2Tm8ksAjg6CHAAbqrtvyWTxkddW1TOr6m9V1XFV9dSq+sWl/adtj8jkvrNvTPLqNSjj95L8q6p6UFWdmK/dQ3c4l3su9eYk31NVT6qq4zJZnOXLSf5imb7vTPLoqjohSarqflX13VV1QlVtrarnJflHSd4x7f+7SZ5eVY+vqq/PZNGYt3b3rdPzj0/ymOm4ABxFBDkANlx3vzrJjyd5SSYrUe5OcmHuvgz/c6rqtkwuE7wsk0syH9Pd161BCW9IcmmS9yT5v5nMEP7oGoyb6X1yz8/kUsgbM5lFfHp337FM389lsirm/scuHJfk5zP5Tm6c1vTM6ZiZrt75okwC3eczuYzyR2aGfEaSd6/RdwTAJlLdh3ulCACw1qbPnrskyWP7CP+Srqr3JTm/uz++JsUBsGkIcgAAAINxaSUAAMBgBDkAAIDBCHIAAACDOWoeCH7yySf36aefvtFlAAAArJkrr7zyxu4+ZenxoybInX766dm5c+dGlwEAALBmqmrXcsddWgkAADAYQQ4AAGAwghwAAMBgBDkAAIDBCHIAAACDEeQAAAAGI8gBAAAMRpADAAAYjCAHAAAwGEEOAABgMIIcAADAYAQ5AACAwQhyAAAAg9mQIFdVb6iqz1fVx1dor6r65aq6pqo+WlWPXu8aAQAANquNmpH7rSRnHaD9qUkeOt0uSPJr61ATAADAEDYkyHX3e5LcdIAu5yT57Z74X0nuV1Xb1qc6AACAzW2z3iN3apLdM/t7pscAAACOeZs1yNUyx/oenaouqKqdVbXzhhtuWIeyAADma9vCYqpqxW3r8fde87YRz92MNfk8m7umg7VvW1jc6P/8D8nWjS5gBXuSnDazv5DkuqWduvviJBcnyZlnnnmPoAcAsBG2LSzm+r27V2zfcq8Tsu+O21ds377j8hXbdl109orth9s24rmbsaYjOXcz1nQk527GmlZz7kg2a5C7LMmFVfXGJI9Lckt3f3aDawIA+KqDhbVj5ZdJYGNsSJCrqt9L8oQkJ1fVniQvS3JcknT3rye5IsnTklyT5G+S/PBG1AkAHLsOFtSSlcOaMAbM24YEue5+7kHaO8m/WKdyAIBj1JHOqgFslM16aSUAwNxdv3e3WTVgSJt11UoAgDVxoFUgAUZlRg4AOKqZdQOORmbkAIChHey5awBHIzNyAMDQDjTjlph1A45OZuQAAAAGI8gBAJueBUsA7s6llQDApmfBEoC7MyMHAAAwGEEOAABgMIIcALDhPEIA4NC4Rw4A2HAeIQBwaMzIAQAADEaQAwAAGIwgBwAAMBhBDgBYFx7qDbB2LHYCAKwLD/UGWDtm5AAAAAYjyAEAAAxGkAMAABiMIAcAADAYQQ4AWBMHWpXSypQAa8uqlQDAmjjQqpSJlSkB1pIZOQAAgMEIcgAAAIMR5AAAAAYjyAEAAAxGkAMAABiMIAcArNqBHjEAwPrx+AEAYNUO9IgBjxcAWD9m5AAAAAYjyAEAAAxGkAMAABiMIAcAADAYQQ4AAGAwghwAAMBgBDkAAIDBCHIAwN146DfA5ueB4ADA3XjoN8DmZ0YOAABgMIIcAADAYAQ5AACAwQhyAAAAgxHkAAAABiPIAQAADEaQAwAAGIwgBwAAMBhBDgCOMdsWFlNVK24AbH5bN7oAAGB9Xb93d7bvuHzF9l0Xnb2O1QBwOMzIAQAADEaQAwAAGIwgBwAAMBhBDgAAYDCCHAAAwGAEOQAAgMEIcgAAAIMR5AAAAAYjyAEAAAxGkAMAABiMIAcAR6FtC4upqmU3AMa3daMLAADW3vV7d2f7jsuXbdt10dnrXA0Aa82MHAAAwGAEOQAAgMEIcgAAAIPZkCBXVWdV1dVVdU1VvXiZ9sWq+u9V9aGq+mhVPW0j6gQAANiM1j3IVdWWJK9N8tQkZyR5blWdsaTbS5K8ubv/bpLzkrxufasEAADYvDZiRu6xSa7p7mu7+44kb0xyzpI+neSk6ev7JrluHesDAADY1DYiyJ2aZPfM/p7psVkvT/L8qtqT5IokP7rcQFV1QVXtrKqdN9xwwzxqBQAA2HQ2Isgt9yTSXrL/3CS/1d0LSZ6W5NKquket3X1xd5/Z3WeecsopcygVAABg89mIILcnyWkz+wu556WT5yd5c5J093uTnJDk5HWpDgAAYJPbiCD3gST/f3v3Hi9XVR58/PdI5CYCykUjIQEsUHjVoqKloqigiDYFaUWh3lF5RbGC1QIvvohYfBtvtLZeWyhILRYvRRpRoeKltSKgXJIQAuESQiCCyh1CBNb7x1o7s84+e8LlnJxzdvL7fj7nc2bmmbVn7TVrr72evffM7BgR20fE+uQvMzmn9ZwbgX0AImIXciLntZOSJEmSxCQkcimlB4EjgO8DC8nfTrkgIk6MiP3L0/4SeFdEXA6cCbwtpdS+/FKSJEmS1knTJuNFU0rnkr/EpH7s+Or2lcCeE10vSZIkSeqDSflBcEmSNDbTZ8wkIob+SZLWbpNyRk6SJI3N8mVLmXX03KHxJXNmT2BtJEkTzTNykiRJktQzJnKSJEmS1DMmcpIkSZLUMyZykiRJktQzJnKSJEmS1DMmcpIkSZLUMyZykiRJktQzJnKSJEmS1DMmcpIkSZLUMyZykiRJktQzJnKSJEmS1DMmcpIkSZLUMyZykiRJktQzJnKSJE1R02fMJCI6/yRJ67Zpk10BSZLUbfmypcw6em5nbMmc2RNcG0nSVOIZOUmSJEnqGRM5SZIkSeoZEzlJkiRJ6hkTOUmSJEnqGRM5SZIkSeoZEzlJkiRJ6hkTOUmSJEnqGRM5SZIkSeoZEzlJkiRJ6hkTOUmSJEnqGRM5SZIkSeoZEzlJkiRJ6hkTOUmSJEnqGRM5SZIkSeoZEzlJkiRJ6hkTOUmSJsn0GTOJiKF/kiQNM22yKyBJ0rpq+bKlzDp67tD4kjmzJ7A2kqQ+8YycJEmSJPWMiZwkSZIk9YyJnCRJkiT1jImcJEmSJPWMiZwkSZIk9YyJnCRJkiT1jImcJEmSJPWMiZwkSZIk9YyJnCRJkiT1jImcJEmSJPWMiZwkSZIk9YyJnCRJkiT1jImcJEmSJPWMiZwkSZIk9YyJnCRJkiT1jImcJEmSJPWMiZwkSZIk9YyJnCRJa9D0GTOJiM4/SZIer2mTXQFJktZmy5ctZdbRcztjS+bMnuDaSJLWFp6RkyRJkqSeMZGTJEmSpJ4xkZMkSZKknjGRkyRJkqSeMZGTJEmSpJ4xkZMkSZKknjGRkyRJkqSeMZGTJEmSpJ4xkZMkSZKknjGRkyRJkqSeMZGTJEmSpJ6ZlEQuIvaLiEURsTgijhnynNdHxJURsSAi/nWi6yhJkiRJU9W0iX7BiFgP+BzwSuAm4OKIOCeldGX1nB2BY4E9U0q3R8TWE11PSZIkSZqqJuOM3AuBxSml61JKK4GvAQe0nvMu4HMppdsBUkq3TnAdJUmSJGnKmoxEbhtgaXX/pvJYbSdgp4j4aURcGBH7dS0oIg6LiEsi4pLbbrttDVVXkiRJkqaWyUjkouOx1Lo/DdgReBlwCPBPEbH5qEIpfTmltHtKafetttpq3CsqSZIkSVPRZCRyNwHbVvdnADd3POfbKaXfpZSuBxaREztJkiRJWudNRiJ3MbBjRGwfEesDBwPntJ5zNvBygIjYknyp5XUTWktJkh6l6TNmEhGdf5IkrQkT/q2VKaUHI+II4PvAesCpKaUFEXEicElK6ZwS2zcirgQeAj6UUvrNRNdVkqRHY/mypcw6em5nbMmc2RNcG0nSumDCEzmAlNK5wLmtx46vbifgA+VPkiRJklSZlB8ElyRJkiQ9fiZykiRJktQz43JpZUQ8BXgGcD9wQ0rp4fFYriRJkiRptMedyEXEZsB7yb/ztj5wG7Ah8LSIuBD4fErph+NSS0mSJEnSKmM5I/cN4CvAS1JKd9SBiHg+8OaI2CGldMpYKihJkiRJGulxJ3IppVeuJvYL4BePd9mSJEmSpOHG/GUn5fff6vvrRcRXx7pcSZIkSVK38fjWypkRcSxARGwA/DtwzTgsV5IkSZLUYTwSubcDzy7J3H8AP0wpnTAOy5UkSZIkdRjLt1Y+r7r7d8CXgJ8CP46I56WUfjnWykmSJEmSRhvLt1Z+unX/dmDX8ngC9h7DsiVJkiRJQ4zlWytfPp4VkSRJkiQ9OuPxGTkiYu/6vyRJkiRpzRmXRA74VOu/JEmSJGkNGa9ErhHjvDxJkiRJUst4J3KSJEmSpDXMRE6SJEmSesZETpKkRzB9xkwiYuifJEkTbSy/I1e7p/y/e5yWJ0nSlLF82VJmHT13aHzJnNkTWBtJksbpjFxKaa/6vyRJkiRpzfHSSkmSJEnqmTElchGxeURcE9UHBCLi9Ij4k7FXTZIkSZLUZUyJXErpDuAiYD+AiHgysCfwnbFXTZIkSZLUZTwurfwn4NBy+w3A11NKD4/DciVJkiRJHcacyKWUfgj8r4h4KvBWcmInSZIkSVpDxuvLTs4A/hp4KKV07TgtU5IkSZLUYbx+R+404EYGl1hKkiRJktaQcUnkUkq3RMSLgCvGY3mSJEmSpOEe96WVEbFJfT+ldHFK6YESe+ZYKyZJkiRJ6jaWz8hdHhGvrx+IiA0j4q+B742tWpIkSZKkYcaSyO0LvD0izo+I34uIA4B5wAbAc8eldpIkSZKkUR73Z+TKt1O+OiI+BFwFLAdelVJaMF6VkyRJkiSNNpbPyE2LiGOB/w28B7gE+GxE7DxelZMkSZIkjTaWSysvBbYBnp9S+nJK6bXAycC3I+Lj41I7SZIkSdIoY0nk3pZSOiKldGfzQEppLvnzcWnMNZMkSZIkdRpLIvfLrgdTSvenlI4DiIgYw/IlSZIkSR3Gksj9MCLeFxEz6wcjYv2I2DsiTgfeOrbqSZIkSZLaHve3VgL7AYcCZ0bE9sAdwIbAesB5wMkppcvGXkVJkiRJUm0sPz+wAvg88PmIeCKwJXB/SumO8aqcJEkTZfqMmSxftnSyqyFJ0qPyuBO5iNgQeDfwe8AVwKkppQfHq2KSJE2k5cuWMuvouZ2xJXNmT3BtJElavbF8Ru50YHdgHvAa4NPjUiNJkiRJ0mqN5TNyu6aUng0QEacAF41PlSRJkiRJqzOWM3K/a254SaUkSZIkTZyxnJH7g4i4q9wOYKNyP4CUUtp0zLWTJEmSJI0ylm+tXG88KyJJkiRJenTGcmmlJEmSJGkSmMhJkiRJUs+YyEmSJElSz5jISZIkSVLPmMhJkiRJUs+YyEmSJElSz5jISZIkSVLPmMhJkiRJUs+YyEmSJElSz5jISZIkSVLPmMhJkiRJUs+YyEmSJElSz5jISZIkSVLPmMhJktYJ02fMJCKG/kmS1CfTJrsCkiRNhOXLljLr6LlD40vmzJ7A2kiSNDaekZMkSZKknjGRkyRJkqSeMZGTJEmSpJ6ZlEQuIvaLiEURsTgijlnN814XESkidp/I+kmSJEnSVDbhiVxErAd8Dng1sCtwSETs2vG8JwN/Afx8YmsoSZIkSVPbZJyReyGwOKV0XUppJfA14ICO530M+ASwYiIrJ0mSJElT3WQkctsAS6v7N5XHVomI5wLbppSGf0+0JEmSJK2jJiOR6/rV1bQqGPEE4GTgLx9xQRGHRcQlEXHJbbfdNo5VlCRJkqSpazISuZuAbav7M4Cbq/tPBp4F/CgibgD2AM7p+sKTlNKXU0q7p5R232qrrdZglSVJkiRp6piMRO5iYMeI2D4i1gcOBs5pgimlO1NKW6aUtkspbQdcCOyfUrpkEuoqSZIkSVPOhCdyKaUHgSOA7wMLgbNSSgsi4sSI2H+i6yNJkiRJfTNtMl40pXQucG7rseOHPPdlE1EnSZIkSeqLSflBcEmSJEnS42ciJ0mSJEk9YyInSZIkST1jIidJkiRJPWMiJ0mSJEk9YyInSZIkST1jIidJWmtMnzGTiOj8kyRpbTIpvyMnSdKasHzZUmYdPbcztmTO7AmujSRJa45n5CRJkiSpZ0zkJEmSJKlnTOQkSZIkqWdM5CRJkiSpZ0zkJEmSJKlnTOQkSZIkqWdM5CRJkiSpZ0zkJEmSJKlnTOQkSZIkqWdM5CRJkiSpZ0zkJEmSJKlnTOQkSZIkqWdM5CRJkiSpZ0zkJEmSJKlnTOQkSZIkqWdM5CRJkiSpZ0zkJEmSJKlnTOQkSb0xfcZMImLonyRJ64ppk10BSZIereXLljLr6LlD40vmzJ7A2kiSNHk8IydJkiRJPWMiJ0mSJEk9YyInSZIkST1jIidJkiRJPWMiJ0mSJEk9YyInSZIkST1jIidJkiRJPWMiJ0mSJEk9YyInSZIkST1jIidJkiRJPWMiJ0mSJEk9YyInSZIkST1jIidJkiRJPWMiJ0mSJEk9YyInSZIkST1jIidJkiRJPWMiJ0mSJEk9YyInSZpSps+YSUR0/kmSpGzaZFdAkqTa8mVLmXX03M7YkjmzJ7g2kiRNTZ6RkyRJkqSeMZGTJEmSpJ4xkZMkSZKknjGRkyRJkqSeMZGTJEmSpJ4xkZMkSZKknjGRkyRJkqSeMZGTJEmSpJ4xkZMkSZKknjGRkyRJkqSeMZGTJEmSpJ4xkZMkSZKknjGRkyRJkqSeMZGTJEmSpJ4xkZMkTbjpM2YSEZ1/kiTpkU2b7ApIktY9y5ctZdbRcztjS+bMnuDaSJLUP56RkyRJkqSeMZGTJEmSpJ6ZlEQuIvaLiEURsTgijumIfyAiroyIKyLiBxExazLqKUmSJElT0YQnchGxHvA54NXArsAhEbFr62mXArunlJ4DfAP4xMTWUpIkSZKmrsk4I/dCYHFK6bqU0krga8AB9RNSSj9MKd1X7l4IzJjgOkqSJEnSlDUZidw2wNLq/k3lsWHeAXx3jdZIkiRJknpkMn5+oOtHglLnEyPeBOwOvHRI/DDgMICZM2eOV/0kSZIkaUqbjDNyNwHbVvdnADe3nxQRrwCOA/ZPKT3QtaCU0pdTSrunlHbfaqut1khlJUmSJGmqmYxE7mJgx4jYPiLWBw4GzqmfEBHPBb5ETuJunYQ6SpIkSdKUNeGJXErpQeAI4PvAQuCslNKCiDgxIvYvT/sksAnw9Yi4LCLOGbI4SZIkSVrnTMZn5EgpnQuc23rs+Or2Kya8UpIkSZLUE5Pyg+CSJEmSpMfPRE6SJEmSesZETpI07qbPmElEDP2TJEljMymfkZMkrd2WL1vKrKPnDo0vmTN7AmsjSdLaxzNykiRJktQzJnKSJEmS1DMmcpIkSZLUMyZykiRJktQzJnKSJEmS1DMmcpIkSZLUMyZykiRJktQzJnKSJEmS1DMmcpIkSZLU2sJABAAAIABJREFUMyZykiRJktQzJnKSJEmS1DMmcpIkSZLUMyZykqTHZfqMmURE558kSVqzpk12BSRJ/bR82VJmHT23M7ZkzuwJro0kSesWz8hJkiRJUs+YyEmSJElSz5jISZIkSVLPmMhJkiRJUs+YyEmSJElSz5jISZIkSVLPmMhJkiRJUs+YyEmSJElSz5jISZIkSVLPmMhJkjpNnzGTiBj6J0mSJs+0ya6AJGlqWr5sKbOOnjs0vmTO7AmsjSRJqnlGTpIkSZJ6xkROkiRJknrGRE6SJEmSesZETpIkSZJ6xkROkiRJknrGRE6SJEmSesZETpIkSZJ6xkROktZhq/vRb0mSNHX5g+CStA5b3Y9++4PfkiRNXZ6RkyRJkqSeMZGTJEmSpJ4xkZMkSZKknjGRkyRJkqSeMZGTJEmSpJ4xkZMkSZKknjGRk6S1nL8VJ0nS2sffkZOktZy/FSdJ0trHM3KSJEmS1DMmcpIkSZLUMyZykiRJktQzJnKSJEmS1DMmcpIkSZLUMyZyktRzq/t5AX9iQJKktZM/PyBJPbe6nxcAf2JAkqS1kWfkJEmSJKlnTOQkSZIkqWdM5CSpB1b3OThJkrTu8TNyktQDq/scnJ+BkyRp3eMZOUmSJEnqGRM5SZIkSeoZEzlJmgL8LThJkvRY+Bk5SZoC/C04SZL0WHhGTpIkSZJ6xkROkiaIPyEgSZLGi5dWStIE8ScEJEnSeJmUM3IRsV9ELIqIxRFxTEd8g4j4txL/eURsN/G1lKTHxi8skSRJE2XCz8hFxHrA54BXAjcBF0fEOSmlK6unvQO4PaX0exFxMDAHeMNE11WS2qbPmMnyZUuHxv3CEkmSNBEm49LKFwKLU0rXAUTE14ADgDqROwA4odz+BvAPEREppTSRFZW0bnq8yZqJmiRJmiiTkchtA9QzpJuAPxz2nJTSgxFxJ7AF8OsJqaGkKe+Rkq311t+Qh1aueMyxhsmaJEmaymKiT3JFxEHAq1JK7yz33wy8MKX0vuo5C8pzbir3ry3P+U1rWYcBh5W7OwOLJmAVxmpLhiekjzfWx7JTsU5jKTsV6zSWslOxTmMpOxXrNJay1mnNl52KdRpL2alYp7GUnYp1GkvZqVinsZSdinUaS9mpWKexlJ2KdRpL2TVZp6liVkppq1GPppQm9A/4I+D71f1jgWNbz/k+8Efl9jRyA8dE13UNrf8l4x3rY9mpWCfXZ2rXyfWxTq6P6zOV6+T6TO06uT5Tu05TdX2m+t9kfGvlxcCOEbF9RKwPHAyc03rOOcBby+3XARek0tqSJEmStK6b8M/IpfyZtyPIZ93WA05NKS2IiBPJWfE5wCnAGRGxGPgtOdmTJEmSJDFJPwieUjoXOLf12PHV7RXAQRNdrwny5TUQ62PZqVinsZSdinUaS9mpWKexlJ2KdRpLWeu05stOxTqNpexUrNNYyk7FOo2l7FSs01jKTsU6jaXsVKzTWMpOxTqNpeyarNOUNuFfdiJJkiRJGpvJ+IycJEmSJGksJvvbVtaVP2A/8s8jLAaOacVOBW4F5neU2xb4IbAQWAC8v4ptCFwEXF5iHx3y2usBlwJzW4/fAMwDLqPjW3uAzck/yH5Vef3mm0R3LmWav7uAI6tyR5X6zAfOBDZsLff9JbYAOLJr/YGnAucDdwIrgSur2EGlbCJ/hrIu98lS3yvK+t3Win+sxH4DPABc1bHeHyzLbpc9AVhWyv4OuKFV7n3lPb4duLdV9t9KW/0GeAi4v4rtBlxYLffaKvYHwM/K+3Q+8JN2Xyht9RPgPuCeEn9/1VaLyvpc3yrXtNXCsq6LWvGPldjdZbmLqPpf9ZwEXN0qewKwvJRdASxhZN/9v6W+D5C/lfb9rXZaANxfytbL3Q34ZVnu/cB1Vaxpq/nlPZhHtV0A25O3lxXAHcCVVewI8raZyvIvb5X9alnH+8h9ro6dUp4/r8RGvG61rf6qvPd12dPI/fTesj7XVrEATgKuKbFlrbL/VV73XnK/uauK7VOtx90M+kwT37vE5wNfoRofSjv9vLzuWeX9mNvRTlvSGltKOy0qy/3nVqxppyvI48qmdI9Lf0/ub3XZ08j9txlzrqpiTTtdXdbz/a2y/1WVu7m893Nb7XQZ8N/ATq2yTTutJPepVWMlgzGqeX8WtOL1OLW4FavHqXs7yjbj1Mry/s2nNUaT+1oi97em3AnkfnJZKXsDrfGdPE79jrwd/Koq22x7lwEPlnWq69SMUyvJ28HVVawep74LnE2136ja6trymldXsaadHgZ+0CpXt9Nc4NuteNNO88pyF1Ptq1rj+Tmtsk1bzSP3iaWM3M814/nC8r8u27TVvPL+rahiTTs148ENVaxpp0XkfdsVVPvQ0k4/JY+Ld5dlNLG6nRbR2v+WtrquvG93tMo27bSwPDaf1r6bvF9fxqBPNWVPKG17P4Mxqi73vup1f9Wq07+V17yf3G/ur2JNOy1k0J/qsk1b3Vza4krKfILBGHVbaccFVaweoz5May7CYIy6hbxN17F6jLq81G3UPIY8pjzUKnsagzFqWWmnOt6MU7eW9/fmKlaPUXdW71ETb8apZeT+dnUVa8aoZn0WVO9NPUZdVdqwjtd9anErVm97V3SUbfrUTeX9WUQ1DyzPObu8D1dV5U5gMEbdRN4+FjByDvk+cl9aQZ4fHNkxRv2Gwbh7ZGuMuonB/KCZY/6W3M/mAf8BzKra5nzgKdX+5LOlPa4Anvdo5viT+TfpFVgX/siTnWuBHYD1yQPErlV8L+B5dCdy05uOBDy5bMC7lvsBbFJuP5E8sO3RsYwPAP9KdyK35WrqfTrwznJ7fWDzIeu2nPz7FpB/zP16YKNy/yzgbdXzn0UeoDYmf0bzP4E/b68/8AngmNI2nwVuq2K7kHc6lwJvbJXbF5hWbn+VPLjW8U2rNv8E8NvW+mxL/iKe5eQBsp3IfbDr/QJeXtZlgxLfZ8j7uRdwBvCr6rHzgFeX2PuAe6vYxcBLy+2jgH9s94WyHieVOh0DnFzFdgFeDFwC7N4qt295D6aXdprTim9aYs8D/oK8k6v7X3OQ4RbypL4uewLwUTr6bmmrnwB/WGLb18ut+v0ZwPGtsucx6C+vIe8Am9jFwEvJ28Xh5B3Nqu2C3BcPBjYBvgi8t4o9F9iOvE00fbku+5qy3E3IO9C6bNOngpyEHENreyxtfyY5QamXexr5m3lHbcfA28lJ1hPK627dsdymTt8sz2/KXk1+74Pcb06ryr6IPGndqep/FzJIXs4CDi63/4ec/Daxup22pDW2VO0U5MlFXXbT6v39DHliPmJcKu10BnmiUy/3NOB1XeNZ3U7l/vHt5VbLv5w8OWzKXg3sUm6/p9T3X0vdntC0U1nfTwLvaI9R5fbtwGdbr9WMUyuAfVqxepy6s6Ns06duIP9Ezxc7xqn7S/22rB4/AfjgsPGdwTjVvH9bDxn77wT+pvVYM07dQN6OfjRknPop8B/1foPBeH46ua/OqWJNOy0HPtYqV7fTPOC7rXjTTqeTt68vUu2rGIzn9zCY7DVlTyCP56P2c4wcz08HjuraD5bY98l9rinbtNPpwN8BP6pidTsdSh6jVu1DGdmnjin3m1jTTj8Cdm/vf1ttNadVtt72/qK0U3vf3bTVEvJY05Q9gdKnOl5zVTuV2Nbt5VblPg18pCp7HvDqatz4UWvZFwN/Rp5P/O/SVmcBbyv/Dy+xfyy3m1gzRi0t6zJiLlJeq5mnnNUq2/SnbcjbwIfb85jy3t4D3NNa7mnksbxzDkQep77exEpbtedH25ATtXe0yl5N3rddTz5QdVqJHVrW84/J86qPA+8q78mODLa7Z5V2/TSDedeO5D41u7zmnq1YMz94FjlhbpfdlMF87i+BLzWxUvdXkBO8G4GnVeVOIG93XXPBHcl96mfkBG1j8lxg1XLTYB75a3KfqMueB7y7LPdA4McM5pgLgOuqbe9/GLmtzan64nfJ+7A9gJ93jZFT6c9LKyfGC4HFKaXrUkorga8BBzTBlNJPyEcLRkkp3ZJS+mW53RxZ36bcTymle8pTn1j+Ul0+ImaQN/J/eiwVjohNyYnFKeW1VqaU7uh46j7kM0hLqsemARtFxDTyhnhzFdsFuDCldF9K6UHyhjaD0et/AHB6aZszyIMGpS4LU0rNEc276kIppfPKciEf9d+8Fb+r/P8Jua1GtBc5Cfor8uTr9o71HfZ+HU6e+DxQ4td2lSUnHvuUuq9aJHkH8pNy/3dVbGdy0tOsz56lDnVfOAD4h9JPTicPRAuBbUpb/Td5xzOiXNNWKaVbyEe6Z7Tid1X970nkI6qr+l9pqyPJk+5R/RO4e0jfPRw4MaX08xK7vlUO8k7nZcCZrbIJeKgsdzMGR9G3adoq5dF4LnkSUG8XewPfKNvM6cBrm1hK6dKU0g3lte8t/59Yxc+ttreLgJlVrO6D08prrSobEeuRk4APtJfbFBqyHTft9HBK6Z6U0q3tsmVdo6zbuVWs6VOJfNT25qrsQ8ADKaWry/jw1LIMIqJZ1jdK7IlNrLxe3U7TaY0tTTuV92MT8gSkid1VvcaWwO/XZat2Opk8oRs1Zg0Zz1a1U4m/dEjZnckJ/0nVw4nB2LIteXLVlN2iaady/8fkPtU4gNyPIG9fr6lfrxqnRmmNUw8Az2jF6z61Md3j1G87Hn8khwN/U73Ore0nlPfnScC32tVm0FabMnJc3xn4SdlvbAs8syy/2W8cQE7g9iKfMXltE0spLSQfDNqMPA5Rxc5L+ZuuNyW/N79txe+q9lVX5NCIfdXJ5ANKGwD/0qoTDA68tfdzTTs18b9tl61ed1fyONXEEnniuhf5AMnNVawez88n96d6H1r3qdOBQ5rYkP60TxWv+9SFwPOrWN2fnlTq2N53N/u+VOre3q+Pek2q/V5pn1s7ltv0qdeTE6smVvenzcj9qS67c1mPaeSDA39G3hZuIY9R3ymxr5Mn7RuXtq7HqFFzkZS/bK+JXU7ur02sbqf1gGl12TJGfZiy/x4yx+l83dJWf9vEyH25XfZJJfafrbKJfEBzGnlcuqXE7iWPHxuXtvougwTmQAb9aRfy2e7Z1bzrwLLtbUSeRz3QijX9aRfyGbCnt+J3ldiF5AMVD1evCznJOr88/lArBt1zwQNLO50P/KzEbhlSdkPgK62yiUG/2ZB85q+ZY84kn5GjLP/5jNzWXltuH1CWm1JKFwKbR8R0pjATuYmxDXnC2biJkZPWRyUitiMfbfp59dh6EXEZ+XT9+c3kuPK35MH54Y5FJuC8iPhFRBzWiu1APgrzzxFxaUT8U0Q8qWMZB5OPhOYFprQM+BT5KMwtwJ0ppfOq588H9oqILSJiY/LkZ9uO5T6tbMCUejyeb1g9lHyUb4SIOCkilpI33Furx/cHlqWULl/NMo+IiCvIR7rq7Wcn4CUR8fOI+DHwnCHlX0I+krSyeuxI4JOlTseRLylozAf2L7cPorRVqy+saqvy/+m0+km1jtsNiR0KfLcdr9rqjeQjn88Fft7VVh3LPiIiroiIUyPiOVVsRFuVZbXr9BLyWctrWsut2+pTwOeqWN1WrycP6LcyuKTrjjIpbJKEveneZp4wbJuKiA3IicD76lhE/DM5+fx98tG/uuwR5Mu6biXvNNvLPam0062t2DOBN0TEJRHx3Yi4sqtOwJ+Sk61rq9g7gXMj4ibgzeSjrk1bXAQ8MSJ2J48P1wBblWVt0bRTiX2EnHR1OYnhY8vfkXfeI9q2aqf9yL8VWpdt2un/kLeP9nJPIr/Hy8mTrMaqdiKfef77IXU6g7xTv6d6rG6n9wJvqcr+mkE7JfLlOS+vxsp6jHoQ2G7IWJqAzw2JQU54n9+OR8RJ5AnIB4EXNbFm2ytt9DTypK9ebjNGbQH8oLXcncjb1tOB6yNiYUedXkJ+777YKttcvjcD+Afg2VWs2fZ2KPd3bO03nkaepN4G/D/gma19yg7kA1gfGbK/aa5m2bYj/hlyIvxXwIubWNVO95Hf07/vKPveUreryzbYxJp2+mlpx3M6yu5APuC3EXBWFTuyrOMzyOPMc6pY13he70PbY/nWVazLwUPih5L3matirbH8+Lpsx3h+YGu5q8Zy8jbSxNpj+QuG1Okl5P3aXlWsPZYf2yo7n3yG/lPAL8hj653l9h0ppRtL7N/JY3l7rvEQef8wai5S5imfAU4kn4lfFStjVHOp4gdbZY8gH1D9BLk/t+c4J5GTqcUdr/tM8sHJRB6Lb+2o8x7kAxILWmXfSU42nkxOJN9V2uIsBgfv9gLeRE5YmnlV05/mAy8AntYx75pPTqQ3GzInm0++LPi/OuL7kMfxt5D7/GvI2+j+5P3Ks8jzpI1a5Y4A/ho4KCJ2aC13J/I298aI+GlEvLijThuS+/dvW2WPBN5Q6vQZ8kGcJnZ1aT/I2976HdsajNN8fSKZyE2M6HjsMR1JjYjm8qkj66NGKaWHUkq7kXeuL4yIZ1VlZgO3ppR+MWSxe6aUnke+VOC9EbFXFZtGvnztCyml55KP/BzTqtP65J3S16vHnkI+orE9eUf2pIh4U1XfheTLPs4Hvkc+IvYg4ywijivLPbsdSykdl1LatsS2KM/fmJxEHd9+fuUL5MF4N/IgXB+lmQY8hTwQf4i8A+lyCHmyWjucfOnOtuSjWPWgcSj5vfkFeRBaOawvlPXYhLyDGRUjD6ajyrXaakS8aquvk89yHVme226rJ7XK1m31a+CCKla31fFl2e36HgKc2bGudVsdQ95pNrG6rTYhf05kBvmM+C7NglNKD5ETiatobTPFw8O2KfIE9svkvr0qllJ6e3lsITkBasruRd5p/H153ftbyz2WPEF5QVmXz1axDYAVKaXdyUn0b4bU6WDgHa3YUcBrUkozyJ9Vu6hqi/9VypxOnmBdS570wODMXJP4zaN7rNoI+HXX2FLK7kK+TGteHSvt9K6y7J2qMs8o7XRtibUTsWPJl+98jdz/DqliG5An1CeQL7f+yyF1ehq5X9aOIu/om8tx3lLVNZHb6WRyX/oyeYLWHishnym/m+6x9FLyBGtUrGx7PyYnBSPiKaXjyJOyE8mXDDWxZtvbkzzZO7iK1dvdqeRJb73cZtvbgTwJ27ijvoeQz7K09w2Hl/aaWdbnt1XsUHJSdCZ5/LqvY7+xap9S2qodezL5jHnX/uYw8mTzQx3x5jLBM8lnEe8l94WmnaaRk8B/bpX9Avlg3vrkz0deUsWadnp7aaPnl7q367wz8NXWcg9ncFb5JPKBhyY2ajyntQ9tlP3rE7tiVXxU2dKnHiJv56ti1Vj+VfLllfsDXx+y79uvKlv3qV+RLx9sYu393llD1ueQjlg9lh9F7q91/FDyZYQfI4+pt5P3M68u69nMNV5EHndHzDXI89tX0zEXKWU/SE60t6pjZYzalTzG/Z+q7FvIY9QZ5XXvbS23GctfWf7/Qyu+AXl8XUxOzK7sqPObyf2mXeejyAnKL8njwbdLW7yRvP2/v7wX+5MvKx0xr6rmXZvQmneV2I3kOUvXnOxPyUnQYR1l300eOzdl8JntZn7wvvKaTyN/tq2JNf1pl1LmotZyp5H77xHk+dl/dtTpRaUN2vPIw8vrvpu8r72wiv0V8NRq2xs2Bx/zfH3CpSlwfefa/kc+mvH96v6xwLGt52xHx2eqSuyJ5EnRBx7hdT7CyGvZ/x+DD5MuJx+Z/JchZU9olX061Zd5kCd832mVOQA4r/XYQcAp1f23AJ9fTZ0/Tj4iNmL9yR+cnV5uv4B82r9d9kfAn7TbjXw05mfkHfDq2nVP8kQZ4NnkCeQN5e9B8tHcUV+GUp7/4qZsuf894GXV/SXAwlaZaeQd4R6tdb2TwU+BbEe+dLDrNXcif25gRF9o2qr0kx+Sk/d22R+XNvlA6/GmrTYd1sfKcn8M3LKatrof+Mgjla3bikG//jWwVUc7bdexrneSB9qm7IrVtNVF1XbxofI6zWdI/qiUb28zNzDyM0er4uX22Qw+izWibHnspQw+f/URBp8Jadqq+VB5V9mXkZPlj5AnGVcB25VYkI/Otuu0BTnB27C1rvUX5sykfFlQq2wzPiwv79995Ener8mXld1EThQeoDV2kBObm+kYW8g75/u7YtXr3loeb+K3l9t3kPtTKv/r5db1XdHEmnaq4g931Olk8uRgSRX7TtNOpewt5Il151hJ/szIWQw+41GPUdOBRUPG0h8x+EzTqhjVODVsHC6PzSInmSeQvySove01Zyba5bajjDNVndvj1LXkswtNnZptb0a7Towcp4J8OVZ7XZ9e3oNm23tJaedF5KsUbmjaimqfUsqtqNqpjr2VnGQtqV6nXfaGqp1eQr6MrGmnpeT+dGN5blfZ7aqy32EwRjXxa8kT/rrsNuQ+NaO1rndW5Zp26tp/7kSeIJ9XPVb3qbdRfV663Z/o3v82feqgdqzVn5Y0cUaP580Bp6d3lH0X+ZL5Yfu9W4Aftso0ferQ1rq2+9N9HetzEPmy153IE/63kBOBX5MTm1MYjOUj5hplnepxZ1WcnFgsYTCWt8seVN7LuVX8evLYcCv5QEQzlj+asp8nj1PvKXWOsv51nbYoyz2tVecvkPtf0xYzyUngqLkVgzGqmVcNG6M+DrxnyBi1Kkb3GDWibGuM+jg5qewao/6uo9x2DMaops5dY9TfVnXqGqOasl1j1Kg5Jrk/3T+kbb4EHNK1TU7VP8/ITYyLyZeabF+Ooh3M6LMynSIiyBvvwpTSZ1qxrSJi83J7I/KHS69q4imlY1NKM1JK25XXvCCl1ByRelJEPLm5TR4A5ldllwNLI3+uBPLR2ytb1TuE0ZdQ3AjsEREbl7rvQz5aVtd76/J/JvloT9elIeeQBxHIRwDbZ5c6RcR+wNHA/iml+zriO1Z3X8Hg813zUkpbp5S2K+11E/lytAersvUZuH3JE4/G2eTLO4iInRh8FqnWvD/LW4/fTE4AIB9pWnXZZdVWTyBfUrGS0X2haatTyuue1lrnIB85vr4uV7cV+ejhwlZ8x6r/PUy+zGhEW5GPHK4gf57xo3VbVWUhJ3PttjqFvOO/n7xjbrfTiR3r2rTVKeRL5BZ0tNXW5EsqvlhtFwvJSe7byzbzVvJnykZsM+SjuJuW5azapiLineTPZr075c9iNbFFEfF75flbkfvqVVX8Fymlp5MPRuxGnqw8u1ru9Go7fm2pS1Ons4G9y3L/mHz5V3s7fzv5INGK1rpuFhE7lbL7Awtb67N1SulY8pHRBeQjzxeklN5Y2umylM/mfZs8CVk1dhR3AM9pjy2lndYDnlrHgDc37VRe6ytluU3Zp6SUnp5S2jylNI18tPsV1XKnl/puSz4r962qTmcDe5f4m8hnoUaMd+Sd8b+klGZVdTqgaadS9sPkbzOr12frMlZuQd5WTmMwVp4DvLWMn+8Cvt0eS8v99arb+wLzq23v4CHxHasxurlMaV/g4pTS1uSzLc8mj1MvJo8b85sxqizr4PJYXaezgVdFxJPLOLVBKd+M/a8gJxd3tutE3vZeVeq0N3mC1dS3uSyp+RxncyVEs984h3zmcyn5jOm3q1izv1lBnhCuKle106uBG9v7o4jYsdlXkc9yXFViv6zG823J4/xB5blN2elV2cPKOjZ1avrUcvLYtHH5X+8Hn02eeDeXWjaxm8lnZJaSJ9vXVK/ZHs9vZ+T+r97vHcXIcbNtxP63NZ7/WStW7/f2J49zZ0Lnvm8F8Fdl3dv7vcMZOQ9o7/c2I2/btWa82re1rvV+b+/yunWdt6bMJ8gHoL7IoI1/SP5yiz3IVyM0/ameazwI7N6ei5QxahfyGLNhK9aMUTcCfwgsruKfKWP5n5T4faUOTdnpVdk9yONsPQc6m5ww7FHa4upWnQ8if37yBa06X1naNZWyf1zKNK/b9KkZ5Pf/WwzmVXV/eg95jOqadz2xLGNVrNWfNumI71i9T/uTE+M/JX++rJkfvJA8Rv0J8KpSru5PbyaPH3Wdmv3e1qVPbUQ+Q9zUt+lPK9t1ovSpUqe9yYlkE2uuvmq2vR9VbfNWyudzS5u9JbI9yAdQm0vop6bJziTXlT/yTuxq8s7vuFbsTPKE9nfkTl9/M9qLyRtw8zXFl5EvmYJ8hPPSEpsPHL+a138ZI78dbgfyKefma9aP6yizG/lI6BXkjespVWxj8pmAzTrKfZS8oc0nX4awQSv+X+TB6XLyYDRq/Smf7yDvKB9oxQ4stx8qfw9XscXkHehlDH4GoC77zVKvO8g7jlFtXup4DznhqsueweCrqle0YuuTzw7MJ19y9Jv2ssmTwIs71vXF5Mnn7eTBqY69v/Sbq8vyR/WF0laXlFjzldVN7EDy5Cox+Ir6Jta01TUl/pvWcr9J/vreVMo1X5H+mo7+uaBV9gxyX0/kSeH8KrY++QhqIidxixnZr08jfxana11fTO5bibwjXVTFmra6gXzEbsR2Qe7z88j96Y5S5yb2F6XNHyzt9NtW2QdLW93H4Gu2jydPiH5alntNVW7E9shgW32otdwLGHx9/e3k7aKJbU4+snsNg6+cbi/3YgZfk1wv98BSp0XkPnFVK/5JBl+rfiTV+FDa6aKy3K+TLxWa29FON5MvTarLPlje9+Y9O5XBN0A27TSffOZvU1rjUmv7q5d7QVX2X8gT+7mtdppHPnr8B+3lknfa+7XHwqqdLi/P2aEV/2RphxUMfv7huBJrxqjrGfxEQB0/kLytP0zuU/dUsWbbu5LBgYy67DfLe3M/eftZRDVGMxi/V5b3tinXjFFXMfha9nq565PH8uYM7A2t5Z5GnuSM2jeQt715pey9VPsyRo5Tp9Lab1RttYTBWNLEmvG8GfvurmL1eL6IPJbVy23G86sZ/KTIiH1Vqd/NZRl12aatRpVl5HjebCcj9oOlrf66Y12b8XyrRr3wAAAE4UlEQVRRec+vqWJ1O32K1j60aqfFpS1mVbGmnR4gjz8rW2WbtmouJTu1ijXtdAX5ANbtdO+7NyaPUdtXjzXtNK+85k5VrG6nS8l9brPWMk8jX+7WXtemnS4nj2N3tOJNW/2m/K2aTzAYo37LoD81sXqMurssty7bjFHNwYNfVbF6jLqCwZg7Yh5DnuM83FruBa2yi1rxZpxqfsphcb1cyhhFx/yJwTjVXC2wqIo1Y3lzhcPllG/JZdCfrintcFUr3vSph0u73FXF6m3vntLWddmmT91b2nlBE2vN9VaW5+3T6k/Nz0Bd3Vpu06fqn+TZp9Wf3k1rHtnqU/cw+EmLZo55J4N50LmttvkB+eAj5DN5nyuvO49ypnIq/zWnICVJkiRJPeGllZIkSZLUMyZykiRJktQzJnKSJEmS1DMmcpIkSZLUMyZykiRJktQzJnKSpN6IiO0iYv4jPOcZEfGNx7jcH0XEooi4PCIujojdxlbTx6b8btEFEbFpRGwbEddHxFNL7Cnl/qzyu4Pfm8i6SZKmJhM5SdJaJaV0c0rpdY+j6BtTSn9A/rHyT45ztR7Ja4DLU0p3pZSWAl8A/qbE/gb4ckppSUrpNuCWiNhzgusnSZpiTOQkSb0UETtExKUR8YLW46vO2kXE2yLiWxHxvYi4JiI+8SgW/TNgm2p5X4iISyJiQUR8tHr8hoj4aET8MiLmRcTvl8e3iojzy+NfioglEbFlib0pIi6KiMtKbL2yuDcC367qcDKwR0QcSf6h209XsbPL8yVJ6zATOUlS70TEzsA3gbenlC5+hKfvBrwBeDbwhojY9hGevx85WWocl1LaHXgO8NKIeE4V+3VK6XnkM2gfLI99BLigPP7vwMxS511KPfZMKe0GPMQgIdsT+EWz0JTS74APkRO6I1NKK6vXvAR4ySOsgyRpLTdtsisgSdJjtBX57NWfpZQWPIrn/yCldCdARFwJzAKWdjzvqxHxJGA94HnV46+PiMPI+8zpwK7AFSX2rfL/F8CfltsvBg4ESCl9LyJuL4/vAzwfuDgiADYCbi2xp6aU7m7V59XALcCzgPOrx28FnvHIqy1JWpt5Rk6S1Dd3khOxR/s5sQeq2w8x/CDmG4HtgX8FPgcQEduTz7Ttk1J6DvAdYMOOZdfLjSHLD+D0lNJu5W/nlNIJJfZgRKzaJ5cvW3klsAdwVERMr5azIXD/kNeQJK0jTOQkSX2zEngt8JaI+PPxXHC5pPHD5M+n7QJsCtwL3BkRTyOfJXsk/w28HiAi9gWeUh7/AfC6iNi6xJ4aEbNKbBGwQ3k8yJdqHplSupH8xSufqpa/E7Dab+6UJK39TOQkSb2TUroXmE0+W3XAOC/7fvKXi3wwpXQ5cCmwADgV+OmjWMRHgX0j4pcMLo+8O6V0JTlJPC8iriBfLtmcafsO8LJy+13AjSml5nLKzwO/HxEvLfdfXp4vSVqHRUppsusgSdJaIyI2AB5KKT0YEX8EfKF8ucnqykwHvpJSeuWjWP5PgANSSrc/0nMlSWsvv+xEkqTxNRM4q3zmbSX5DNtqpZRuiYh/jIhNU0p3DXteRGwFfMYkTpLkGTlJkiRJ6hk/IydJkiRJPWMiJ0mSJEk9YyInSZIkST1jIidJkiRJPWMiJ0mSJEk9YyInSZIkST3z/wG09rrfd63HbgAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "\n", " \n", "def f_poisson(lam,k):\n", " return lam**k/(math.factorial(k)*(np.e ** lam))\n", "\n", "def display_poisson(lam,limit=15):\n", " X = list(range(limit+1))\n", " probs = [ f_poisson(lam,k) for k in range(limit+1)]\n", " \n", " fig, (ax,ax1) = plt.subplots(2,1,figsize=(12,12), sharex=True) \n", " plt.tight_layout(pad=0.4, w_pad=4, h_pad=6.0)\n", " plt.setp(ax.get_xticklabels(), visible=True)\n", " ax.bar(X,probs,tick_label=X, width=1.0,edgecolor='black')\n", " ax.set_title('Probability Distribution for Poi('+str(lam)+')')\n", " ax.set_ylabel(\"P(X=k)\")\n", " ax.set_xlabel(\"k in Range(X)\")\n", " \n", " cum_probs = np.zeros(len(probs))\n", " for i in range(len(probs)):\n", " for j in range(i+1):\n", " cum_probs[i] += probs[j]\n", " ax1.bar(X,cum_probs, tick_label=X,width=1.0,edgecolor='black')\n", " ax1.set_title('CDF for Poi('+str(lam)+')')\n", " ax1.set_ylabel(\"P(X<=k)\")\n", " ax1.set_xlabel(\"k in Range(X)\")\n", " plt.show()\n", "\n", "\n", "# Modify the parameters in this next line to see different examples\n", "display_poisson(50,limit=100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Poisson Approximation to the Binomial\n", "\n", "The Poisson is regarded as a good approximation for the Binomial when N is large (say $\\ge 50$) and p is small (so that $Np \\le 5$). In this section we will compare the two and quantify the accuracy of the approximation. " ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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tJt2roVn33c2Re241KH7kmTePQWskSZLk8BJJkiSpMZNuSZIkqTGHl6zChhu7fcN1V8MQw0skSZI0Nky6V2HDjd3e8w8XjUFrJEmSNByHl0iSJEmNNU26I2KXiLgpIqZExKFDTN8xIq6MiEURsVcn/lcRcXXnb35E7FmnnRQRt3embdtyHSRJkqQnqtnwkogYB3wTeAswFbg8IiZm5g2dYncB+wOf6M6bmb8Dtq31PBeYApzXKfLJzDyjVdslSZKk0dRyTPf2wJTMvA0gIk4F9gAeT7oz8446bfFS6tkLOCcz57ZrqiRJktROy6R7I6D71RpTgdevQD37AF/ti30pIo4A/hs4NDMXrFgTV21XXXc9Z61956D4Pffey1m//s0Q5Wc/Gc2SJElSn5ZJdwwRy+WqIOIFwCuAczvhw4DpwJrAccCngUG/bR4RBwIHAmy66abLs9hVxtx5C9hwqzcNii967DI23Oo1g8tfeN6gmCRJktpr+UHKqcAmnecbA9OWs453Az/PzEd7gcy8N4sFwPcow1gGyczjMnO7zNxuwoQJy7lYSZIkafS0TLovB7aMiC0iYk3KMJGJy1nHe4EfdwO195uICGBP4PpRaKskSZLUTLOkOzMXAQdRhobcCJyemZMj4qiI2B0gIl4XEVOBvYHvRMTk3vwRsTmlp/x/+qr+YURcB1wHbAB8sdU6SJIkSaOh6S9SZubZwNl9sSM6jy+nDDsZat47KB/G7I/vNLqtlCRJktryFyklSZKkxky6JUmSpMZMuiVJkqTGTLolSZKkxky6JUmSpMZMuiVJkqTGTLolSZKkxky6JUmSpMZMuiVJkqTGTLolSZKkxky6JUmSpMZMuiVJkqTGTLolSZKkxky6JUmSpMZMuiVJkqTGTLolSZKkxky6JUmSpMZMuiVJkqTGTLolSZKkxky6JUmSpMZMuiVJkqTGTLolSZKkxky6JUmSpMZMuiVJkqTGTLolSZKkxky6JUmSpMZMuiVJkqTGTLolSZKkxky6JUmSpMZMuiVJkqTGTLolSZKkxky6JUmSpMZMuiVJkqTGTLolSZKkxky6JUmSpMZMuiVJkqTGTLolSZKkxky6JUmSpMZMuiVJkqTGTLolSZKkxky6JUmSpMZMuiVJkqTGTLolSZKkxky6JUmSpMZMuiVJkqTGTLolSZKkxky6JUmSpMZMuiVJkqTGTLolSZKkxpom3RGxS0TcFBFTIuLQIabvGBFXRsSiiNirb9pjEXF1/ZvYiW8REZdFxC0RcVpErNlyHSRJkqQnqlnSHRHjgG8CbwO2Bt4bEVv3FbsL2B/40RBVzMvMbevf7p34McDXMnNLYCZwwKg3XpIkSRpFLXu6twemZOZtmbkQOBXYo1sgM+/IzGuBxSOpMCIC2Ak4o4ZOBvYcvSZLkiRJo69l0r0RcHfn+dQaG6m1I2JSRFwaEb3Een1gVmYuWsE6JUmSpCfd+IZ1xxCxXI75N83MaRHxIuD8iLgOeHikdUbEgcCBAJtuuulyLHb1NfP+P3HkwR8cFF/veZvw8cOPGoMWSZIkPTW0TLqnApt0nm8MTBvpzJk5rf6/LSIuAF4N/BRYLyLG197uYevMzOOA4wC222675Un2V1tPi0c5cs+tBsWPPPPmMWiNJEnSU0fL4SWXA1vWbxtZE9gHmLiMeQCIiOdExFr18QbA/wFuyMwEfgf0vulkP+CsUW+5JEmSNIqaJd21J/og4FzgRuD0zJwcEUdFxO4AEfG6iJgK7A18JyIm19lfBkyKiGsoSfa/ZuYNddqngUMiYgpljPcJrdZBkiRJGg0th5eQmWcDZ/fFjug8vpwyRKR/vouBVwxT522Ub0aRJEmSVgn+IqUkSZLUmEm3JEmS1JhJtyRJktRY0zHdWrksWLCAs379m0Hxq66bPQatkSRJeuow6X4KyUw23Oo1g+JzLzxvDFojSZL01OHwEkmSJKkxk25JkiSpMZNuSZIkqTGTbkmSJKkxk25JkiSpMZNuSZIkqTGTbkmSJKkxk25JkiSpMZNuSZIkqTGTbkmSJKkxk25JkiSpMZNuSZIkqbHxY90ALdvnjj6WqdMfGBSfMXPmGLRGkiRJy8ukexUwdfoDbLPbhwbFJ51zyhi0RpIkScvLpHsVcPs1F/Hw9FsHxXP+nDFojSRJkpaXSfcqYNzC2Ryy8w6D4h+95LExaI0kSZKWlx+klCRJkhoz6ZYkSZIaM+mWJEmSGjPpliRJkhoz6ZYkSZIaM+mWJEmSGjPpliRJkhoz6ZYkSZIaM+mWJEmSGjPpliRJkhoz6ZYkSZIaM+mWJEmSGjPpliRJkhoz6ZYkSZIaM+mWJEmSGjPpliRJkhoz6ZYkSZIaM+mWJEmSGjPpliRJkhoz6ZYkSZIaM+mWJEmSGjPpliRJkhoz6ZYkSZIaM+mWJEmSGjPpliRJkhoz6ZYkSZIaM+mWJEmSGmuadEfELhFxU0RMiYhDh5i+Y0RcGRGLImKvTnzbiLgkIiZHxLUR8Z7OtJMi4vaIuLr+bdtyHSRJkqQnanyriiNiHPBN4C3AVODyiJiYmTd0it0F7A98om/2ucAHMvOWiHghcEVEnJuZs+r0T2bmGa3aLkmSJI2mZkk3sD0wJTNvA4iIU4E9gMeT7sy8o05b3J0xM2/uPJ4WEX8CJgCzkCRJklYxLYeXbATc3Xk+tcaWS0RsD6wJ3NoJf6kOO/laRKz1xJopSZIktdUy6Y4hYrlcFUS8APgB8MHM7PWGHwb8GfA64LnAp4eZ98CImBQRk+6///7lWawkSZI0qlom3VOBTTrPNwamjXTmiFgX+BXwmcy8tBfPzHuzWAB8jzKMZZDMPC4zt8vM7SZMmLBCKyBJkiSNhpZJ9+XAlhGxRUSsCewDTBzJjLX8z4HvZ+ZP+qa9oP4PYE/g+lFttSRJkjTKmiXdmbkIOAg4F7gROD0zJ0fEURGxO0BEvC4ipgJ7A9+JiMl19ncDOwL7D/HVgD+MiOuA64ANgC+2WgdJkiRpNLT89hIy82zg7L7YEZ3Hl1OGnfTPdwpwyjB17jTKzZQkSZKa8hcpJUmSpMZMuiVJkqTGTLolSZKkxky6JUmSpMZMuiVJkqTGTLolSZKkxky6JUmSpMZMuiVJkqTGTLolSZKkxky6JUmSpMZMuiVJkqTGTLolSZKkxky6JUmSpMZMuiVJkqTGTLolSZKkxky6JUmSpMZMuiVJkqTGTLolSZKkxky6JUmSpMZMuiVJkqTGTLolSZKkxky6JUmSpMZMuiVJkqTGTLolSZKkxky6JUmSpMZMuiVJkqTGTLolSZKkxky6JUmSpMZMuiVJkqTGTLolSZKkxky6JUmSpMZMuiVJkqTGTLolSZKkxky6JUmSpMZMuiVJkqTGTLolSZKkxky6JUmSpMZMuiVJkqTGTLolSZKkxsaPdQM09mbe/yeOPPiDg+LrPW8TPn74UWPQIkmSpNWLSbd4WjzKkXtuNSh+5Jk3j0FrJEmSVj8OL5EkSZIaM+mWJEmSGnN4iViwYAFn/fo3g+JXXTd7DFojSZK0+jHpFpnJhlu9ZlB87oXnjUFrJEmSVj8OL5EkSZIaM+mWJEmSGjPpliRJkhoz6ZYkSZIaa5p0R8QuEXFTREyJiEOHmL5jRFwZEYsiYq++aftFxC31b79O/LURcV2t8xsRES3XQZIkSXqimiXdETEO+CbwNmBr4L0RsXVfsbuA/YEf9c37XOBzwOuB7YHPRcRz6uT/Ag4Etqx/uzRaBUmSJGlUjCjpjogdIuKbEXFtRNwfEXdFxNkR8fcR8exhZtsemJKZt2XmQuBUYI9ugcy8IzOvBRb3zbsz8JvMnJGZM4HfALtExAuAdTPzksxM4PvAniNfXUmSJOnJt8ykOyLOAT4EnEvpVX4Bpef6M8DawFkRsfsQs24E3N15PrXGRmK4eTeqj1ekTkmSJGlMjOTHcfbNzAf6YnOAK+vfVyJigyHmG2qsdY6wXcPNO+I6I+JAyjAUNt100xEuVpIkSRp9y+zp7iXcEfG2/mkR8eFumT5TgU06zzcGpo2wXcPNO7U+XmadmXlcZm6XmdtNmDBhhIuVJEmSRt/yfJDysxGxU+9JRHyavjHafS4HtoyILSJiTWAfYOIIl3Uu8NaIeE79AOVbgXMz815gdkS8oX5ryQeAs5ZjHSRJkqQn3fIk3bsDR0fEGyPiS5QPSg41lhuAzFwEHERJoG8ETs/MyRFxVG8MeES8LiKmAnsD34mIyXXeGcAXKIn75cBRNQbwEeB4YApwK3DOcqyDJEmS9KQbyZhuoAwhqcnyb4ErgL3qN4gsbZ6zgbP7Ykd0Hl/OksNFuuVOBE4cIj4J2Gak7ZYkSZLG2jKT7oiYzZIfVlwTeBGwV0RkZq7bqnGSJEnS6mCZSXdmPuvJaIgkSZK0ulquX6SMiHW7/yVJkiQt2/L+DPwFff8lSZIkLcPyJt09Q/1IjSRJkqQhrGjSLUmSJGmETLolSZKkxlY06V7q93NLkiRJGrC8SXf0/ZckSZK0DMubdL+n778kSZKkZVhm0h0R6/QeZ+bN3f8R8eJ2TZMkSZJWDyPp6b4mIt7dDUTE2hHxReDXbZolSZIkrT5GknS/FfhgRPwmIl4SEXsA1wFrAa9u2jpJkiRpNTB+WQUy81bgbRHxSeCPwHRg58yc3LpxkiRJ0upgJGO6x0fEYcD/Az4KTAK+EREvbd04SZIkaXUwkuElVwEbAa/NzOMyc0/ga8BZEXF009ZJkiRJq4GRJN37Z+ZBmflQL5CZv6SM5/ZHciRJkqRlGEnSfeVQwcycl5n/DBAR/liOJEmSNIyRJN2/i4h/iIhNu8GIWDMidoqIk4H92jRPkiRJWvUt89tLgF2AvwV+HBFbALOAtYFxwHnA1zLz6nZNlCRJklZtI/nKwPnAt4BvRcTTgA2AeZk5q3XjJEmSpNXBMpPuiFgb+DDwEuBa4MTMXNS6YZIkSdLqYiRjuk8GtqP8CuXbga80bZEkSZK0mhnJmO6tM/MVABFxAvCHtk2SJEmSVi8j6el+tPfAYSWSJEnS8htJT/erIuLh+jiAp9fnAWRmrtusdZIkSdJqYCTfXjLuyWiIJEmStLoayfASSZIkSU+ASbckSZLUmEm3JEmS1JhJtyRJktTYSL69RE+Szx19LFOnPzAoPmPmzDFojSRJkkaLSfdKZOr0B9hmtw8Nik8655QxaI0kSZJGi8NLJEmSpMZMuiVJkqTGTLolSZKkxky6JUmSpMZMuiVJkqTG/PaSlcjt11zEw9NvHRTP+XPGoDWSJEkaLSbdK5FxC2dzyM47DIp/9JLHxqA1kiRJGi0OL5EkSZIaM+mWJEmSGjPpliRJkhoz6ZYkSZIaM+mWJEmSGjPpliRJkhoz6ZYkSZIaM+mWJEmSGjPpliRJkhprmnRHxC4RcVNETImIQ4eYvlZEnFanXxYRm9f4+yLi6s7f4ojYtk67oNbZm7Zhy3WQJEmSnqhmSXdEjAO+CbwN2Bp4b0Rs3VfsAGBmZr4E+BpwDEBm/jAzt83MbYF9gTsy8+rOfO/rTc/MP7VaB0mSJGk0tOzp3h6Ykpm3ZeZC4FRgj74yewAn18dnAG+OiOgr817gxw3bKUmSJDXVMuneCLi783xqjQ1ZJjMXAQ8B6/eVeQ+Dk+7v1aElnx0iSQcgIg6MiEkRMen+++9f0XWQJEmSnrCWSfdQyXAuT5mIeD0wNzOv70x/X2a+Anhj/dt3qIVn5nGZuV1mbjdhwoTla7kkSZI0ilom3VOBTTrPNwamDVcmIsYDzwZmdKbvQ18vd2beU//PBn5EGcYiSZIkrbRaJt2XA1tGxBYRsSYlgZ7YV2YisF99vBdwfmYmQESsAexNGQtOjY2PiA3q46cBuwLXI0mSJK3ExreqODMXRcRBwLnAOODEzJwcEUcBkzJzInAC8IOImELp4d6nU8WOwNTMvK0TWws4tybc44DfAt9ttQ6SJEnSaGiWdANk5tnA2X2xIzqP51N6s4ea9wLgDX2xR4DXjnpDJUmSpIb8RUpJkiSpMZNuSZIkqTGTbkmSJKkxk25JkiSpMZNuSZIkqTGTbkmSJKkxk25JkiSpMZNuSZIkqTGTbkmSJKkxkynZ+oUAACAASURBVG5JkiSpMZNuSZIkqTGTbkmSJKkxk25JkiSpMZNuSZIkqTGTbkmSJKkxk25JkiSpMZNuSZIkqbHxY90ArbwenDGDAz72qSGnbfz8Dfj84UNPkyRJ0pJMujWseXMe4uHptw457ffXXAQm3ZIkSSNi0q1hrb3GYg7ZeYshpx1x/C1PcmskSZJWXY7pliRJkhoz6ZYkSZIaM+mWJEmSGjPpliRJkhoz6ZYkSZIaM+mWJEmSGjPpliRJkhoz6ZYkSZIaM+mWJEmSGjPpliRJkhoz6ZYkSZIaM+mWJEmSGjPpliRJkhoz6ZYkSZIaM+mWJEmSGjPpliRJkhoz6ZYkSZIaM+mWJEmSGjPpliRJkhoz6ZYkSZIaM+mWJEmSGjPpliRJkhoz6ZYkSZIaM+mWJEmSGjPpliRJkhoz6ZYkSZIaM+mWJEmSGjPpliRJkhprmnRHxC4RcVNETImIQ4eYvlZEnFanXxYRm9f45hExLyKurn/f7szz2oi4rs7zjYiIlusgSZIkPVHNku6IGAd8E3gbsDXw3ojYuq/YAcDMzHwJ8DXgmM60WzNz2/r34U78v4ADgS3r3y6t1kGSJEkaDS17urcHpmTmbZm5EDgV2KOvzB7AyfXxGcCbl9ZzHREvANbNzEsyM4HvA3uOftMlSZKk0dMy6d4IuLvzfGqNDVkmMxcBDwHr12lbRMRVEfE/EfHGTvmpy6hTkiRJWqmMb1j3UD3WOcIy9wKbZuaDEfFa4MyIePkI6ywVRxxIGYbCpptuOuJGS5IkSaOtZU/3VGCTzvONgWnDlYmI8cCzgRmZuSAzHwTIzCuAW4GtavmNl1Endb7jMnO7zNxuwoQJo7A6kiRJ0oppmXRfDmwZEVtExJrAPsDEvjITgf3q472A8zMzI2JC/SAmEfEiygcmb8vMe4HZEfGGOvb7A8BZDddBkiRJesKaDS/JzEURcRBwLjAOODEzJ0fEUcCkzJwInAD8ICKmADMoiTnAjsBREbEIeAz4cGbOqNM+ApwEPB04p/5JkiRJK62WY7rJzLOBs/tiR3Qezwf2HmK+nwI/HabOScA2o9tSSZIkqR1/kVKSJElqzKRbkiRJasykW5IkSWrMpFuSJElqzKRbkiRJasykW5IkSWrMpFuSJElqzKRbkiRJasykW5IkSWrMpFuSJElqzKRbkiRJasykW5IkSWrMpFuSJElqzKRbkiRJasykW5IkSWrMpFuSJElqzKRbkiRJasykW5IkSWrMpFuSJElqzKRbkiRJasykW5IkSWrMpFuSJElqzKRbkiRJasykW5IkSWrMpFuSJElqzKRbkiRJamz8WDdAq6YHZ8zggI99alB84+dvwOcPHxyXJEl6KjPp1gp5bPFittntQ4Pi1//i+DFojSRJ0srN4SWSJElSYybdkiRJUmMOL9EKWTh3Nhd/97BB8Qfvmz4GrZEkSVq5mXRrhay9xmIO2XmLQfEjjr9lDFojSZK0cjPpHgOfO/pYpk5/YFB8xsyZY9AaSZIktWbSPQamTn9gyG/+mHTOKWPQGkmSJLXmByklSZKkxky6JUmSpMZMuiVJkqTGTLolSZKkxvwg5Ri4/ZqLeHj6rYPiOX/OGLRGkiRJrZl0j4FxC2dzyM47DIp/9JLHxqA1kiRJas3hJZIkSVJjJt2SJElSYybdkiRJUmMm3ZIkSVJjJt2SJElSYybdkiRJUmMm3ZIkSVJjJt2SJElSYybdkiRJUmNNk+6I2CUiboqIKRFx6BDT14qI0+r0yyJi8xp/S0RcERHX1f87dea5oNZ5df3bsOU6SJIkSU9Us5+Bj4hxwDeBtwBTgcsjYmJm3tApdgAwMzNfEhH7AMcA7wEeAHbLzGkRsQ1wLrBRZ773ZeakVm2XJEmSRlPLnu7tgSmZeVtmLgROBfboK7MHcHJ9fAbw5oiIzLwqM6fV+GRg7YhYq2FbJUmSpGZaJt0bAXd3nk9lyd7qJcpk5iLgIWD9vjJ/A1yVmQs6se/VoSWfjYgYauERcWBETIqISffff/8TWQ9JkiTpCWmZdA+VDOfylImIl1OGnPy/zvT3ZeYrgDfWv32HWnhmHpeZ22XmdhMmTFiuhkuSJEmjqWXSPRXYpPN8Y2DacGUiYjzwbGBGfb4x8HPgA5l5a2+GzLyn/p8N/IgyjEWSJElaabVMui8HtoyILSJiTWAfYGJfmYnAfvXxXsD5mZkRsR7wK+CwzLyoVzgixkfEBvXx04BdgesbroMkSZL0hDVLuusY7YMo3zxyI3B6Zk6OiKMiYvda7ARg/YiYAhwC9L5W8CDgJcBn+74acC3g3Ii4FrgauAf4bqt1kCRJkkZDs68MBMjMs4Gz+2JHdB7PB/YeYr4vAl8cptrXjmYbJUmSpNb8RUpJkiSpMZNuSZIkqTGTbkmSJKkxk25JkiSpMZNuSZIkqTGTbkmSJKkxk25JkiSpMZNuSZIkqTGTbkmSJKkxk25JkiSpsaY/A6+nngdnzOCAj31qUHzj52/A5w8fHJckSXoqMOnWqHps8WK22e1Dg+LX/+L4MWiNJEnSysHhJZIkSVJj9nRrVC2cO5uLv3vYoPiD900fg9ZIkiStHEy6NarWXmMxh+y8xaD4EcffMgatkSRJWjk4vESSJElqzKRbkiRJasykW5IkSWrMpFuSJElqzKRbkiRJasykW5IkSWrMpFuSJElqzKRbkiRJasykW5IkSWrMpFuSJElqzKRbkiRJasykW5IkSWrMpFuSJElqzKRbkiRJasykW5IkSWrMpFuSJElqzKRbkiRJasykW5IkSWps/Fg3QE8ND86YwQEf+9Sg+MbP34DPHz44LkmStDox6daT4rHFi9lmtw8Nil//i+PHoDWSJElPLpNuPSkWzp3Nxd89bFD8wfumj0FrJEmSnlwm3Q197uhjmTr9gUHxGTNnjkFrxtbaayzmkJ23GBQ/4vhbxqA1kiRJTy6T7oamTn9gyCEVk845ZQxaI0mSpLFi0t3Q7ddcxMPTbx0Uz/lzxqA1kiRJGism3Q2NWzibQ3beYVD8o5c8NgatkSRJ0ljxe7olSZKkxky6JUmSpMZMuiVJkqTGTLolSZKkxvwgpcaUPw8vSZKeCky6NabmzXloyK9V/P01F4FJtyRJWk2YdGtM+UuVkiTpqcAx3ZIkSVJjTZPuiNglIm6KiCkRcegQ09eKiNPq9MsiYvPOtMNq/KaI2HmkdUqSJEkrm2bDSyJiHPBN4C3AVODyiJiYmTd0ih0AzMzMl0TEPsAxwHsiYmtgH+DlwAuB30bEVnWeZdWp1cA9d9/JW3Z45aD4M5+7IWf+6rdj0CJJkqQV13JM9/bAlMy8DSAiTgX2ALoJ8h7AkfXxGcB/RkTU+KmZuQC4PSKm1PoYQZ1aDawVizjqQ28dFD/i+PPGoDWSJElPTMukeyPg7s7zqcDrhyuTmYsi4iFg/Rq/tG/ejerjZdWp1dhwPeAPzFnIa/5q90Fxv3pQkiStDCIz21QcsTewc2Z+qD7fF9g+M/+hU2ZyLTO1Pr+V0qN9FHBJZp5S4ycAZ1PGoC+1zk7dBwIH1qcvBW5qsqIjtwHwwGoYXxnbZNz4UyG+MrbJuPGnQnxlbJPxpcefTJtl5oQhp2Rmkz9gB+DczvPDgMP6ypwL7FAfj6dsqOgv2ys3kjpX1j9g0uoYXxnbZNz4UyG+MrbJuPGnQnxlbJPxZe+zleGv5beXXA5sGRFbRMSalA9GTuwrMxHYrz7eCzg/y1abCOxTv91kC2BL4A8jrFOSJElaqTQb051ljPZBlF7qccCJmTk5Io6ivBKZCJwA/KB+UHIGJYmmljud8gHJRcDfZ+ZjAEPV2WodJEmSpNHQ9BcpM/NsyljsbuyIzuP5wN7DzPsl4EsjqXMVcdxqGh/LZRs3/lSOj+WyjRt/KsfHctnGVyy+Umj2QUpJkiRJhT8DL0mSJLU21p/kfCr8AbtQvrJwCnBojZ0I/Am4vq/sJsDvgBuBycDBNb425cOk19T45/vmGwdcBfyyE7sDuA64ms4neoH1KD9G9Me6nB0oX6t4defvYeDjtfw/1mVeD/wYWLvGD66xmcDs7roAzwXuoYzJnwM8p8b3ruWT8kNHvfJfBmbV8g8D69X4Fyjj/R+ty3hhZ54TayyBDWrsSOCRWn4e8PZO+Utq/fOBY2vstLq+DwKPAfM65bet+6hX1/Y1/lbgoVrPbOBTNb5NbevCus69ff3h2qYEbu3s02/X+Py6zr3y/17nn1//f7bv2Liv1nV4jX8VWFDLzwO+3Sl/c2faf9f4xNru+bWtU2t85856zQO+UuOvonxv/tw6/Ubq8Uc5bubUZTwEfKHGP17rScpx1iv/41r3vHoc9MqfVOufV+s5uu+4v7/un149P6jL7NX17U75aXXaAuCcGv/fuq3n1f35x8652Ys/AnyjxncCrqQc3w8Cv6rxLYDLgFtq+3vxgyjndwLXUs9D4IeUc7+/nhMo5/K1tZ5z+s7n/6zr+8vO9rmdcqzOBS6s8aAMw7u5bu/ra/z3DJzLjwLTa/zNdb2urvvt/M769o6TGdTrBeU8nlenzQau6pzHC+v63tQp/2UGzpdZnfJfqOXnUY71a/quU/fWuq7unMeLOvv3lk75Bzv7vrdep3XqXwjM7ZzDvbJzgRs6x/QfKMfa7LoOO9T1/V2NPdKJ70057rO2t3fd/HLd9rP66vlC3eezaj23MPBNXevV/Z513h3q+k6r5ecDd3XKf6rWvaCu+w4MXLeuY+Aa0mvTtpQvHZhV1/v2Gt+dgWP9obofPk75mt5e/bM78YNr2d4+7sWPZ+AaMasT/1Znfz1c6/o4A/eWe2pdvfh/dPZZb//0yk/tLGNBjZ/dKbuQcn58nPIDeY906phT46+q+6p3ff0J5fqwBXAnA9es02r8IMp1Juu2/HGN/5ByH5hPOVdPrfET6jrNr/X8hIF74z8ycE/p1XNSjfXW4ZwaD+A3DJx/V9T472v9vWvW1Bp/c33cu2b9osZ3ovyOyfy6Xw7pnMN/rPXPoX7jG+WY7p13tzJwv/8y5R7T226Hdc7hXnvmAEd0zsmDO3X9c+cc7h2D84DvdMqfweD70mmd9VoI3NM5h+/o1HN93R9TKPf064BfA+dTzrPfMJBvBPCNWvZa4DVjng+OdQNW9z9KMnwr8CJgTcqNdmtgR+A1DE66X9A7MIBnUS7KW9eDZ50afxrlxv+GznyHAD9icNK9wRBtOhn4UH28JjXB7WvzdGAzyo8S3Q48vU47HdifkmBeDzwD+Kvanps7dRxLSSpfU+s6psZfBrwPmMSSSfdbaz2voVz4euXX7WyradTkqk77G+DieoJ2k+5v9m/bWvckyo8pXQ9s2LfOO1ISufs6sfOAT9a67gAuqPGrO9vvo5QL6dZ1ub2k7QhK8rI18EbgncAFdTm9fboP8Lpa/mud8lt2joFPUi5cW9dj422UDxLfRbmQbA38G/C1IY6Zv6n7Za0av7VTT6/+b1C+qnPr2r6DOtt2bo1fDrwJWAf4W0qSdxnwBsrxsF+d5zjKsfIG4NV13juA53fKv73WE5SbV6/8ugwc31+v6/eGWu6Ndd/M6dRzEvD+/vMB+CDlPFijxq/o1NOr/2d1W7yhbqvX1njvpvvnlJvXVpTz6jpqkljXd58avwW4rsZfDWxe9+FPGUiW316XfUjdFr3y63bO2xuBGzvH3XaUY/VRlky696LvPK/r+33gn2r8vL7j+pC6LXvJ782Uc/CQul/vrtvqbsoNbwPK7yQc0DmPZ9b4oSx5Hk8FLgK26zuP76jlj2HJ87gX/xhLnsd3U26Yd7LkeTyDvusX5TyeR33xTec87tT/FWpCQDmH76vxtzNwDl9OuVF/iIFjer26vlfU+KGUBGS9ur4/pySf21Gvm3V9v1/LH9Mpvy71OlvX9zgGOhJ+QrkG3Uk5F9er6zuJvutyXd9pwIdrfCM61+u6jHMp15vePOcBv63LfjvwPzV+OfCmOt8BlPNps7rOvRf8h3XiL6MkwBdQEvPePeGtwPjO8dErv26nXQdTrh+b1eeb1HbeWffHZnWdPzHEPeevavvXqvE/9erp1P9VSvK+WV3ft9X4rpT7wWaU6/S9wNPrPr6Bcu/6Ra3z6ZR71BU1/lbKsXgn5Xjp3ev2pd4DKQl0r/xLO/GvUpK6/es+uodyPs7p1HN6Xff+e+k/1nV5Ro2f1amnV/9PKde4/YHbKOfe0yn3n9vr+t1LOb+fQUmQb6DcS06s2/YZwOGU82RLYLda/kLKffG3Nf53DNzbj+2Uf30n/vHahi0pucAfKcnunZTjbUvKi7B7a/nxnfo/WLfLejX+P516evV/lXKN3pJyj7+jxnet22oPyvHVO57PYSB5716n3l6nBeV6f9mTlfsN9+fwkva2p/50fWYupCQae2TmhZSbyhIy897MvLI+nk25IW+UxZxa7Gn1r7yUi9gYeAelB2KpIqKXxJ5Ql7EwM2f1FXszcGtm3lmfjweeHhHjKQf+NMoF+dLMnJuZv6P0JK7bqWMP4PN1HWcBe9bl3ZiZP6T0YnXX+7xazwzKybRxjT/c2VZr9Na5ei/l4tLvdgZv249QTsb7ar1/6pv++7reD3WbRUlYZlAu/tNq/EXU7Ue5gK9JuUD+NfAvNf5dyj7aKDN/n5k/r/G5DOzTUzPz8hq/kNJrsVFm3tI7BijbfmaN30u5WX4KWExJ+jaiXMDuqev1+DEDvIfS67Cgxq/v1ZOZV0ZEUF4MXF3LL6AkndR1mlHjL6X0rM6hXFjfxcDxtxOlJwjKTWb90oy8KjNvqPHHj9fMPDsz52S5Il5J6aHJup/n1DY9s27vpOzzo+o601kulF6SJeqn7OcjMnNxjUWtP2v9z6Lc1HvvkCQDHyh/LqVn6rG6LeYycF69oLZtJ0rvyjso70g8r273qyjH9NMpLxCo8bPrNnwH8Ku6vmTmw53z9pZe+YgYR3khNI++c6S2r/88/wgloXt7jS/s1LUxpXfzOdTjvq7vi2s9V9dtuH5d397yfkN50QXlPO5dd06mcx4P0T4y87zO00vpnMed+DNZ8jx+LuVa0Y0N5yOUc3Rhrbf/PAZ4NyU5otYZ9fGzGTiHX1r/TqCs7zvrdfCdwIQaPxnYvcbvofS43VuX27tuXkp5UXhCffzCzvW0d519JvBYZs6q19+3UzoeEni0ll+L0gPbf13+h9r+79T4Pb36O9fyrYEfd+ZZA3hlrevZlB7DWXV9L6xtmw+sUa/xe9R1hXLtHJeZd9Zrde9H5V5HvSfUa3Vv38+lvDt4Z98+fiXwUOce8jXKObwWcEcn3tO953wE+NfMXFDjt3TL1/Pw/ZROnjvrduzde/68s9wXM3BOnk9J/O8F/g/leH86cEqNT6O8m0vd3uMYuNedT70HUl4YrVvjczrxZ1CuN9Pq9l+fgXtTrx5qvf330g/Uutau8e69ZjzleNyJch+YVtf3aXW5z6nr+Egtf2FmzqW8EBlPOZ53piSkc4HvUTo93km5Fl1IuZc8Rkl+30m5X19ay19COd/eCWzaiT+9tuWdlFxgLeATtW0X1/gGwF01R1jUqf/vajtn1fhvO/VcSrn27U15R/addTvdWpf7LMqLjjfUZfaO563qfoTOdYpybH+/Xv8vBdaLiBcwllpm9P4llN6p4zvP9wX+sz7enL6e7r55N6ckfb1esXEMvC18TKfcGcBrgb9kyZ7u2ymJzRXAgTW2LeVt1ZMow1GOB57Zt9wTqT2e9fnBdZn3Az+ssZdRXiWvTzkprgQe7Mwzq7uOwMy+ZVxKp6e7b50fpvZi1tiXKCf4fGBCje1OSXo2Z3BP9x2UxHMmA28zXU25sV9FuUC9rm+5O1J6Krq94y+r238apddxsxq/mPLCCcqFdTHlQjyrbz0Ws2TvzwWU3oW7uvE67beUHud1O+t8N6VnbWqtf3fg3+v0qZ14b52vpfSe3F3jvXW+rG7v6X3t6a3zXbV8b33vrmXvqfGLKRevcQy8RXwM5aI6hYHj8hHg/k794xgYanNMX/xqyoX+h534SXU7L2JgaMvBlF7Zq3vL7ZS9iYG3Iv+txh8EPkNJBhYBx/Ut984a79XzxjrPwrq/vka56d4J/DflvDqDckz21rd3vu0NPNx3Hk6r2+qXffHXU86XizvxO+qyrwLO7qzvNbX+eSzZ0z2bkqD/pFP+Qcr5dUPdz+f3LfcIys3ul531XUBJwu+g9Pb21vceynl8HwNDjmax5HXkkb7rS+9F3oFDXHdmASd0rwkMDCfovfW9O+WmfmVtVy9+JAPDVB5g4K3vqynn9SN12V/qW+7NdVrveveyur8X1r9DO/XcXLfr1DrtmbXO7vVxQY33rpvTKb16x/fFT6rr8btOfBoDwx5OqfGDax0n1bp/UOPfrs9n1H36/Rq/qe6X+2vbzqRer+sybqzb5/FrOSVRWVCX3evoeSZLXrcuA+Z3r9Wda//cvmvTBZTe14O68TrtLuDkvmv13XUfHdrZx73r1mzg033X6mvrvvhk37X6MkqSfOwQ1+oHGHhXrnvdeoSB4XgXUzo/5tS/Rxk4h3v3tAf71v9gynXgAZa8Nh3cqeO8TvyyWn4hcGqn7M9r+WTgnnkS5dx6jHJ9+nHnHP5ljS8EJvYtd37dn7163ljXczHl2D6Ncg7fQzmP16e86/oIZQjPwyx5r15U4717+P9SXohc0hdfnzKk55ZO/MG6nMmUd07+g9LbPrOWv7MT/8+6vSZTEuE/1PiNtZ4rKJ1d1/Ytd1fK9aDXnnfUeu6hnFNXMDAcsXc8zwNmd7bbzPr/l8BfdOL/TeedubH4G/OkdHX/o9yY+5Pu/6iPN2eYpJvyavQK4F1DTFuPcnHfph6g36rxv2TJm/3jb8FSbuQ7Ut4aXQS8vk77d+q42vp8TcoF53n1+XMor/QnUF5dn8nA2/oH1JPjQkpv5wOdelY06f4y5SIRffHNKTerz1MuHJdRenE2Z8mk+3mU5GoLyluIJ9b49ZQexM0pb1vd3l0G8F/AF1ky6f4Gpcdvc8pF/bc1/meUnoSr6kVgdt869/bdnL51+D3lgvOuvvjnKRet/vg6lAvNaX3rvA7lIrxf3zo/i3KT+u++dV6nLve+vnX+LuVG9a6+9V2H0ptwTd/6XgF8jpIY/I5y8e8OEXo55UazTSd2B+Wdgd/1xb9bt3l/fBwlebiRcrz+LwNvZc/h/7d39kFeVtcd/xw1QKAaUAFRoqszEU2DYTQ1OiJQCYTSNGg1plSCTUwzrX+kZEonTU2yMiZqY4qtM0qMQ8dEE9JMfEkiYdsESlKpVXQFXd5C0BUi8ia4IIvAwu0f33N57j4sL6augD2fmd/sb89zfve597nnnnue+9x7n8ruB6GOpicaYX/B5a8Df+v6k1CgV6Y/B7XBnM7DVG3hK16fH0CjNmtRR/EACqj6uyy3t31BN94Ovbz7gu5Cfh8Kguvy41GbWgScjjqoGa5TBt2fcv2eKFBeUegsKPL/ai39OSjwzun8N/CjwuZX+/dLkX09hR7t7vDr/xqd/UgHMCL7FxSQjcH9SyG/CY3sd5L736+htjzCzznE5auRzY5ANj0YjRrmqVcj/PhMr/uPonZQnncGstHs7+6imrLxWRT0jUB2vhfZWaOX9xY/XvrHN1ye/eYz/v1favIZKNCqyz+Mpmz8D/JtLYW8FY1g34KmNnSgEbyvIzu4BQWIe13/Yjqvm/iQH8sBbT73D1AA92E06r/a5bkdN6OAbHPNb2Xfvy8IdfkvkR0MrMm/6te/Lu/h6X+Tzn6rh+fr/Jrf6okCqO/X/FYPP+9LdPZb96J2nvuo7Ld6oL4jr3e4GAV3i5GP3YXa0QtUfdrZfk0nUfV1q9GUuEdr8gf8XHX5QHTT1IxGrZ9A/qW/5zPrn+f6Z6CbqmUufx0Ftv2RT9lUS/8XXo85nZ+iEff+wBeRHU1CbTjfdL7k6dzp17Dsq3dSTUe8Adl8s5ehlK/1NOryZtR/Pu3pP4mm5jWj9nK/yweiNtfs13S5y1u8TM2oD91aS38j6qO/5fp3oZuIZjS48FvkA35N1S/toPOgXw66Z7N/0H3RwWK27v4c8aD0nf7hIK+u5wBBNwpu/x0f9TlAuo0oMLjNjbAVdWTtwINd6N/s+qehx3tZfjm+uMv/n0DnO/lP0Hm0ajIedNTSvxtYW/y/AgVGDd7YVtT09wu60dtJm4ElXaTfQLUgbSgKqFu97Mkb9Wld6fv/TeimpMHTWEU1an4CCkgvoXPQ3YY69/ybclQz19FtwFNFmfPcxcayzK6/GZheK9dnkFP84gFsIC/IKsu8A3Ve+8pc1y/KPDrbUq3MvZDznVYr77sK/a1d1MO5KDBrRPPNN1EFxZeiIGFqod+KRpcaqeZvNqIO5LhSXvxmpF/LRmTTrf7ZizrRuv4o15+KbK3B5YY6gXzeU/z3vYr8ryrSOdOvcb1dbUYB0fdQ+8ryvFDqwUK/A9lSeyFv8//X1eT1dLagDrjDP8nLXNffXJz3VXSj1erpp0J/revl8872c+R0NuT0a9dzLAr6pvp1HeTyQV7fZf3OR8HfzcV1vh4FHr1LefGbs/zcX6Gy6VYvcxv7LxJvKOqlCRhVHNsMNNba8WAqf9dGtTWuIZvv5AeRTS/16/MbYE1R3tUuP83zmMt7eSHfWJS3lLcW5X0BdfibvJy5vOtRAFLqN7j+bBR0rSvK+zLwc/9+htfv4NKXoyCmtSjzdvb38Y/T2W8Ncvl89vfVz6NpBXVfvRwfiKgdm4CCu7rfWo/sre6r9+nXfPUEFFTVffVrwC+78NNZP98I7+u7vI5XoZujrVSDMZd6+e7J+lQ+a3Ihb6byWaU8pz8SBZAvUm0s0OrlXd+F/ijXv8fr9N+K+mov9HMb7+XnnYHac07nTP/9PbU6GIuCz3O4oAAACvFJREFU+hvZvw2/CtzYRRu+Ncvp3IZvLfULm96IRuK7asN/30Ub3uj5qbfhLVSbEZRt+FbX76oNf5nOffULVOtWBlENStwLTKzHJXWbfTs/Mae7+3lTr673+Woz0cKq6YW8v5n19e/vRvOHl6eUvpRSGpxSavC056WUJplZH5+/ipn1QY2wJaW0DlhjZkM86dGow8lMpJoPCb6gzcx6e95Go8aMmQ3wv2eiXSDKueE/QQ0XNDL/44NdJDMbh+7aP0sxt9PM3leonehlfj6lNMDLPBw9erowpbSuNl/rJOT4QQ7zCv/eg2pUB/xaImdWshY5U9Dj2ZVFuWdSzZ3+VlHmH7t8Zy5zUaftaFS2LPN05HD/sVbmnP6GXGY0cvAr5EjW1Mqc9TfXyjzd5Y/lMnt+HkNTQRpr5X3M9ReX5XX764ec3Uy/ZsvQQrrJ/vvP+N/lpb2iDuMjLp+C5rRORCNcHwFWmNnFZta3mGfeB41gDAWGeV23I1tdbma/X+hfjTqH5eiG4Y/9vGPwnUrMrL/n8zHkuHP++5rZRa4/HnWqy9HIy2CqxVILU0rXoaBmqudnAdoNY1Juhyig/RzeDlFHvwQF/H+GgqhPoU5zMBpp+wUKkvqllH4vpXRCSukEdMPwM0/nrkJ/HvCiy+9D8/YbgNvRfNZJKaUvobnwDxbnnYCCtCtc/360cHiSmTWY2Ylm1hMNDCRkR3PQHExQ29wJtJT+xet3rMsn+O8/7tc5yy8o9K/x67zQyzPU8/My6hSfMLNzCv1Pun4Letw9DsDMPuh28qT7uD/xutuSz4tuSMYV9bvb5XuRHzwP2fRKZFuPAB3uH69H7Wxp9ptoLitUfnMYsr0vJM05zfITqfzsx70um1NKp6Jg5qPIVr6Dgi8r9K+isvUfAjvNbIiZnYueQi3yPAxFwV2fWp5eBrZ6WlegoGVp9teo7Rmd/db1Lt/I/r56IGpX+HXPvnoZ1XqO0ldPxEc2a776P5F/qvvqiZ7nuq+eiOy27qt3IdvNZD890a9NXiOxDfVdfVAdr/PrsxAYY2a9vdzbvSzl4u18PZehOj4P+bdUyPd6+r2R7b0L+dtxntb7UT02uf72Qv9KFGAuQ+1/uMtHUq37We3XYQ5qd7l+ewEjXH8MCnSXuZ8e4G34q8guZqH6vdHL9Hn/O8vrLNvEQLRWZ5bX7z8guz21kL+v0L8e+e/vppQGoJ29GlB72wDca2aDCv1Pu/4sVL8f8/OPRDZ9n+tdjdrwcfm8VFP2QL4seZmO9zSOQwNRq4q8ZRv+CTDZxCXIP77CkeRIRvz/Xz7I2f8aGUXeTmcWMtC8FVDeLWA41bZjecuv8WhhyrMub6HYrqc4zyiqx8jnoMApbzF4U6E3DD0aeg41gDzvuTe6C35PLd1pqCG0oEdsPV3+X8gJbPHf7SsLCjLWIYewFznVG6g6lOSfN1z+G6qt/hIa8bsBrdp+zeV7UQO8oXYNU5Z7/vbTR467tUh/Y5HO/cgRd6oPr4vNRVrrXf7PnkaeG5vraHwh34ZGUMYjB5ZHLXejkZbxVKP0eSukTS6fX8jbvP7G09k2dhXpN9X0W1w+qrjG7X6Ny3R+S2cb++sinbxd2ng0mtHq6WygsD+0m8p2qu238pZ+t1NtKbcbeMblHXTe6m8ucrDP+v95u6uvu35p93uK8z5Z0/+ayy/zfOTtw+4u0tmGRkTK/E8p8rKd6jHnHajjW4HmJpbt6im/lvOp5lZ/nmqkexPVtI0O1O4X+W9WeHkXeP21oIV8TV2053J6ybyaft4KsS+6EXge2Uk5AjgfBQCjinSuct3Fnqe8ZeC3/Vq+gdpB9lMXUm0n93pxnf+Kah58B76lH7KTchu4J13eVMi2Uc2pL/3UrqLeHyn0twK3uXwI8jf52Mwinc1eB/v8HXosn7eiLO3hb9Aj+GzTj6LH+afg8509n7NdfhXVSO1u/97P63RdcY4XXf6QH2v3/DdR+dnsf3ehm4h+yG+tpNqWc47Le3gecnkfL9K5H03V6eTLUfte6mm1o2C3n5d5JWpHd1KNHp7iOnuQzZxc2Epew7EBf2Lr5cq2/hzVdp0P+bXv8PyfUdhi7lvKHWoeoJpu8zOq0dgeyLd3IBu9okgn72L0nkI2HI1Ed/i1uKio47xeY6P/tieylZdd3oZuHHqiNryVymetdHkHsq28heEily9AdrAT+aAfUPWNuc/cU5x3Xk1/lsv7Um352Y4GBnoW7WkNRd9LZYtvIJ/1iMvv8N/v9PKNLur3Nap+6cqifndS2fTCon7zdn47gJ8W9Zu3p2wDri3qIMcCu9Ci5FxXpf4nivrNWzC249MB/dh65H8WF/kfTrXF7XaqvnqP53sd6pPnep3NpbJhQ0/hVyG/d0Tnc6eU4o2UQRAEQRAEQdDdxPSSIAiCIAiCIOhmIugOgiAIgiAIgm4mgu4gCIIgCIIg6GYi6A6CIAiCIAiCbiaC7iAIgiAIgiDoZiLoDoIgOMrwfbNbDqFzupn96E2mO9/MVpjZYjNbaGbD/m85fXP4frnzzOwkM3uvmb1oZif7sX7+/1m+z3vT25m3IAiC7iaC7iAIgmOQlNLalNI1v8NPr0spfRC99e6Otzhbh2I8sDiltDWltAa9Ye92P3Y78O2U0ksppY3AK2Z22ducvyAIgm4jgu4gCIKjGH8747Nm9gc1+b7RcDP7CzN72MyazGylmX3jMJJ+Ar1RNac3w8yeNrMlZjatkLea2TQzazaz5/0tjvktuT93+b1m9pKZnerHJpnZU2a2yI8d78ldR+c3Ht6J3tI3Bb0E45+KY4+6fhAEwTuCCLqDIAiOUvxV3g8Bn04pLTyE+jD0yvShwCfN7L2H0B+HAtvMTSmlD6G3d440swuKY5tSSheikempLmtEb7S8EL0V70zP8/mej8tSSsPQm+Ny8HwZ8ExONKW0G/g7FHxPSSntKs75NHD5IcoQBEFwzHDCkc5AEARB0CX90ajw1SmlJYehPzel1AZgZkuBs9ArpOt8z8z6AMej17xnrjWzz6F+YRDwfvSab4CH/e8zwJ/69+HoVdKklJrMbIvLRwMXAQvNDODd6LXPoNczb6vl54/Qa50/gF5xn9kAnH7oYgdBEBwbxEh3EATB0UkbCpoPd17zzuL7Hg48qHIdcDbwfeBuADM7G41gj04pXQDMBnp1kXaZrh0gfQO+k1Ia5p8hKaWb/ViHme3rd3wh5xjgEuALZjaoSKcXsOMA5wiCIDjmiKA7CILg6GQXcCUw2cz+/K1M2Kd1fBnNpz4fOAnYDrSZ2UA0+nwoHgeuBTCzsUA/l88FrjGzAX7sZDM7y4+tAM5xuaHpKlNSSqvRos5vFumfCxx0B5cgCIJjiQi6gyAIjlJSStuBj6FR4Alvcdo70MLFqSmlxcCzwBLgX4EFh5HENGCsmTVTTRHZllJaigL6/zCz59CUkTyCPRsY5d//ElidUspTSu4BzjOzkf7/H7p+EATBOwJLKR3pPARBEATHGGbWE9iTUuows0uBGb5w8mC/GQR8N6U05jDS/xUwIaW05VC6QRAExwKxkDIIgiD4XTgT+KHP0d6FRq4PSkrpFTO7z8xOSiltPZCemfUHpkfAHQTBO4kY6Q6CIAiCIAiCbibmdAdBEARBEARBNxNBdxAEQRAEQRB0MxF0B0EQBEEQBEE3E0F3EARBEARBEHQzEXQHQRAEQRAEQTcTQXcQBEEQBEEQdDP/C+3zCcWa+lgFAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Sum of Absolute Differences: 0.0252\n", "Sum of Squared Differences: 0.0001\n", "Euclidean Distance: 0.0082\n" ] } ], "source": [ "def display_poisson_and_binomial(N,p):\n", " X = list(range(N+1))\n", " lam = p*N\n", " probs1 = [ f_poisson(lam,k) for k in range(N+1)]\n", " probs2 = [ f_binomial(N,p,k) for k in range(N+1)]\n", " \n", " fig, ax = plt.subplots(1,1,figsize=(12,8)) \n", " ax.bar(X,probs1,tick_label=X, width=1.0,edgecolor='black',alpha=0.5)\n", " ax.bar(X,probs2,tick_label=X, width=1.0,edgecolor='black',alpha=0.5)\n", " # ax.scatter(X,probs2)\n", " # ax.plot(X,probs2,'--',alpha=0.3)\n", " ax.set_title('Probability Distributions for Poi('+str(lam)+') and B(' + str(N) +',' +str(p)+')')\n", " ax.set_ylabel(\"P(X=k)\")\n", " ax.set_xlabel(\"k in Range(X)\") \n", " plt.show()\n", " \n", " sum = 0\n", " for k in range(N+1):\n", " sum += abs(probs1[k]-probs2[k])\n", " print(\"Sum of Absolute Differences: \" + str(round4(sum)))\n", " \n", " sum = 0\n", " for k in range(N+1):\n", " sum += (probs1[k]-probs2[k])**2\n", " print(\"Sum of Squared Differences: \" + str(round4(sum)))\n", " \n", " print(\"Euclidean Distance: \" + str(round4(sum**0.5)))\n", " \n", "display_poisson_and_binomial(100,0.05)\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exponential Distribution: Exp(λ)\n", "\n", "Motivation: If we have a process in which events arrive (hence, called arrivals) independently through time, with some mean rate λ = # arrivals/unit time, then the Exponential characterizes the inter-arrival time, e.g., \"how long until the next arrival\"?\n", "\n", "Definition: X ~ Exp(λ) if\n", " \n", "
\n", "$\\begin{aligned}\n", " Rng(X) & = [ 0, \\infty ) &\\\\\n", " f(t) &= \\,\\lambda \\, e^{-\\lambda\\, t} &\\\\\n", " F(t) &= 1.0 - \\, e^{-\\lambda\\, t} &\\\\\n", " & &\\\\\n", " E(X) &= \\frac{1}{\\lambda} &\\\\\n", " Var(X) &= \\frac{1}{\\lambda^2} &\\\\\n", " & &\\\\\n", " P(X > t) &= e^{-\\lambda\\, t} &\\\\\n", " P(X \\le t) &= 1.0 - \\, e^{-\\lambda\\, t} &\\\\\n", "\\end{aligned}$\n", "
\n", "\n", "where $e = 2.71828183\\ldots$ (Euler's constant). \n", "\n", "NOTE: Sometimes the exponential is specified by using the expected value, which is denoted $\\beta$; i.e., \n", "$$\\beta = \\frac{1}{\\lambda}.$$\n", "Then we simply replace $\\lambda$ in all the formulae by $\\frac{1}{\\beta}$:\n", "
\n", "$\\begin{aligned}\n", " f(t) &= \\,\\frac{e^{-\\frac{t}{\\beta}}}{\\beta} &\\\\\n", " F(t) &= 1.0 - \\, e^{-\\frac{t}{\\beta}} &\\\\\n", " & &\\\\\n", " E(X) &= {\\beta} &\\\\\n", " Var(X) &= {\\beta^2} &\\\\\n", " & &\\\\\n", " P(X > t) &= e^{-\\frac{t}{\\beta}} &\\\\\n", " P(X \\le t) &= 1.0 - \\, e^{-\\frac{t}{\\beta}} &\\\\\n", "\\end{aligned}$\n", "
\n", "\n", "Canonial Example: If earthquakes occur on average 3 times per year, what is the probability that the next earthquake will occur within the next six months?\n", "\n", " time unit = year, λ = 3, t = 0.5\n", "\n", "
\n", "$\\begin{aligned}\n", "\\text{Solution:} &\\; 1.0 - \\, e^{-3 / 2} = 0.7769.\\\\\n", "\\end{aligned}$\n", "
" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "scrolled": false, "slideshow": { "slide_type": "-" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "def f_exponential(lam,t):\n", " return lam*np.exp(-lam*t)\n", "\n", "def F_exponential(lam,t):\n", " return 1.0 - np.exp(-lam*t)\n", "\n", "def display_exponential(lam,limit=10):\n", " X = np.linspace(0,limit,100)\n", " Y = [f_exponential(lam,t) for t in X]\n", " YCum = [F_exponential(lam,t) for t in X]\n", " \n", " fig, (ax,ax1) = plt.subplots(2,1,figsize=(12,10), sharex=True)\n", " # fig.subplots_adjust(hspace=.5)\n", " plt.tight_layout(pad=0.4, w_pad=4, h_pad=6.0)\n", " plt.setp(ax.get_xticklabels(), visible=True)\n", " \n", " ax.fill_between(X, Y, interpolate=True)\n", " ax.plot(X,Y,color='k')\n", " ax.set_title('Probability Distribution for Exp('+str(lam)+')')\n", " ax.set_ylabel(\"f(x)\")\n", " ax.set_xlabel(\"x in Range(X)\")\n", " \n", "\n", " ax1.set_title('CDF for Exp('+str(lam)+')')\n", " ax1.set_ylabel(\"P(X <= k)\")\n", " ax1.set_xlabel(\"x in Range(X)\")\n", " ax1.fill_between(X, YCum, interpolate=True)\n", " ax1.plot(X,YCum,color='k')\n", " plt.show()\n", " \n", "print()\n", "display_exponential(0.7)\n", "print()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "## Normal Distribution: N( $\\mu$, $\\sigma^2$ )\n", "\n", "Motivation: The normal is the limiting case of the binomial $B(N,1/2)$ as $N \\rightarrow \\infty$, parameterized with respect to its mean and variance. It describes the distribution of data expressed as real numbers which exhibits the \"bell-shaped curve\"; this describes a wide variety of phenomena such as in biostatistics (height, weight, dimension of various body parts, intelligence, etc.), errors in measurement, etc. \n", "\n", "Definition: $X \\sim N( \\mu, \\sigma^2 )$, where $\\mu$ is the mean and $\\sigma$ the standard deviation, if\n", " \n", "
\n", "$\\begin{aligned}\n", " Rng(X) & = (-\\infty, \\infty ) &\\\\ \n", " f(x) &= \\frac{1}{{\\sigma \\sqrt {2\\pi } }}e^{-(x-\\mu)^2 \\,/\\, 2\\sigma^2} &\\\\\n", " F(x) &= \\frac{1}{2} \\left[ 1 + erf\\left( \\frac{x-\\mu}{\\sigma\\sqrt{2}} \\right)\\right] &\\\\\n", " & &\\\\\n", " E(X) &= \\mu &\\\\\n", " Var(X) &= \\sigma^2 &\\\\\n", " & &\\\\\n", "\n", "\\end{aligned}$\n", "
\n", " \n", "\n", "Canonial Example: If the heights of BU students are normally distributed with $\\mu = 66$ and $\\sigma=3$ (inches), what is the probability that a randomly-selected student will be taller than 6 feet?\n", "\n", "Solution: The variance is 9, so we have $X\\sim N(66,9)$ and we are asking for $P(X>72) = 1.0 - P(X<72)$.\n", "\n", "
\n", "$\\begin{aligned}\n", "\\text{Solution:} &\\; 1.0 - \\, F(72) = 0.0228.\\\\\n", "\\end{aligned}$\n", "
" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "# PDF and CDF for normal: note that these take the variance as a parameter, not standard deviation\n", "\n", "def f_normal(mu,var,x):\n", " return (1/(math.sqrt(var*2*math.pi))) * math.exp(-(x-mu)*(x-mu)/(2*var))\n", " \n", "def F_normal(mu,var,x):\n", " return (1 + math.erf((x-mu)/(var**0.5 * 2.0**0.5))) / 2\n", " \n", "def normalRange(mu,var,low,high):\n", " return F(mu,var,high) - Phi(mu,var,low)\n", "\n", "\n", "def display_normal(mu,var,limit=4,absoluteLimits=False,lo=0,hi=0,showSigmas=True): # limit is +/- in terms of standard deviations\n", " sigma = var**0.5\n", " X = np.linspace(mu-sigma*limit,mu+sigma*limit,100)\n", " Y = [f_normal(mu,var,x) for x in X]\n", " YCum = [F_normal(mu,var,t) for t in X]\n", " \n", " fig, (ax,ax1) = plt.subplots(2,1,figsize=(12,10), sharex=True)\n", " # fig.subplots_adjust(hspace=.5)\n", " plt.tight_layout(pad=0.4, w_pad=4, h_pad=6.0)\n", " plt.setp(ax.get_xticklabels(), visible=True)\n", " \n", " ax.fill_between(X, Y, interpolate=True,alpha=0.5)\n", " ax.plot(X,Y,color='k')\n", " ax.set_title('Probability Distribution for N('+str(mu)+','+str(var)+') $\\sigma$ = ' + str(round4(sigma)))\n", " ax.set_ylabel(\"f(x)\")\n", " ax.set_xlabel(\"x in Range(X)\")\n", " if(absoluteLimits):\n", " ax.set_xlim([lo,hi])\n", " \n", "\n", " ax1.set_title('CDF for N('+str(mu)+','+str(var)+')')\n", " ax1.set_ylabel(\"P(X < k)\")\n", " ax1.set_xlabel(\"x in Range(X)\")\n", " \n", " ax1.fill_between(X, YCum, interpolate=True)\n", " ax1.plot(X,YCum,color='k') \n", " \n", " if(showSigmas):\n", " extra = f_normal(mu,var,mu) / 10\n", " ax.plot([mu-sigma*limit,mu+sigma*limit],[0,0],color='k')\n", "\n", " ax.plot([mu,mu],[0,f_normal(mu,var,mu)+extra/2],'--',color='k')\n", " ax.text(mu+sigma/10,0.75*f_normal(mu,var,mu),r'$\\mu$',fontsize=12,color='k')\n", " \n", " ax.plot([mu-sigma,mu-sigma],[0,f_normal(mu,var,mu-sigma)+extra],'--',color='g')\n", " ax.plot([mu+sigma,mu+sigma],[0,f_normal(mu,var,mu+sigma)+extra],'--',color='g')\n", " ax.text(mu+sigma,f_normal(mu,var,mu-sigma)+2*extra,r'$\\mu\\pm\\sigma$',fontsize=12,color='g')\n", " \n", " ax.plot([mu-2*sigma,mu-2*sigma],[0,f_normal(mu,var,mu-2*sigma)+extra],'--',color='orange')\n", " ax.plot([mu+2*sigma,mu+2*sigma],[0,f_normal(mu,var,mu+2*sigma)+extra],'--',color='orange')\n", " ax.text(mu+2*sigma,f_normal(mu,var,mu+2*sigma)+2*extra,r'$\\mu\\pm2\\sigma$',fontsize=12,color='orange')\n", " \n", " ax.plot([mu-3*sigma,mu-3*sigma],[0,f_normal(mu,var,mu-3*sigma)+extra],'--',color='r')\n", " ax.plot([mu+3*sigma,mu+3*sigma],[0,f_normal(mu,var,mu+3*sigma)+extra],'--',color='r')\n", " ax.text(mu+3*sigma,f_normal(mu,var,mu+3*sigma)+2*extra,r'$\\mu\\pm3\\sigma$',fontsize=12,color='r')\n", " \n", " plt.show()\n", " \n", "print()\n", "display_normal(39.8,2.05*2.05)\n", "print()" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def display_normal_range(mu,var,lo=0,hi=0,leftSideOnly=False,rightSideOnly=False,limit=4): # limit is +/- in terms of standard deviations\n", " sigma = var**0.5\n", " X = np.linspace(mu-sigma*limit,mu+sigma*limit,1000)\n", " Y = [f_normal(mu,var,x) for x in X]\n", " if(leftSideOnly):\n", " Xrange = [x for x in X if(x <= hi)]\n", " Yrange = [f_normal(mu,var,x) for x in Xrange]\n", " elif(rightSideOnly):\n", " Xrange = [x for x in X if(x>=lo)]\n", " Yrange = [f_normal(mu,var,x) for x in Xrange]\n", " else:\n", " Xrange = [x for x in X if(x>=lo and x <= hi)]\n", " Yrange = [f_normal(mu,var,x) for x in Xrange]\n", " \n", " fig, ax = plt.subplots(1,1,figsize=(12,4), sharex=True)\n", " # fig.subplots_adjust(hspace=.5)\n", " plt.tight_layout(pad=0.4, w_pad=4, h_pad=6.0)\n", " plt.setp(ax.get_xticklabels(), visible=True)\n", " \n", " ax.fill_between(Xrange, Yrange, interpolate=True)\n", " ax.plot(X,Y,color='k')\n", " ax.plot([mu-sigma*limit,mu+sigma*limit],[0,0],color='k')\n", " if(not leftSideOnly):\n", " ax.plot([lo,lo], [0, f_normal(mu,var,lo)],'--', color='red')\n", " if(not rightSideOnly):\n", " ax.plot([hi,hi], [0, f_normal(mu,var,hi)],'--', color='red')\n", " ax.set_title('Distribution for X ~ N('+str(mu)+','+str(var)+')')\n", " ax.set_ylabel(\"f(x)\")\n", " ax.set_xlabel(\"x in Range(X)\")\n", " \n", " if(leftSideOnly):\n", " ans = F_normal(mu,var,hi)\n", " ax.text(mu+1.5*sigma,0.75*f_normal(mu,var,mu),'P( X < ' + str(hi)+ ' ) = ' + str(round4(ans)),fontsize=12)\n", " elif(rightSideOnly):\n", " ans = 1.0 - F_normal(mu,var,lo) \n", " ax.text(mu+1.5*sigma,0.75*f_normal(mu,var,mu),'P( X > '+str(lo)+ ' ) = ' + str(ans),fontsize=12)\n", " #ax.text(mu+1.5*sigma,0.75*f_normal(mu,var,mu),'P( X > '+str(lo)+ ' ) = ' + str(round4(ans)),fontsize=12)\n", " else:\n", " ans = F_normal(mu,var,hi) - F_normal(mu,var,lo)\n", " ax.text(mu+1.5*sigma,0.75*f_normal(mu,var,mu),'P( '+str(lo)+ ' < X < ' + str(hi)+ ' ) = ' + str(round4(ans)),fontsize=12)\n", " \n", " plt.show()\n", " \n", "display_normal_range(25, 3.54,lo=18,hi=32)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "display_normal_range(25,18.75,lo=35.5,rightSideOnly=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Normal Approximation to the Binomial\n", "Since the normal distribution with $p$ close to $0.5$ can be viewed as the limit of the binomial as $N$ gets large, we can use the normal distribution to approximate the binomial. We must define the normal in terms of the mean of the binomial, $Np$, and the variance of the binomial, $Np(1-p)$. \n", "\n", "First we show the relationship between the a binomial B(N,p) and a normal with the same mean and variance, i.e., $N(Np,Np(1-p))$, then show how the approximation works, then present a way of making the approximation more accurate. \n" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "\n", "def display_binomial_and_normal(N,p=0.5):\n", " X = list(range(N+1))\n", " probs = [ f_binomial(N,p,k) for k in range(N+1)]\n", " fig, ax = plt.subplots(1,1,figsize=(12,6), sharex=True) \n", " plt.tight_layout(pad=0.4, w_pad=4, h_pad=6.0)\n", " plt.setp(ax.get_xticklabels(), visible=True)\n", " \n", " ax.bar(X,probs,tick_label=X, width=1.0,edgecolor='black')\n", " # draw center lines in bins\n", " for k in range(N+1):\n", " ax.plot([k,k],[0,probs[k]],'--',color='w')\n", " \n", " # now draw normal on top of it\n", " X2 = np.linspace(-0.5,N+0.5,1000)\n", " Y = [f_normal(N*p,N*p*(1-p),x) for x in X2]\n", " print()\n", " ax.plot(X2,Y,color='black')\n", "\n", " ax.set_title('Probability Distributions for B( '+str(N)+', '+str(p)+' ) and N( '+str(N*p)+', '+str(N*p*(1-p))+' )')\n", " ax.set_ylabel(\"P(X=k)\")\n", " ax.set_xlabel(\"k in Range(X)\")\n", "\n", " \n", " plt.show()\n", "\n", "# Change N to see the relationship; note that p = 0.5\n", "N = 10\n", "display_binomial_and_normal(N)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "def display_binomial_and_normal_range(N,p=0.5,lo=0,hi=0,leftSideOnly=False,rightSideOnly=False,limit=4): # limit is +/- in terms of standard deviations\n", " mu = N*p\n", " var = N*p*(1-p)\n", " sigma = var**0.5\n", " \n", " X2 = list(range(N+1))\n", " probs = [ f_binomial(N,p,k) for k in range(N+1)]\n", " fig, ax = plt.subplots(1,1,figsize=(12,6), sharex=True) \n", " plt.tight_layout(pad=0.4, w_pad=4, h_pad=6.0)\n", " plt.setp(ax.get_xticklabels(), visible=True)\n", " \n", " ax.bar(X2,probs,tick_label=X2, width=1.0,edgecolor='black',alpha=0.5)\n", " # draw center lines in bins\n", " for k in range(N):\n", " ax.plot([k,k],[0,probs[k]],'--',color='w')\n", " \n", " X = np.linspace(mu-sigma*limit,mu+sigma*limit,1000)\n", " Y = [f_normal(mu,var,x) for x in X]\n", " if(leftSideOnly):\n", " Xrange = [x for x in X if(x <= hi)]\n", " Yrange = [f_normal(mu,var,x) for x in Xrange]\n", " elif(rightSideOnly):\n", " Xrange = [x for x in X if(x>=lo)]\n", " Yrange = [f_normal(mu,var,x) for x in Xrange]\n", " else:\n", " Xrange = [x for x in X if(x>=lo and x <= hi)]\n", " Yrange = [f_normal(mu,var,x) for x in Xrange]\n", " \n", " # fig.subplots_adjust(hspace=.5)\n", " plt.tight_layout(pad=0.4, w_pad=4, h_pad=6.0)\n", " plt.setp(ax.get_xticklabels(), visible=True)\n", " \n", " ax.fill_between(Xrange, Yrange, interpolate=True)\n", " ax.plot(X,Y,color='k')\n", " ax.plot([mu-sigma*limit,mu+sigma*limit],[0,0],color='k')\n", " if(not leftSideOnly):\n", " ax.plot([lo,lo], [0, f_normal(mu,var,lo)],'--', color='red')\n", " if(not rightSideOnly):\n", " ax.plot([hi,hi], [0, f_normal(mu,var,hi)],'--', color='red')\n", " ax.set_title('Distribution for X ~ N('+str(mu)+','+str(var)+')')\n", " ax.set_ylabel(\"f(x)\")\n", " ax.set_xlabel(\"x in Range(X)\")\n", " \n", " if(leftSideOnly):\n", " ans = F_normal(mu,var,hi)\n", " ax.text(mu+1.5*sigma,0.75*f_normal(mu,var,mu),'P( X <= ' + str(hi)+ ' ) = ' + str(round4(ans)),fontsize=12)\n", " elif(rightSideOnly):\n", " ans = 1.0 - F_normal(mu,var,lo) \n", " ax.text(mu+1.5*sigma,0.75*f_normal(mu,var,mu),'P( X => '+str(lo)+ ' ) = ' + str(round4(ans)),fontsize=12)\n", " else:\n", " ans = F_normal(mu,var,hi) - F_normal(mu,var,lo)\n", " ax.text(mu+1.5*sigma,0.75*f_normal(mu,var,mu),'P( '+str(lo)+ ' <= X <= ' + str(hi)+ ' ) = ' + str(round4(ans)),fontsize=12)\n", " \n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Continuity Correction\n", "When using a continuous distribution to approximate a discrete distribution, you will generally get a better\n", "approximation if you include the entire bin for the lower and upper bounds: to do this, subtract 0.5 from the \n", "lower bound and add 0.5 to the upper bound. You can see the effect of this by changing the lower and upper bounds in the\n", "next cell. Search for \"continuity correction normal approximation to binomial\" on Google or Youtube to get further explanation. " ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# change these to see effect of continuity correction: \n", "N = 10\n", "lowerBound = 0\n", "upperBound =7\n", "# First show without the continuity correction \n", "display_binomial_and_normal_range(N,0.5,lo=lowerBound,hi=upperBound)\n", "\n", "# Now show with the continuity correction: subtract 0.5 from lower bound and add 0.5 to upper bound\n", "display_binomial_and_normal_range(N,0.5,lo=lowerBound-0.5,hi=upperBound+0.5)" ] } ], "metadata": { "celltoolbar": "Slideshow", "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 2 }