{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "f0fc7c49-06fd-4261-ab1e-00a9a32d28a8", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import seaborn as sns\n", "import matplotlib.pyplot as plt\n", "import random\n", "import scipy\n", "from scipy.stats import norm\n", "\n", "import ipywidgets as widgets\n", "from ipywidgets import interact, interactive, fixed, interact_manual\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "08591852-1e27-4288-bb86-dc199f0ee43b", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [], "source": [ "import sys\n", "\n", "sys.path.append('/home/ewout/enem_atp/')\n", "from util import load_sample, load_acertos,provas,score_inep,load_padr,item_info_inep, params_inep, scalecalparams, notas_to_enem_scale\n", "%load_ext autoreload\n", "%autoreload 2" ] }, { "cell_type": "markdown", "id": "73e380e3-2ae0-4571-8922-993311baa356", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "# Como funciona a TRI\n", "A teoria de resposta ao item (TRI) é uma metodologia para calcular notas a partir de padrões de respostas a \"itens\" (questões). Ao invés de simplesmente somar o número de acertos, o cálculo da nota pela TRI usa todo o padrão de resposta do candidato, levando em conta as características das questões (dificuldade, poder de \"discriminação\"). Assim, como veremos abaixo, candidatos com o mesmo número de acertos podem ter notas completamente diferentes, dependendo de *quais* questões acertaram, não somente o número delas. \n", "\n", "Por um lado, a metodologia TRI tem vantagens, o principal delas sendo o fato que as notas calculadas pela TRI podem ser comparadas entre edições da prova, por exemplo em anos diferentes. É por esta razão que avaliações educacionais como o SAEB, o sistema que monitora o desempenho de alunos do ensino básico, usa TRI. Mas por outro lado, há a grande desvantagem que o cálculo da nota pela TRI é um processo opaco para o candidato. Como explicar a alguém com 10 acertos que ele recebeu, digamos, 400 pontos e um outro candidato recebeu 520 pontos?\n", "\n", "Com um pouco de esforço, é possíve abrir a caixa opaca da TRI. É possível reproduzir as notas do ENEM usando as padrões de resposta dos candidatos. Vamos começar mostrando os dados que temoss, carregando uma amostra de alguns dos milhões de candidatos que fizeram a prova de 2023.\n", "\n", "```{admonition} Microdados\n", "Para este projeto baixamos [os microdados do ENEM](https://www.gov.br/inep/pt-br/acesso-a-informacao/dados-abertos/microdados) disponibilizados pelo INEP. Para ver o nosso *pipeline* de processamento de dados e as funções que usamos abaixo, veja o nosso repositório de código: https://github.com/atp/enem\n", "```\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "fd494d5b-f292-43b5-a3f4-c712d5cb02a7", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " 40724 60332 126604 117631 43890 85436 26042 83558 64023 \\\n", "candidato \n", "210060105242 1 0 1 1 1 1 1 0 0 \n", "210060522409 0 0 0 0 0 0 0 0 0 \n", "210061890057 0 0 0 1 0 0 0 1 0 \n", "210059579028 0 0 0 0 0 1 0 0 1 \n", "210058117429 0 0 1 1 0 0 0 1 0 \n", "\n", " 87989 ... 111665 84422 83378 117887 66330 48492 63155 \\\n", "candidato ... \n", "210060105242 0 ... 0 0 1 0 0 0 0 \n", "210060522409 0 ... 0 0 0 0 0 1 0 \n", "210061890057 1 ... 0 0 1 0 0 1 1 \n", "210059579028 0 ... 0 0 1 1 0 0 0 \n", "210058117429 0 ... 0 0 1 0 0 0 0 \n", "\n", " acertos caderno nota_inep \n", "candidato \n", "210060105242 15 1224 532.8 \n", "210060522409 6 1221 329.2 \n", "210061890057 11 1224 441.8 \n", "210059579028 9 1221 419.2 \n", "210058117429 5 1221 427.5 \n", "\n", "[5 rows x 48 columns]" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "load_acertos(2023,'CN',5)" ] }, { "cell_type": "code", "execution_count": null, "id": "27dddbb4-98b3-4f7d-81f1-431dafbe4a4e", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "0255b79f-2351-4e3b-bd83-eb2484fb5b33", "metadata": {}, "source": [ "Com os dados neste formato, podemos reproduzir as notas dadas pela INEP. Vamos transformar os 45 acertos e erros, ou \"0\"s e \"1\"s dos candidatos, em notas calculadas pelo TRI, usando os parâmetros das questões (itens, no jargão das especialistas em avaliação) fornecido pelo INEP. O resultado vai ser uma nota na \"escala ENEM\", que varia na prática entre 300 e 800 ou 900.\n", "\n", "```{admonition} Interpretação da escala ENEM\n", "Uma das interpretações equivocadas da escala ENEM mais comuns é equiparar as notas, ainda implicitamente, a uma nota escolar do 0 até 10. Porém, não é correto interpretar 600 ou 700 na escala ENEM como sendo \"mais ou menos satisfatória\", como faríamos com notas escolares. Ao vez disso, a interpretação correta é que 500 é a média da população referência (alunos no final do ensino médio em 2009) e 100 pontos na escala ENEM corresponde a um desvio padrão da população de referência. Assim, uma nota acima de 700 na escala ENEM seria atingido por somente 2,5% da população de referência. \n", "```" ] }, { "cell_type": "markdown", "id": "668d9a28-e343-4399-b92b-263ca95ebbb4", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "## A nota TRI é bem diferente do que o número de acertos\n", "Antes de mostrar como notas são calculadas na escala ENEM, mostramos o que todo mundo que já fez o ENEM sabe: dois candidatos com o mesmo número de acertos podem ter notas ENEM bem diferentes. Não é somente o número de acertos que conta, é também o padrão de respostas que é levado em conta:" ] }, { "cell_type": "code", "execution_count": 5, "id": "09cde245-5579-49cc-a176-4205caa4f951", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ano = 2023\n", "area = 'CN'\n", "df = load_acertos(ano,area,5000)\n", "ax = df.plot(kind='scatter',x='acertos',y='nota_inep')\n", "df.query(\"acertos == 9\").plot(kind='scatter',x='acertos',y='nota_inep', color='r',ax=ax)\n", "df.query(\"nota_inep > 497 & nota_inep < 502\").plot(kind='scatter',x='acertos',y='nota_inep', color='k',ax=ax)" ] }, { "cell_type": "markdown", "id": "9febdf4e-1e1d-4459-9bcf-2cb42dc29731", "metadata": {}, "source": [ "Vemos que para pessoas com 9 acertos a nota ENEM pode variar de 330 até 530, dependendo quais questões acertaram. E, para quem tirou uma nota ENEM de 500, o número de acertos pode ter sido entre 9 e 16." ] }, { "cell_type": "markdown", "id": "7882f54a-ee61-4c30-99c0-cbdcb2b82cfe", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "## O \"peso\" da questão não é sua dificuldade" ] }, { "cell_type": "markdown", "id": "93a236a4-6103-405c-9159-e9684fa718f3", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "O que explica esta diferença é o padrão de respostas dos candidatos. De uma forma geral, quem acerta de forma mais consistente ganha uma nota maior. Mas, contrário ao senso comum, não é verdade que questões mais difíceis \"pesam mais\" e levam a uma nota maior. Talvez surpreendentemente, dado um certo número de acertos, é melhor acertar itens fáceis do que acertar itens difícil. Podemos mostrar isso com candidatos reais." ] }, { "cell_type": "markdown", "id": "30cbdfd2-21dd-43f7-9de2-41626b9c6ec5", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "O INEP fornece os parâmetros dos itens, as características das questões determinadas durante o processo de testagem. O parâmetro $a$ representa a \"discriminação\" do item, $b$ é a dificuldade e $c$ a probabilidade de acerto por acaso. Mais abaixo explicamaremos melhor como interpretar estes parâmetros. Agora vamos mostrar que o parâmetro `b` *não* deve ser interpretado como o \"peso\" da questão. " ] }, { "cell_type": "code", "execution_count": 6, "id": "32420ffe-6d8a-470c-b48d-3e77e034fa31", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " a_inep b_inep c_inep u\n", "CO_ITEM \n", "64023 1.81427 1.41990 0.25187 1\n", "97149 0.99037 1.55817 0.20321 1\n", "84041 3.68114 1.27129 0.10000 1\n", "66259 2.34079 1.00185 0.23885 1\n", "117866 2.33748 1.77344 0.10811 1" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "prova = 1222\n", "params = params_inep(prova=prova)\n", "params[:5]" ] }, { "cell_type": "markdown", "id": "6398268e-365e-42d7-8162-0ee0d34c9ece", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "Com algumas manobras, podemos mostrar a diferença entre as padrões de resposta de dois candidatos com o mesmo número de acertos. Observe que a nota alta é obtida para quem acerto as questões mais fáceis. O padrão com acertos em itens difíceis mas erros em itens fáceis é pouco provável e o algoritmo TRI associa uma nota baixa. " ] }, { "cell_type": "code", "execution_count": 7, "id": "e5d84bb0-7d8f-46ee-9d72-1075977ff9d8", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "c2051a245e8a425a85d72b73f0e40f4d", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(IntText(value=9, description='Acertos:'), Output()), _dom_classes=('widget-interact',))" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "itens_a = pd.qcut(params['a_inep'],3,labels=['Baixa','Média','Alta'])\n", "itens_b = pd.qcut(params['b_inep'],3,labels=['Baixa','Média','Alta'])\n", "itens = pd.concat([itens_a,itens_b],axis=1)\n", "itens.columns = ['discriminação','dificuldade']\n", "\n", "def compare_padr(nacertos=9):\n", " padrmin = df.loc[df.query(\"acertos == @nacertos\")['nota_inep'].idxmin()]\n", " padrmax = df.loc[df.query(\"acertos == @nacertos\")['nota_inep'].idxmax()]\n", " notamin,notamax = padrmin['nota_inep'], padrmax['nota_inep']\n", " padrmin = padrmin[:-3]; padrmax = padrmax[:-3]\n", " padrmin.index = padrmin.index.astype(str);padrmax.index = padrmax.index.astype(str)\n", " result = params.join(itens).join(padrmin).join(padrmax)\n", " result.columns = ['a','b','c','u','discriminação','dificuldade','nota_baixa','nota_alta']\n", " result = result.sort_values(['b'],ascending=True).query(\"nota_baixa == 1 or nota_alta == 1\")\n", " result.columns = ['a','b','c','u','discriminação','dificuldade',f'nota = {notamin}',f'nota = {notamax}']\n", " return result\n", "\n", "iw = widgets.IntText(\n", " value=9,\n", " description='Acertos:',\n", ")\n", "interact(compare_padr, nacertos=iw);" ] }, { "cell_type": "markdown", "id": "1d126e52-38f6-45fb-8490-974a0f96d00f", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "Podemos também comparar dois candidatos com notas parecidas do ENEM. Vemos na figura acima que candidatos com uma nota de 500 podem ter acertado entre 6 e 15 itens. Qual é a diferença entre os padrões de resposta deste dois candidatos?\n", "\n", "Veja abaixo como o padrão de resposta é diferente para dois candidatos com essencialmente a mesma nota ENEM. O primeiro, com poucos acertos, acertou quase todas as questões fáceis. O segundo também acertou uma fração das questões fáceis, mas errou alguns. Apesar de ter acertadas itens difíceis, não adiantou. Acertar uma questão difícil sem acertar as fáceis não leva a notas maiores no TRI. " ] }, { "cell_type": "code", "execution_count": 8, "id": "da0ec542-53c7-46b9-ae7d-721a29811b27", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/html": [ "
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discriminaçãodificuldadeacertos: 8.0, nota: 499.7acertos: 17.0, nota = 500.4
CO_ITEM
83378BaixaBaixa1.00.0
40724BaixaBaixa1.01.0
126604AltaBaixa1.00.0
117631BaixaBaixa1.01.0
141723MédiaBaixa1.01.0
111665AltaBaixa0.01.0
87989MédiaBaixa0.01.0
47317MédiaBaixa0.01.0
63155AltaMédia0.01.0
64023BaixaMédia0.01.0
48641AltaMédia0.01.0
97149BaixaMédia1.00.0
60332AltaMédia1.00.0
83552MédiaMédia0.01.0
117866MédiaMédia0.01.0
82333MédiaAlta0.01.0
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54162BaixaAlta1.01.0
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66330BaixaAlta0.01.0
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" ], "text/plain": [ " discriminação dificuldade acertos: 8.0, nota: 499.7 \\\n", "CO_ITEM \n", "83378 Baixa Baixa 1.0 \n", "40724 Baixa Baixa 1.0 \n", "126604 Alta Baixa 1.0 \n", "117631 Baixa Baixa 1.0 \n", "141723 Média Baixa 1.0 \n", "111665 Alta Baixa 0.0 \n", "87989 Média Baixa 0.0 \n", "47317 Média Baixa 0.0 \n", "63155 Alta Média 0.0 \n", "64023 Baixa Média 0.0 \n", "48641 Alta Média 0.0 \n", "97149 Baixa Média 1.0 \n", "60332 Alta Média 1.0 \n", "83552 Média Média 0.0 \n", "117866 Média Média 0.0 \n", "82333 Média Alta 0.0 \n", "97767 Baixa Alta 0.0 \n", "111466 Alta Alta 0.0 \n", "54162 Baixa Alta 1.0 \n", "48492 Baixa Alta 0.0 \n", "66330 Baixa Alta 0.0 \n", "\n", " acertos: 17.0, nota = 500.4 \n", "CO_ITEM \n", "83378 0.0 \n", "40724 1.0 \n", "126604 0.0 \n", "117631 1.0 \n", "141723 1.0 \n", "111665 1.0 \n", "87989 1.0 \n", "47317 1.0 \n", "63155 1.0 \n", "64023 1.0 \n", "48641 1.0 \n", "97149 0.0 \n", "60332 0.0 \n", "83552 1.0 \n", "117866 1.0 \n", "82333 1.0 \n", "97767 1.0 \n", "111466 1.0 \n", "54162 1.0 \n", "48492 1.0 \n", "66330 1.0 " ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nota1, nota2 = 499,501\n", "dfn = df.query(\"nota_inep <= @nota2 and nota_inep > @nota1\")\n", "padrmin = dfn.loc[dfn['acertos'].idxmin()]\n", "padrmax = dfn.loc[dfn['acertos'].idxmax()]\n", "notamin,notamax = padrmin['nota_inep'], padrmax['nota_inep']\n", "acertosmin,acertosmax = padrmin['acertos'], padrmax['acertos']\n", "padrmin = padrmin[:-3]; padrmax = padrmax[:-3]\n", "padrmin.index = padrmin.index.astype(str);padrmax.index = padrmax.index.astype(str)\n", "result = params.join(itens).join(padrmin).join(padrmax)\n", "result.columns = ['a','b','c','u','discriminação','dificuldade','nota_baixa','nota_alta']\n", "result = result.sort_values(['b'],ascending=True).query(\"nota_baixa == 1 or nota_alta == 1\")\n", "result.columns = ['a','b','c','u','discriminação','dificuldade',f'acertos: {acertosmin}, nota: {notamin}',f'acertos: {acertosmax}, nota = {notamax}']\n", "result = result.drop(columns=['a','b','c','u'])\n", "result" ] }, { "cell_type": "markdown", "id": "ee944832-761e-487a-ada0-b503e0d9c96e", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "## O modelo TRI determina a probabilidade dos padrões de resposta\n", "A teoria de resposta ao item faz uma modelagem probabilística para as respostas de um candidato às questões da prova. Vamos chamar a habilidade (presuposto uma quantidade unidimensional nos modelos simples) $\\theta$ e os padrões de resposta $x_i = 0$ (errou) ou $1$ (acertou) para $i=1\\ldots 45$. Então o model TRI postula que um candidato com habilidade $\\theta$ tem uma certa probabilidade $P_i(x_i = 1|\\theta;a_i,b_i,c_i)$ que o candidato acertar a questão $i$. É esta \"habilidade\" $\\theta$ que vai virar a nota do ENEM.\n", "\n", "Vamos ver exemplos concretos desta função $P_i(x_i = 1|\\theta;a_i,b_i,c_i)$, usando os parâmetros das primeiras cinco questões da prova que estamos ananlisando:" ] }, { "cell_type": "code", "execution_count": 9, "id": "86c7411c-ead8-475b-9dc4-140fcb18fe7d", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sns.set_context('paper',font_scale=1.4)\n", "\n", "params = params_inep(ano,area)[:5]\n", "theta = np.arange(-3,3,0.01)\n", "def P(theta,a=1,b=0,c=0):\n", " return c + (1-c)*1/(1+np.exp(a*(b-theta)))\n", "i = 0\n", "for item,value in params.iterrows():\n", " i += 1\n", " a,b,c = value['a_inep'],value['b_inep'],value['c_inep']\n", " sns.lineplot(x=theta,y=P(theta,a,b,c), label=f\"$P_{i}$: a={a:.1f}, b={b:.1f}, c={c:.2f}\")\n", "ax = plt.gca()\n", "ax.set_xlabel(r\"$\\theta$\");ax.set_ylabel(r\"$P_i(\\theta)$\");" ] }, { "cell_type": "markdown", "id": "7be3a0a4-716e-404c-a721-ef3e56eb3945", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "Vemos que a probabilidade de acertar depende da habilidade do candidato e das características das questões (parametrizado acima com três parâmetros, mas pode haver outros modelos para as características das questões). Qualquer modelo razoável vai dar uma probabilidade maior de acerto para habilidades $\\theta$ maiores. Da mesma forma, a probabilidade de acerto deve diminuir para questões mais difíceis (para uma determinada habilidade fixa). Grande parte do problema técnica da TRI é estimar, baseado em muitas padrões de resposta a provas como estas que vimos acima, as características das questões. Por agora vamos supor que esta calibração das características das questões foi feito e que conhecemos os parâmetros das questões e portanto as funções $P_i$. Agora vamos se perguntar: dado uma certa habilidade, quais serão as padrões de resposta mais prováveis? Uma vez que temos um modelo para esta pergunta, vamos inverter a questão e perguntar: dado um certo padrão de resposta, qual é a habilidade correspondente mais provável?\n", "\n", "A probabilidade de um determinado padrão de respostas $\\{x_1, x_2 \\ldots x_{45}\\} = \\{x_i\\} = \\vec{x}$, dado uma certa habilidade é\n", "\n", "$$ \\text{prob}(\\vec{x}|\\theta)= \\prod_{i=1}^{45} P_i(\\theta)^{x_i} (1-P_i(\\theta))^{1-x_{i}} $$\n", "\n", "Isso parece uma expressão complicada, mas é possível de entender. Estamos supondo que as probabilidades de acertar questões são todas independentes. Neste caso, as leis da probabilidade dizem que precisamos multiplicar as probabilidades de acerto para todas as 45 questões da prova. Vamos supor que queremos saber a probabilidade de um determinado padrão de resposta, digamos $\\{0,1,1,0\\ldots\\}$. A probabilidade de *errar* a primeira questão é $(1-P_1)$, a probabilidade de *acertar* a segunda questão é $P_2$, a terceira $P_3$, a de *errar* a quarta $(1-P_4)$, e assim até a última questão e precisamos multiplicar todas estas probabilidades. Observe que os expoentes $P_i^{x_1}$ na expressao acima é só notação que escolha $P$ para um acerto ($x_i = 1)$ e $(1-P)$ para um erro ($x_i = 0)$. \n", "\n", "A expressão acima para as $2^{45}$ probabilidades, um para cada padrão de respostas possível, é o *modelo* da TRI para as padrões de resposta. As probabilidades de cada padrão de resposta podem ser considerada como uma função da habilidade $\\theta$. Mas para determinar o $\\theta$ (a nota TRI) dado um determinado padrão de respostas, precisamos \"inverter\" a expressão acima. Conhehecendo o padrão de resposta há duas formas de determinar a habilidade $\\theta$. Primeiro vamos ver o método tradiconal em estastística, \"máxima verossimilhança\". Segundo, o método Bayesiano. \n", "\n", "### Estimar $\\theta$ por meio do método de máxima verossimilhança\n", "Para demonstrar como a inferência da habilidade $\\theta$ funciona, dado um padrão de respostas, vamos analisar o modelo concreto usado no ENEM. Vamos assumir que conhecemos as características das questões (as funções $P_i$, veja acima, mas para simplificar a exposição vamos usar $c=0$) e como exemplo vamos analisar um dos $2^{45}$ padrões de resposta possível: 45 cinco respostas (acertos ou erros para cada uma das questões): $\\{0,1,1,0\\ldots\\}$. \n" ] }, { "cell_type": "markdown", "id": "81d81916-2f3c-4c65-992d-d537db690c2c", "metadata": {}, "source": [ "Vamos inicialmente imaginar que só temos informação sobre o acerto ou erro da primeira questão. No nosso exemplo, o candidato errou e $x_1 = 0$. Por enquanto, o nosso modelo diz:\n", "\n", "$$ \\text{prob}(x_1 = 0|\\theta) = P_1(\\theta)^{0} (1-P_1(\\theta)^{1-0} = 1-P_1(\\theta)$$\n" ] }, { "cell_type": "code", "execution_count": 10, "id": "e02f1641-0457-4a50-81a0-4ce0813a9637", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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M11a8BkYEJiYmsLW1xa1bt3h6TU8IggAzMzM4OztDLpdrZZssR0REIvN2aoaf3uiJnWfT8enueMz7+Tx+OZ2GJSM7wo2jbTc4KysrNG/eHGq1mteD6bjya4y0/YcEyxERkQ4QBAHDO7dE33Z2WPZbAracTMFLX0chuF9rzHjOHUYGvES0IdXHL1zSH/zXRkSkQyxkhvh0REf8+EZPtGoux4p9VzAs7BgSbuWKHY2oyWA5IiLSQX4KK+x5OwDB/VrjamYehq36E+ujrkPFsZGI6h3LERGRjjI2kOIfL3rgpzd6omVzORbvjseE9SeRnl0odjSiRo3liIhIx/k4N8fuYH+M7+6M49fvYsBXR/H7hQyxYxE1WixHRER6wMTIAJ+N6IiNU7rCUCrBG5tPY/Gvl1BaphI7GlGjw3JERKRH+rWzx+5gf/i6NMf6Yzfw6roTyMjhaTYibWI5IiLSMw6Wcmyb0QOvB7giNvk+Bq88hqird8SORdRosBwREekhQ6kEHw72wpogX5QqVZi88RTC/7zBQQuJtIDliIhIj73UoQV2vuUPhbUpFu26hAU7LvA6JCINsRwREek5VxtT7JjdG/6tbfDDqRRM3HAS9/NLxI5FpLdYjoiIGgFLE0Nses0Pk3u64MT1e3h59Z+4fidP7FhEeonliIiokTCQSrBoeAeEDm+P1PuFeGXNcZy9mS12LCK9w3JERNTITOypwNogX+QXKzHuPyd4JxtRHbEcERE1Qs972WPz9O4wkAiYuikaO8+mix2JSG+wHBERNVJ+CitEvNETVqZGeHvbGXz7V5LYkYj0AssREVEj1q6FBX6e1Quu1qYI2XkR66Ouix2JSOexHBERNXJOzU2wfWZPtLEzw+Ld8Vh7JFHsSEQ6jeWIiKgJsDU3xg8zesDD3hxLfkvA6sPXxI5EpLNYjoiImggbM2Nsfb072rUwx/LfLyPs4FWxIxHpJJYjIqImxNrMGFtf7wEvBwus2HcF3xzmKTaiv2M5IiJqYqxMjbBl+sMjSMt+T8CWk8liRyLSKSxHRERNUHNTI3w3rRsU1ib46L8XEBmXJnYkIp3BckRE1ETZmcuweXp3tLCQ4Z8RZ3Eg/rbYkYh0AssREVET5tTcBN9P6w4LuSFmbTmN6KR7YkciEh3LERFRE9fazgzfTe0GA4mA17+LQeKdPLEjEYmK5YiIiNChpSVWT+iCB0VKTAk/hTsPisWORCQaliMiIgIA9PGww2cjOuDmvUJM+zYaBSVKsSMRiYLliIiIKoz1c0Zwv9Y4l5qDt7aeQZlKLXYkogbHckRERFW8+0JbjPRpiQMJmfh872Wx4xA1OJYjIiKqQhAEfDayI3ycm2HNkUT89wzHQKKmheWIiIiqkRlKsTbIFy0sZHj/53M4ezNb7EhEDYbliIiIamRnIcO6Sb4QAMz4PgaZuUViRyJqECxHRET0WN5OzbD8FW/czi3GjO9jUVRaJnYkonrHckRERE80vHNLzO7jjrib2Vi486LYcYjqHcsRERE91T9f9EBAGxtsi76Jn2NTxY5DVK9YjoiI6KmkEgFfje2MFhYyfPTfC7hy+4HYkYjqDcsRERHVirWZMcLG+6CkTIVZm2ORX8wRtKlxYjkiIqJa66qwwgcvtUPinXzM/+U81GqOoE2ND8sRERHVyfQAV7zoZY+dZ9Ox+WSK2HGItI7liIiI6kQQBHw+uhOcrUwQuusS4jNyxY5EpFUsR0REVGeWckOsGucDlVqNd7bFcfwjalT0ohwplUqEhobC1dUVMpkMnp6eWL16da3XXb16NTp37gxzc3PY2dmhX79++P333+s5NRFR49apVTO883wbXL79AEt/SxA7DpHW6EU5mjVrFkJCQjBgwACEhYWhY8eOmDNnDj777LOnrvvWW29hzpw58PLywooVK/D+++8jIyMDAwcOxI4dOxogPRFR4zWrT2v4KZpj019JOHQ5U+w4RFohqHX8VoO4uDj4+Phg3rx5WLp0acX0sWPHYufOnUhOToadnV2N6+bn56NZs2YYNmwYfv7554rpWVlZcHR0xMCBAxEZGVmnPKdPn4avry9iY2PRpUuXZ3tRRESNSOr9Agz8KgrGhlL8/k4AbMyMxY5EVE1dfn/r/JGjiIgIAEBwcHCV6cHBwSgqKnpiuSksLIRSqYSDg0OV6VZWVpDJZDAxMdF+YCKiJsapuQkWj+iArLxizPvpHG/vJ71nIHaAp4mJiYGTkxMcHR2rTPfz84NEIkFsbCxef/31Gte1sbFBx44dER4ejm7duqFPnz548OABPv/8c6hUKrz77ruP3W9GRgYyMjKqTY+Pj9fsBRERNULDO7fE4ct3sONMGraeSsGE7i5iRyJ6ZjpfjtLT06sVIwAwMjKCtbU10tLSnrj+jz/+iHHjxmHy5MkV0xwcHHD48GF07dr1seutXbsWixYtevbgRERNzKLh7XHy+l18tjsegW1t4dScR+dJP+n8abXCwkIYG9d8/lomk6GwsPCJ65uZmaFDhw4IDg7GL7/8gnXr1sHS0hJDhgxBQsLj766YOXMmYmNjq31s3rxZo9dDRNRYWcgMsXSUN/JLyvDBzxw9m/SXzh85ksvlKC4urnFeUVER5HL5Y9fNy8tDr169MGnSJISGhlZMf/nll9G2bVu899572LVrV43rOjg4VLtWiYiInuy5trZ41a8VtkXfxLbomxjXzVnsSER1pvNHjhwdHZGenl5teklJCe7evVvjKbdyP//8M1JSUjBixIgq021tbREQEICoqCit5yUiauoWDPaEg6UMn+6OR1r2k4/uE+kinS9Hvr6+SE1NrXZtUXR0NFQqFXx9fR+7bnmpKiurPnKrUqmEUsknShMRaZuFzBBLRnZEXrESH/zMu9dI/+h8ORozZgwAYNWqVVWmr1y5EjKZDMOHDwcAFBQUICEhAVlZWRXLeHh4AEC164RSUlJw9OjRJxYrIiJ6dn087DCmqxOirmYhIuam2HGI6kTnrzny8fHB1KlTsXz5cuTk5KBr167Yt28fIiIiEBoaCnt7ewDAqVOn0LdvX4SEhGDhwoUAgKFDh8Lb2xsrV65Eeno6+vfvj6ysLKxevRpFRUUICQkR8ZURETVuHw3xQtTVLCz+NR59POxgbyETOxJRreh8OQKANWvWwNnZGeHh4di4cSMUCgVWrVqFOXPmPHE9Q0NDREVFYdmyZdixYwd2794NQ0NDdOvWDT/88AMCAwMb6BUQETU9FjJDLH65A6Z9G4NPdl3C/03gUwVIP+j840N0DR8fQkRUN7M2x+K3C7ewcUpX9GtnL3YcaqIa1eNDiIhIv4UMbQ8zYwP8678XUVDCG2FI97EcERFRvWphKcPcF9siLbsQX/1xVew4RE/FckRERPVuYk8FvJ0sseHYDVxMzxE7DtETsRwREVG9k0oEfDaiI9RqNRbsuIAyFS93Jd3FckRERA2iQ0tLTO3tirM3s7H1ZLLYcYgei+WIiIgazLsvtEULCxlW7LuCe/klYschqhHLERERNRhTYwMsGOyJnMJSfL73sthxiGrEckRERA1qqLcDurtaYVt0Cs6n8uJs0j0sR0RE1KAEQcDCYe0hAAjZeQEqXpxNOobliIiIGpyngwUm9nDB6ZRs7DiTJnYcoipYjoiISBT/eMEDVqZGWPJbAh4UlYodh6gCyxEREYnC0sQQ7w3wQFZeMVYe4MjZpDtYjoiISDRjurZCx5aWCP8zCTey8sWOQwSA5YiIiEQklQj4eKgXlCo1lv4WL3YcIgAsR0REJDI/hRUGdmiBvRdv48T1u2LHIWI5IiIi8X0wsB0MpQI+3R3PW/tJdCxHREQkOhdrU0zqqcD5tBxEnuWt/SQuliMiItIJb/VrDUu5IT7//TKKSsvEjkNNGMsRERHphGYmRni7fxuk5xRhw7EbYsehJozliIiIdEZQDxcorE2w+tA13HlQLHYcaqJYjoiISGcYGUjwwUBP5JeU4esDV8SOQ00UyxEREemUAe3t4evSHNtO3UTyXQ4MSQ3PQJOV1Wo1zpw5g7/++gupqam4e/cu5HI5bG1t0bFjR/j7+8PGxkZbWYmIqAkQBAHvD/DA2HUn8OX+K/j6VR+xI1ET80zlKDY2Fhs2bMC2bduQk5MDtbr6mBSCIAAAunfvjqlTp2LcuHEwNTXVLC0RETUJ3d2s0cfDFpFx6ZjxnBvaO1qKHYmakDqdVjtz5gwGDhyIbt26YdOmTejduzcWLVqEXbt24eTJk7hy5QrOnTuHI0eOYN26dXj99ddx7949zJgxAwqFAl988QWKi3mBHRERPd17AzwAACv2XhY5CTU1dTpy5OvrCx8fH2zatAkvv/wyzM3NH7tsQEAApk2bBuBhqQoPD8fHH3+MgoIC/Otf/9IsNRERNXrtHS0xrJMjdp5Nx6kb99DN1UrsSNRE1OnI0e7duxEbG4uJEyc+sRj9nY+PD1auXImkpCQMGjSoziGJiKhp+scLbWEgEbD894QaL+Egqg91KkcDBw7UaGe2trbw9fXVaBtERNR0KGxMMdavFWKS7+NgQqbYcaiJ4K38RESk04L7t4HMUILlv19GGR9KSw2gznerKZVKREZG4q+//kJmZiaMjY3h6OiIdu3aoWfPnnB1da2PnERE1ETZW8gwpZcr1hxJxM6zaRjh4yR2JGrk6lSOUlJSMGDAAFy5cqXKud/y2/YBwM3NDRMmTMCbb77JMY6IiEgrZgW6Y+vJZPx7/1UM8XaEoZQnPqj+1Omna86cObhy5QreffddnDx5ElevXsWFCxcwdepUqNVqjBs3Dnl5efjkk0/g6uqKVatW1VduIiJqQixNDPF6gBtS7hXgl9OpYsehRq5O5ejo0aN49dVXsWLFCvj5+cHd3R1eXl5wcnKCIAjYvHkz0tPTsXfvXnTt2hXvvPMOZs+eXV/ZiYioCZnSW4FmJoZYdfAaSpQqseNQI1ancmRoaAhHR8cnLiMIAl544QUcOnQIn3zyCdauXYstW7ZoFJKIiMhc9vDoUer9QvzMo0dUj+pUjvr164effvoJ+fm1exDghx9+iH79+uGrr756lmxERERVTO6lQHMTQ4Tx6BHVozqVo9DQUGRmZuKll15CcnJyrdbx9fXFpUuXnikcERFRZWbGBpjxnDvSsgsREXNT7DjUSNWpHHl4eGDnzp24cOECPDw8MGHCBPz666+PPZJUUFCAPXv28K41IiLSmkk9XWBlaoT/O3QNxcoyseNQI1TncY769++P8+fPY+7cudi+fTu2bdtWMW/q1Klo0aIFjIyMkJmZiZ07dyIjIwOLFy/WamgiImq6TI0NMPM5Nyz5LQER0TcxsadC7EjUyNS5HAGAk5MTtm3bhuTkZGzbtg379+/HqVOnsGnTpirL2dnZYcmSJXj//fe1kZWIiAgAMLGnC/4TdR3/dygRo7u2gsxQKnYkakSeqRyVc3Fxwbx58zBv3jwAQGpqKjIyMlBaWgpbW1u0bt26ygCRRERE2mBiZICZz7nj0z3x2HYqBVN68+kMpD0alaO/c3JygpMTh3UnIqL6F9TDBWuPXsfqw4l4tZszjx6R1nD8dSIi0ktyIyneCHRD5oNi/Mg710iL6nTkyNXVVWunyd555x0EBwdrZVtERNQ0je/ujNWHE7HmyHW82s2Zz1wjrahTOQoMDNRaOVIoFFrZDhERNV0mRgaY5u+Kz/dexn/PpGF011ZiR6JGoE7l6O93oxEREYltYk8XrDmSiNWHEzGyixOkEt4IRJrh8UciItJrFjJDTOmlwI2sfOw5nyF2HGoEWI6IiEjvvdbbFSZGUvzfoWtQqdRixyE9p9Gt/AkJCYiKikJiYiJycnIAAJaWlnB3d0dAQADatWunlZBERERPYmVqhAndnfGfqBs4kJCJF7zsxY5EeuyZytGZM2cwZ84cnDx5Emp1zQ1dEAR0794dq1evRufOnTXJSERE9FSvB7jh2+PJCDt0Dc972nEQYnpmdS5H586dQ0BAAFQqFaZMmYLnn38e7u7usLCwAADk5uYiMTER+/fvx/bt2+Hv74/jx4+jY8eOWg9PRERUzs5ChrFdW+H7E8k4di0LAW1sxY5EeqrO5WjBggUwNjZGVFQUvLy8alymW7duGDduHObOnQt/f38sWLAAu3bt0jgsERHRk8wMdMMPp1IQdvAayxE9szpfkP3nn39i/Pjxjy1GlXl5eWH8+PGIiop6pnBERER14dTcBCN8WuLkjXuITrondhzSU3UuR2VlZXU6jysIAlQqVV13Q0RE9Exm9XGHRADCDl4TOwrpqTqXoy5dumDr1q24du3pP3RXrlzB1q1b4evr+0zhiIiI6srN1gyDvR1x5ModXEjLETsO6aE6l6OPP/4Y2dnZ8PHxwZw5c/Dzzz8jLi4O169fx/Xr1xEXF4eff/4Zs2fPhq+vL3JzcxESElIf2YmIiGr0RqAbAGDt0esiJyF9VOcLsvv164f//ve/mDVrFr755husWbOmxuXUajWcnJzwzTffoE+fPprmJCIiqrX2jpZ4rq0tdp9Lx/sDPNDKykTsSKRHnmmcoyFDhmDAgAHYv38/oqKicO3aNeTm5gIALCws0Lp1awQEBOD555+HkZGRVgMTERHVxhvPueHolTv4T9R1fDK8g9hxSI888wjZhoaGGDRoEAYNGqTNPERERFrR090a3k6WiIi5ibf7t4G1mbHYkUhP8NlqRETUKAmCgJnPuaOoVIVvjyeLHYf0CMsRERE1Wi91aAEXaxN8dzwJBSVKseOQnmA5IiKiRksqEfB6gBuyC0qxPfqm2HFIT+hFOVIqlQgNDYWrqytkMhk8PT2xevXqWq9fVlaGsLAw+Pj4wMTEBFZWVvD398f+/fvrMTUREemCV3ydYGNmhPVRN1BaxkGJ6eme+YLshjRr1ixs2LABM2bMQNeuXbFv3z7MmTMH2dnZWLBgwRPXValUGD16NPbs2YPJkydjzpw5KCgowMWLF5GamtpAr4CIiMQiM5RiSi8FVuy7gt3nMvCyT0uxI5GO00o5ioyMRGRkJDZu3Fjj95qIi4vD+vXrMW/ePCxduhQAMH36dIwdOxahoaGYPn067OzsHrt+WFgYdu3ahYMHDyIgIEDjPEREpH+Cerhg9eFErDmSiOGdHev0GCxqerRyWi0uLg7ffvvtY7/XREREBAAgODi4yvTg4GAUFRUhMjLyseuqVCp88cUXGD58OAICAqBSqZCXl6eVXEREpD+amRhhXDdnJNx6gCNX7ogdh3Sczl9zFBMTAycnJzg6OlaZ7ufnB4lEgtjY2Meum5CQgJSUFHTp0gVvvvkmzMzMYG5uDmdnZ6xdu/aJ+83IyMDp06erfcTHx2vldRERUcOa5u8KA4mAtUf4SBF6Mp2/5ig9Pb1aMQIAIyMjWFtbIy0t7bHrXrlyBQDw73//GyYmJvjqq69gbm6OdevW4Y033kBZWRlmz55d47pr167FokWLtPMiiIhIdI7N5BjW2RG/nE7D2ZvZ6NSqmdiRSEfpfDkqLCyElZVVjfNkMhkKCwsfu275KbScnBycPHkSbm4PH0Q4evRodOjQAYsWLcIbb7wBiaT6AbSZM2di2LBh1abHx8cjKCjoWV4KERGJbOZz7vjldBrWHEnEN0G+YschHaXz5Ugul6O4uLjGeUVFRZDL5U9cFwB69+5dUYwAwMDAAK+++ioWLVqEy5cvw9PTs9q6Dg4OcHBw0DA9ERHpEo8W5ujrYYu9F28h5W4BnK35QFqqTuevOXJ0dER6enq16SUlJbh7926Np9wqrwsA9vb21ea1aNECAHD//n0tJSUiIn3weoAbVGpg4583xI5COkrny5Gvry9SU1OrXVsUHR0NlUoFX9/HHxbt2LEjjI2NaxzPqHyara2tdgMTEZFO6+luDS8HC0TE3EROQanYcUgH6Xw5GjNmDABg1apVVaavXLkSMpkMw4cPBwAUFBQgISEBWVlZFcuYmZlh6NChOH78OM6dO1cxvaCgAN9//z3c3NzQpk2bBngVRESkKwRBwPQAVxSUlGHrqRSx45AO0vly5OPjg6lTp2L58uUVI2WPHTsWERER+PDDDytOmZ06dQqenp4ICwursv6SJUtgaWmJfv36ITQ0FF999RV69uyJ1NRUfPXVVyK8IiIiEtsQb0fYWxhj0183UKLkI0WoKp2/IBsA1qxZA2dnZ4SHh2Pjxo1QKBRYtWoV5syZ89R1W7dujT///BPz5s3DihUrUFpaii5duuD333/HCy+80ADpiYhI1xgZSDC5lwLLf7+M3efTMcLHSexIpEO0Uo7UajXUavVjv9eUoaEhQkJCEBIS8thl+vTp89h9enp6YufOnVrLQ0RE+m9CNxesOnAN66Nu4OXOLflIEaqgldNqCxcuhEqleuz3REREusbSxBBjujrhYnoujl+/K3Yc0iE6f80RERFRfZnq7wpBADZE8bZ++h+WIyIiarJcrE3xopc9DiRk4lomH0xOD7EcERFRk/Z6wMMnKGw4xqNH9BDLERERNWm+Ls3RqVUz/HI6FXfzan5cFTUtLEdERNSkCYKA1wNcUaxUYfMJDgpJLEdERER4qX0LtGwmx/cnklBUWiZ2HBJZg5ejlBS2ciIi0i0GUgle661AVl4JIuPSnr4CNWoNWo6Ki4vh6urakLskIiKqlbF+rWBubID1UTe0OpAx6Z8GP3LEHzgiItJF5jJDvNqtFa5m5uHIlTtixyERab0cSaXSx36YmJhweHYiItJZU3q7QioRsJ6DQjZpWn/wrJmZGb766iu4ublVm1dcXIyBAwdqe5dERERa0bKZHIM6OmDX2XTEZ+TC08FC7EgkAq2Xo06dOsHExASBgYHV5hUXF/O0GhER6bRp/q7YdTYdG4/dwOejO4kdh0Sg9dNqc+bMgZWVVY3zDA0NER4eru1dEhERaU3nVs3Q1aU5IuPSkfmgSOw4JAKNypFKpao2bezYsXjhhRdq3plEgsmTJ2uySyIiono3PcAVJWUcFLKp0qgcDRkyBAUFBdrKQkREpBNe8GqBVlZybD6RzEEhmyCNytH+/fvh7++PjIyMJy6XlJSkyW6IiIgalFQi4LVerriXX4L/nuGgkE2NRuVo586dSExMRI8ePXD+/Plq81NTU/HGG2/Aw8NDk90QERE1uDGPBoXccIyDQjY1GpWjgQMHIioqCiqVCv7+/ti3bx8A4Pbt2wgODkabNm2wbt06dOrEq/2JiEi/mBkbVAwKefRqlthxqAFpfLeat7c3Tp48idatW2PIkCEYP3483N3dERYWhs6dO2P37t04deqUNrISERE1qMm9FJAIwPqo62JHoQaklVv5zczM8Pzzz0OpVGL79u0wNzfH3r17cfz4cQ76SEREesupuQkGdnRA1NUsXL71QOw41EA0Kkf3799HSEgIFAoFVqxYgQ4dOqBv3764fft2xSk2IiIifTbN/+ED0zce4yNFmgqNypGLiwsWL14Me3t7bN26FWfPnsW+ffswc+ZMfPHFF3jllVdQVMQBtIiISH91cW6OLs7NsCMuDVl5xWLHoQagUTmys7NDeHg4Ll68iLFjx0IQBEgkEnzzzTdYtmwZduzYgT59+iAzM1NbeYmIiBrcNH83lChV2HwiWewo1AA0KkeXL1/GpEmTIJFU38x7772H7du349y5c+jRo4cmuyEiIhLVgPb2aNmMg0I2FRqVI6lU+sT5r7zyCg4cOID8/HxNdkNERCQqA6kEr/VWICuvBDvj0sWOQ/VM6w+e/buePXvixIkT9b0bIiKiejXGrxXMOChkk1CncjR37txnun7I1fXhlf47d+7ETz/9VOf1iYiIxGYhM8SYrq1w+fYDHLvGQSEbszqVo+3bt0OhUGDq1KnYt28fVCrVU9dJTU3FF198AW9vb4wcORI5OTnPHJaIiEhMr/V+OCjkBt7W36gZ1GXha9euYeXKlVi+fDm+/fZbmJmZwdfXFz4+PrCzs0Pz5s1RVFSEe/fu4erVq4iJiUFiYiJUKhUGDBiAb7/9Fj4+PvX1WoiIiOpVKysTDGjfAr9duIVrmQ/Q2s5c7EhUD+pUjoyNjfHee+/h7bffxo4dO/D999/j2LFjOHz4cLVlBUFAu3btMHfuXEydOhVt27bVVmYiIiLRTA9wxW8XbmHDsSQsGdlR7DhUD+pUjsoZGRlh7NixGDt2LNRqNS5duoTU1FTcu3cPcrkctra28PLyQvPmzbWdl4iISFRdnJujU6tm+OV0Kt4b4AErUyOxI5GWPVM5qkwQBLRv3x7t27fXRh4iIiKdJggCpvu74q0fzmDLiWS81b+N2JFIy+r9Vn4iIqLGZmCHFnC0lOHb48koVnJQyMZGK+Xo0KFDmDZtGvz8/ODh4QE/Pz9Mnz4dhw4d0sbmiYiIdIqBVIIpvRXIyivGrrMZYschLdOoHCmVSkycOBHPP/88wsPDcebMGdy/fx9nzpzBxo0b8fzzz2PixIkoK2OrJiKixmWsnzNMjKRYH3Wdg0I2MhqVo8WLF2PLli3o27cvoqKiUFxcjMzMTBQXF+Po0aPo06cPtm7dik8//VRbeYmIiHSCpfzhoJAJtx7geOJdseOQFmlUjjZt2gRvb2/s27cPvXv3rnjWmlQqhb+/P/bt24f27dtjw4YNWglLRESkS17rrYAgAOs5KGSjolE5un37NgYOHAiJpObNSKVSDB48GHfu3NFkN0RERDrJxdoUL3rZ42BCJhLv5Ikdh7REo3Lk4eGB27dvP3GZW7duwcPDQ5PdEBER6axp/m4AgI08etRoaFSO5s+fj23btuHYsWM1zo+KisK2bdswf/58TXZDRESks/wUzeHtZImfT6fifn6J2HFIC+o0COR3331XbVrfvn0RGBiIl156Cb1794atrS3u3LmDY8eOYe/evRg4cCCKioq0FpiIiEiXCIKAaf6ueHtbHLaeSsGcvq3FjkQaEtR1uP9QIpFAEIQ637IoCEKjuZ3/9OnT8PX1RWxsLLp06SJ2HCIi0gGlZSoELDsElVqNY/P6wciAYyzrmrr8/q7TkSMO6khERFSdoVSCyb0UWPZ7An49l46RXZzEjkQaqFM5CgwMrK8cREREem18N2esPHAVG47dwAiflhAEQexI9Iw0fvBsuZs3b+LcuXPIzc2FhYUFvL290apVK21tnoiISKdZmhhidFcnfHc8GSeu30NPd2uxI9Ez0rgcXbx4EbNnz67xjrWAgACsXr0aXl5emu6GiIhI573W2xXfn0jGhmM3WI70mEbl6OrVq/D390dOTg4CAgIQGBgIe3t73L59G0ePHsXRo0cREBCAEydOoE2bNtrKTEREpJNcbUzRv509DiTcxo2sfLjamIodiZ6BRuXo448/Rn5+Pnbt2oXBgwdXm79nzx6MGDECISEh2Lp1qya7IiIi0gvTA1zxR/xthP95A58M7yB2HHoGGt1rePDgQYwdO7bGYgQAgwYNwujRo/HHH39oshsiIiK90d3VCu0dLfBjTCqyCzgopD7SqBzl5OQ89aJrZ2dnPHjwQJPdEBER6Q1BEDA9wBWFpWX44dRNsePQM9CoHCkUChw4cOCJyxw8eBAuLi6a7IaIiEivDO7oCDtzY3z7VxJKy1Rix6E60qgcjRs3DtHR0QgKCkJycnKVecnJyZg4cSKio6Mxfvx4jUISERHpEyODh4NC3sotwp7zGWLHoTrSqBx98MEH6NOnD7Zu3YrWrVtDoVCge/fuUCgUaN26NbZs2YI+ffpg3rx52spLRESkFyZ0d4bMUIL1UTfq/NgtEpdG5cjY2Bh//PEH1qxZg169eiE3NxenT59Gbm4uevfujbVr12L//v0wNjbWVl4iIiK90MzECK/4OuF8Wg6ik+6LHYfqQONBICUSCWbMmIEZM2ZoIw8REVGj8VpvV2w+kYL1UdfRzdVK7DhUSxodORo5ciSWLl2qrSxERESNirutGfq3s8P++NtIvpsvdhyqJY3K0d69e5GTk6OtLERERI3ONH9XqNVA+J9JYkehWtKoHLVv3x43btzQVhYiIqJGp6e7NTwdLBARcxM5haVix6Fa0Kgcvffee4iMjMTx48e1lYeIiKhREQQB0/xdUVBShu3RKWLHoVrQ6ILswsJCBAYGIjAwECNHjoSvry/s7OwgCEK1ZSdNmqTJroiIiPTW0E4OWPZ7Ajb9mYSpvV1hINXo2ATVM43K0ZQpUyq+joiIQERERI3LCYKgUTlSKpVYsmQJNm7ciIyMDLi6uuKtt97C7Nmz67Sd0tJSeHt7IyEhASEhIVi4cOEzZyIiIqotYwMpJvVwwRf7r+C3C7cwtJOj2JHoCTQqR4cOHdJWjieaNWsWNmzYgBkzZqBr167Yt28f5syZg+zsbCxYsKDW2/nyyy9x8yafc0NERA1vQg8XhB26hvXHbmCIt0ONZ1lIN2hUjgIDA7WV47Hi4uKwfv16zJs3r2LYgOnTp2Ps2LEIDQ3F9OnTYWdn99TtpKamIjQ0FAsWLMCHH35Y37GJiIiqsDI1wsguTvjhVApOp9yHrwvHPdJVWjnpeejQIUybNg1+fn7w8PCAn58fpk+frpUjS+Wn6oKDg6tMDw4ORlFRESIjI2u1nXfffRc+Pj58zhsREYlmmr8CALA+ind66zKNjhwplUq89tpr2Lp1K9RqNSQSCaysrJCYmIjY2FiEh4dj/Pjx2LRpE6RS6TPtIyYmBk5OTnB0rHp+1s/PDxKJBLGxsXj99defuI39+/fjl19+QUxMTK33m5GRgYyM6g8LjI+Pr/U2iIiIKmttZ44+HrbYe/EWbt4rQCsrE7EjUQ00OnK0ePFibNmyBX379kVUVBSKi4uRmZmJ4uJiHD16tOKhtJ9++ukz7yM9Pb1aMQIAIyMjWFtbIy0t7Ynrl5SU4K233sL06dPh4+NT6/2uXbsWvr6+1T6CgoLq/BqIiIjKTfd3g4qDQuo0jcrRpk2b4O3tjX379qF3794VR4ekUin8/f2xb98+tG/fHhs2bHjmfRQWFj72wbUymQyFhYVPXP+LL75AZmZmnQvazJkzERsbW+1j8+bNddoOERFRZb1bW6NdC3NExNxEbhEHhdRFGp1Wu337NsaNGweJpOaOJZVKMXjwYHz99dfPvA+5XI7i4uIa5xUVFUEulz923Zs3b2Lx4sVYunQpbGxs6rRfBwcHODg41GkdIiKipxEEAVP9XfH+T+cQEX0T0wPcxI5Ef6PRkSMPDw/cvn37icvcunULHh4ez7wPR0dHpKenV5teUlKCu3fv1njKrdyHH34IGxsbDBw4EElJSUhKSkJqaioAIDs7G0lJSU898kRERKRtwzs7wsbMGBuP3UBpmUrsOPQ3GpWj+fPnY9u2bTh27FiN86OiorBt2zbMnz//mffh6+uL1NTUatcWRUdHQ6VSwdfX97HrpqSkICUlBW3atIGrqytcXV0REBAAAPj666/h6uqKI0eOPHM2IiKiZ2FsIMVrvRVIzynCzrjqBwBIXBqdVisuLkbfvn0RGBiIl156Cb1794atrS3u3LmDY8eOYe/evRg4cCCKiorw3XffVVm3tiNmjxkzBkuXLsWqVasqxjkCgJUrV0Imk2H48OEAgIKCAqSkpMDGxqbiFNrixYuRlZVVZXuZmZmYOXMmxo4di1dffRVdunTR5C0gIiJ6JkE9XPDN4USsOZKIET4tIZFwUEhdobXHh/z222/47bffqi2zZ88e7Nmzp8q0ujxOxMfHB1OnTsXy5cuRk5NTMUJ2REQEQkNDYW9vDwA4deoU+vbtW+WxIP7+/tW2l5SUBABo164dXn755VplICIi0jZLuSEm9HDG2iPXcSAhEy942YsdiR7Ri8eHrFmzBs7OzggPD8fGjRuhUCiwatUqzJkzp0H2T0REVB+m9XZF+LEkrD58Dc971vzgdmp4Ov/4EAAwNDRESEgIQkJCHrtMnz59oFarn7othUJRq+WIiIjqm52FDKN8Hz5S5NSNe+juZi12JIKWHh9CREREz2bmc26QCMA3RxLFjkKPsBwRERGJSGFjioEdHXD48h1cSs8VOw6B5YiIiEh0swLdAQBrePRIJ7AcERERiaxDS0sEtLHBr+fSkXK3QOw4TR7LERERkQ6Y1ccdKjWwLopHj8TGckRERKQDerpZo1OrZoiIScWdBzU/U5QaBssRERGRDhAEAbMC3VGiVCH8zxtix2nSWI6IiIh0xIte9nCzNcX3x5ORW1Qqdpwmi+WIiIhIR0gkAt4IdMeDYiU2n0gWO06TxXJERESkQ17u3BKOljKsj7qBghKl2HGaJJYjIiIiHWJkIMGsPu64l1+CrSdTxI7TJLEcERER6ZjRXVvBztwYa49eR1FpmdhxmhyWIyIiIh0jM5TijUB33HlQjG2nePSoobEcERER6aBx3ZxhY2aENUeuo1jJo0cNieWIiIhIB8mNpJjxnBtu5Rbhp9hUseM0KSxHREREOmpCdxc0NzHE6kOJKC1TiR2nyWA5IiIi0lGmxgaYHuCGtOxC7DidJnacJoPliIiISIdN6ukCS7khwg5dg5JHjxoEyxEREZEOM5cZYmpvV6TcK8DOs+lix2kSWI6IiIh03JTeCpgbGyDs0DWUqdRix2n0WI6IiIh0nKXcEFN6K3D9Tj5+PcejR/WN5YiIiEgPTO3tCjNjA3x94CqvPapnLEdERER6oLmpEaY+OnoUGcejR/WJ5YiIiEhPTAtwg4Xs4dEjjntUf1iOiIiI9ISl3BAzA92Rcq+Ao2bXI5YjIiIiPTKllwJWpkZYeeAqikr5zLX6wHJERESkR0yNDTAr0B0ZOUXYdipF7DiNEssRERGRngnq4QI7c2OEHUpEYQmPHmkbyxEREZGekRtJ8Wa/1sjKK8b3J5LEjtPosBwRERHpobF+rdCymRzfHE5EXrFS7DiNCssRERGRHjI2kOKtfq1xv6AUG4/dEDtOo8JyREREpKdG+TpBYW2C/xy9jnv5JWLHaTRYjoiIiPSUoVSCf77ogQfFSoQdvCZ2nEaD5YiIiEiPDe7oAG8nS3x/Igk37xWIHadRYDkiIiLSYxKJgA8GtkNpmRor9l0WO06jwHJERESk53q526CPhy0i49JxIS1H7Dh6j+WIiIioEZj3UjsIArD0twSxo+g9liMiIqJGwNPBAiN8WuLYtSwcvXJH7Dh6jeWIiIiokfjnix4wMpBg6W8JUKnUYsfRWyxHREREjUTLZnJM6aXApYxcRJ5NEzuO3mI5IiIiakRm93GHhcwAK/ZeQVEpH0r7LFiOiIiIGpFmJkZ4s19rpGUXYuOffKzIs2A5IiIiamQm91LAxdoE/3fwGjJzi8SOo3dYjoiIiBoZYwMpPhzkifySMny+lwND1hXLERERUSP0gpc9ere2xk+nU3E+lQND1gXLERERUSMkCAL+NcQLAoBPfr0ItZq39tcWyxEREVEj1a6FBcZ1c0Z00n3sPp8hdhy9wXJERETUiP3jhbYwlxlgyZ4E3tpfSyxHREREjZi1mTHe7t8GadmFWHf0uthx9ALLERERUSM3qacCbram+L9D13DzXoHYcXQeyxEREVEjZ2QgQejwDihWqrBo10Wx4+g8liMiIqImoHdrGwzt5Ig/4jPxx6XbYsfRaSxHRERETcRHgz1hZmyAhbsuorCEF2c/DssRERFRE2FvIcM7z7dB6v1CrD58Tew4OovliIiIqAmZ0kuBdi3MsfbIddzIyhc7jk5iOSIiImpCDKQShL7cASVlKnwceYEjZ9eA5YiIiKiJ8VNY4RVfJ0RdzcLOs+lix9E5LEdERERN0IJBnrAyNcKiXZdwL79E7Dg6heWIiIioCbIyNULIUC/cyy9B6K+XxI6jU1iOiIiImqhhnRzRr50ddpxJw+HLmWLH0RksR0RERE2UIAgIfbkDTI2k+HDHBeQXK8WOpBP0ohwplUqEhobC1dUVMpkMnp6eWL169VPXu3//Pr788kv069cPLVq0gJmZGTp16oRly5ahqKioAZITERHptpbN5Jg3sB3Ssgvx+d7LYsfRCXpRjmbNmoWQkBAMGDAAYWFh6NixI+bMmYPPPvvsieudPHkS77//PmQyGebOnYsvv/wS3t7emD9/Pl588UWoVKoGegVERES6K6i7C7q6NMe3x5MQm3xf7DiiE9Q6PsBBXFwcfHx8MG/ePCxdurRi+tixY7Fz504kJyfDzs6uxnWTkpKgUqng5uZWZfrChQuxaNEiREZGYtiwYXXKc/r0afj6+iI2NhZdunSp+wsiIiLSQdcy8zDo6yg4WcmxJzgAMkOp2JG0qi6/v3X+yFFERAQAIDg4uMr04OBgFBUVITIy8rHrKhSKasUIAEaNGgUAuHSJV+cTEREBQGs7M/zzxba4ficfy35PEDuOqHS+HMXExMDJyQmOjo5Vpvv5+UEikSA2NrbO20xPfzjgla2trVYyEhERNQbTA9zgp2iO8D+T8Ne1LLHjiMZA7ABPk56eXq0YAYCRkRGsra2RlpZWp+2pVCosWbIEpqamTzyllpGRgYyMjGrT4+Pj67Q/IiIifSGVCFgxuhMGfh2F9346h9/eCYCFzFDsWA1O58tRYWEhrKysapwnk8lQWFhYp+199NFHOHLkCMLCwp545Gjt2rVYtGhRnbZNRESk71ysTfHRYC8s2HEen+y6hBWjO4kdqcHpfDmSy+UoLi6ucV5RURHkcnmttxUWFoYlS5Zg9uzZmDNnzhOXnTlzZo1HluLj4xEUFFTrfRIREembcd1aYd+lW/gpNhUvetnjxfYtxI7UoHS+HDk6OtZ4KqukpAR3796t8ZRbTTZt2oTg4GBMmDABYWFhT13ewcEBDg4Odc5LRESk7wRBwLJR3njx30cx/5fz8HFuDltzY7FjNRidvyDb19cXqamp1a4tio6Ohkqlgq+v71O3sX37dkybNg1Dhw7Fpk2bIAhCfcUlIiJqFOwtZPh0RAfczS/BPyLioFLp9Mg/WqXz5WjMmDEAgFWrVlWZvnLlSshkMgwfPhwAUFBQgISEBGRlVb26fufOnQgKCkLfvn0REREBAwOdP1hGRESkE4Z4O+JVv1aIupqFdVHXxY7TYHS+Kfj4+GDq1KlYvnw5cnJy0LVrV+zbtw8REREIDQ2Fvb09AODUqVPo27cvQkJCsHDhQgAPjy6NGTMGcrkco0ePxo8//lhl297e3vD29m7ol0RERKQ3Qoa2R0zyfazYexndXK3Qxbm52JHqnc6XIwBYs2YNnJ2dER4ejo0bN0KhUGDVqlVPvaj64sWLKC4uRnFxMd54441q80NCQliOiIiInkBuJEXYeB8MD/sTwT+cwe7gAFjKG/ft/Tr/+BBdw8eHEBFRU7T5RDI++u8FDO7ogLDxPnp3/W6jenwIERERiW9Cd2cM7NACu89nYMvJFLHj1CuWIyIiInoqQRCwdKQ3nJrL8cmuS4i7mS12pHrDckRERES1YmliiDVBvhAEYNbmWGTl1TxIs75jOSIiIqJa69DSEp+O6IiMnCK8tfUMlGUqsSNpHcsRERER1ckrvk6Y2MMFx6/fxfK9l8WOo3UsR0RERFRn/xrihS7OzbDu6HX8ei5d7DhaxXJEREREdWZkIME3Qb6wMTPG+z+dw6X0XLEjaQ3LERERET0TewsZ1gR1gbJMjWnfRiMzt0jsSFrBckRERETPrKvCCsteeXiB9vTvYlBYUiZ2JI2xHBEREZFGRvg4Ibhfa5xLzcG72+OgUun3wzdYjoiIiEhj777QFkO8HfD7xVv4fJ9+38HGckREREQaEwQBK0Z3go9zM3xzOBHbo/X3ESMsR0RERKQVMkMp1k3sCqfmcizYcQH7L90WO9IzYTkiIiIirbE1N8b307qjmdwQc7aexsnrd8WOVGcsR0RERKRVrjam+HZqNxhJJZj+bQwupueIHalOWI6IiIhI6zq0tMS6Sb4oVqoweWM0ku/mix2p1liOiIiIqF70crfBynE+uJdfjKANJ3ErRz8GiWQ5IiIionrzUocWWDKyI27eK8Sr647rRUFiOSIiIqJ6NdbPGYtf7oCkuwUY958TOl+QWI6IiIio3gX1cEHoyx1wIysf4/5zArd1+DlsLEdERETUICb2cMEnw9s/LEjrdLcgsRwRERFRg5nUU4FPhrfH9ax8jF17HDfvFYgdqRqWIyIiImpQk3oqsPjlDki+V4BX1vyFy7ceiB2pCpYjIiIianBBPVyw8lUf3MsvwZi1x3E65b7YkSqwHBEREZEohnZyxPrJfihRqjDhPydx9ModsSMBYDkiIiIiEQW2tcXm6d1hZCDBtG+j8d8zaWJHYjkiIiIicfm6NEfEzJ6wMTPGO9vjEHbwKtRqtWh5WI6IiIhIdB4tzLFjdm94OljgQlouROxGMBBv10RERET/08JShoiZPWAolUAiEUTLwXJEREREOsNcZih2BJ5WIyIiIqqM5YiIiIioEpYjIiIiokpYjoiIiIgqYTkiIiIiqoTliIiIiKgSliMiIiKiSliOiIiIiCphOSIiIiKqhOWIiIiIqBKWIyIiIqJKWI6IiIiIKmE5IiIiIqrEQOwA+qawsBAAEB8fL3ISIiIiqq3y39vlv8efhOWojpKSkgAAQUFB4gYhIiKiOktKSkLv3r2fuIygVqvVDZSnUcjKysLevXuhUCggl8u1uu34+HgEBQVh8+bN8PT01Oq2Gxu+V3XD96v2+F7VHt+r2uN7VTf18X4VFhYiKSkJAwYMgI2NzROX5ZGjOrKxscGECRPqdR+enp7o0qVLve6jseB7VTd8v2qP71Xt8b2qPb5XdaPt9+tpR4zK8YJsIiIiokpYjoiIiIgqYTkiIiIiqoTliIiIiKgSliMd4uDggJCQEDg4OIgdRefxvaobvl+1x/eq9vhe1R7fq7oR+/3irfxERERElfDIEREREVElLEdERERElbAcEREREVXCckRERERUCcuRDnvjjTfg4+MDKysryOVyeHh44B//+Afu3LkjdjSdcv/+fXz55Zfo168fWrRoATMzM3Tq1AnLli1DUVGR2PF00vbt2zFp0iS0a9cOEokECoVC7EiiUyqVCA0NhaurK2QyGTw9PbF69WqxY+mcvLw8hISEYNCgQbC1tYUgCFi4cKHYsXRSbGws3nnnHXh7e8Pc3BwtWrTA888/j4MHD4odTeecPn0ao0aNgpubG0xMTGBlZYUePXrg+++/hxj3jfHZajosOjoagYGBFT8sly5dwvr16xEZGYkzZ87AwsJC7Ig64eTJk3j//ffx4osvYu7cubCwsEBUVBTmz5+P3bt34/Dhw5BI+HdAZd988w1iYmLg6+uLnJwcsePohFmzZmHDhg2YMWMGunbtin379mHOnDnIzs7GggULxI6nM7KysvDJJ5/AyckJPj4+2L9/v9iRdNbnn3+OAwcOYNSoUXjzzTeRl5eHTZs2oX///li3bh1ef/11sSPqjOvXr6OwsBCTJ0+Go6MjioqK8Pvvv2PSpEk4e/YsVqxY0bCB1KRXfvzxRzUA9fr168WOojNu3LihTkxMrDY9JCREDUAdGRkpQirdlpKSolYqlWq1Wq0ODAxUu7i4iBtIZGfOnFEDUM+bN6/K9DFjxqhlMpn69u3bIiXTPUVFReq0tDS1Wv3w3x4AdUhIiLihdNSff/6pLiwsrDKtsLBQ7eHhobaxsVGXlZWJlEx/DB48WG1kZKQuKCho0P3yz2k9U376Izs7W9QcukShUMDNza3a9FGjRgEALl261NCRdF6rVq0glUrFjqEzIiIiAADBwcFVpgcHB6OoqAiRkZFixNJJxsbGcHR0FDuGXujVqxdkMlmVaTKZDIMHD0ZWVhYyMzNFSqY/FAoFSkpKUFBQ0KD75Wk1HadUKpGdnY3S0lJcuXIFH3zwAQRBQP/+/cWOpvPS09MBALa2tiInIV0XExMDJyenar/0/fz8IJFIEBsby1MgpDXp6ekwNDSEpaWl2FF0Tn5+PgoLC5Gbm4vDhw8jPDwcPj4+sLa2btAcLEc6LiYmBj179qz4vlWrVtiyZQs6d+4sXig9oFKpsGTJEpiammLYsGFixyEdl56eXuPRECMjI1hbWyMtLU2EVNQYxcfH45dffsGIESMgl8vFjqNz/vnPf2Lt2rUV3/fr1w8bNmxo8BwsRw1ArVajuLi4VssaGBjAwOB//1m8vLywf/9+FBYWIi4uDjt27EBubm59RRWdJu9VZR999BGOHDmCsLCwRn3kSFvvV1NXWFgIKyurGufJZDIUFhY2cCJqjHJycjBq1CiYmpo2/AXGeuKdd97BK6+8gszMTOzZswcZGRnIz89v+CANeoVTE3X8+HE1gFp9PO3CxtOnT6ulUql648aNDRO+gWnjvVq1apUagHr27NkNG14E2ni/eEG2Wt2+fXt1t27dapxna2urHjJkSAMn0g+8ILv2CgoK1AEBAWq5XK4+cuSI2HH0xj/+8Q+1lZWV+s6dOw26X/4Z2QDc3d0RHh5eq2WfdrrMx8cHnp6eWL9+PV577TUtpNMtmr5XmzZtQnBwMCZMmICwsDAtp9M92vzZasocHR0RHx9fbXpJSQnu3r3LC5BJIyUlJRgxYgROnDiBHTt24LnnnhM7kt4YP348vvzyS+zYsaNBr/tjOWoAtra2mDJlita2V1RUhLKyMq1tT5do8l5t374d06ZNw9ChQ7Fp0yYIgqDdcDpI2z9bTZWvry/279+PtLQ0tGzZsmJ6dHQ0VCoVfH19RUxH+kypVGLMmDHYv38/tmzZgsGDB4sdSa+UD+R7//79Bt0vb+XXUffu3auxAO3fvx+JiYno1q2bCKl0186dOxEUFIS+ffsiIiKC19ZQnYwZMwYAsGrVqirTV65cCZlMhuHDh4sRi/ScSqXCpEmTEBkZiTVr1uDVV18VO5LOetywBmvWrAGABv+dx98gOmrnzp0ICQnBqFGj4O7uDrVajdOnT2PLli2wtbVFSEiI2BF1RnR0NMaMGQO5XI7Ro0fjxx9/rDLf29sb3t7eIqXTTUePHsXRo0cBAMnJycjJycHixYsBAC4uLpg4caKY8Rqcj48Ppk6diuXLlyMnJ6dihOyIiAiEhobC3t5e7Ig6JSwsDNnZ2RXjrR09erTi52fYsGH89/bI3Llz8cMPPyAwMBByuRybN2+uMn/EiBEwNTUVKZ1uGTt2LKRSKfz9/eHk5ISsrCxERkbixIkTGD16NPr06dOwgRr0CieqtQsXLqiDgoLU7u7uahMTE7WRkZG6TZs26jfffLNidFp6KDw8XKOL3Jui8tHDa/oIDAwUO54oSkpK1AsXLlS7uLiojYyM1G3btlWvWrVKrVKpxI6mc1xcXB778xMeHi52PJ0RGBj4xP833bhxQ+yIOmPjxo3q/v37q+3t7dUGBgZqCwsLda9evdTffPNNxWj+DUlQq0V4ohsRERGRjuI1R0RERESVsBwRERERVcJyRERERFQJyxERERFRJSxHRERERJWwHBERERFVwnJEREREVAnLEREREVElLEdERERElbAcERE9kpCQgDFjxsDa2hoWFhYYMmQIkpOTxY5FRA2Mjw8hIgJw4MABDB06FLa2tnjllVeQnp6O7du3o02bNjh//jyMjIzEjkhEDcRA7ABERGK7efMmRo0ahc6dO2Pv3r0wNzcHADg6OuLLL79EZGQkRo8eLXJKImooPK1GRE3ee++9h4KCAmzevLmiGAHA2LFjAQB//fWXWNGISAQsR0TUpCUlJeHHH3/EyJEj4ebmVmWelZUVACAzM1OMaEQkEpYjImrStm/fDpVKhfHjx1ebV1xcDAAwNjZu6FhEJCJec0RETdq+ffsAAFFRUTh9+nSVeampqQAeXntERE0HyxERNVlqtRqnTp0CAKxYseKxy7Vr166hIhGRDuBpNSJqslJTU5GXl4dJkyZBrVZX+yg/1dazZ0+RkxJRQ2I5IqImKyMjAwDg4OBQbZ5KpcKBAwfg5uYGd3f3ho5GRCJiOSKiJqu0tBQAahzg8cCBA7h9+3aNF2oTUePGckRETZatrS2Amm/V/+yzz2BiYoK33nqroWMRkchYjoioyWrdujXs7Oywc+dO5OXlVUz/9NNPcfjwYXz66aews7MTMSERiYHPViOiJm3ZsmX44IMP0KFDBwwaNAinT5/GH3/8gRkzZmDNmjUQBEHsiETUwFiOiKhJU6vV+Oyzz7BmzRpkZWXBy8sLb7/9NiZNmiR2NCISCcsRERERUSW85oiIiIioEpYjIiIiokpYjoiIiIgqYTkiIiIiqoTliIiIiKgSliMiIiKiSliOiIiIiCphOSIiIiKqhOWIiIiIqBKWIyIiIqJKWI6IiIiIKmE5IiIiIqrk/wHxory7/67rYgAAAABJRU5ErkJggg==", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "a1,b1,c1 = params['a_inep'].iloc[0],params['b_inep'].iloc[0],0 # os parâmetros do primeiro item\n", "ax = sns.lineplot(x=theta,y=1-P(theta,a1,b1,c1), label=f\"$1-P_{1}$\");\n", "ax.set_xlabel(r\"$\\theta$\");ax.set_ylabel(r\"$\\mathrm{prob}(x_1=0|\\theta)$\");" ] }, { "cell_type": "markdown", "id": "11cee108-dc71-45f2-8643-10dc913350a3", "metadata": {}, "source": [ "Não dá, ainda, para dizer muito sobre a provável habilidade. No método de \"máxima verossimilhança\" (ML, da sigla em inglês), com somente a informação sobre o erro na primeira questão, a única coisa para dizer é que é mais provável que a habilidade é baixa. Veremos abaixo que no método Bayesiano, que leva em conta mais informação do que somente os acertos às questões, poderíamos dizer um pouco mais. Vamos à próxima questão, era um acerto: $x_2 =1$. Agora a probabilidade desta padrão de resposta é\n", "\n", "$$\\text{prob}(x_1 = 0, x_2 = 0|\\theta) = (1-P_1(\\theta))(P_2(\\theta))$$\n", "\n", "e podemos novamente fazer um gráfico da probabilidade desta \"padrão de resposta\" de agora duas respostas:" ] }, { "cell_type": "code", "execution_count": 11, "id": "4b6ad325-7784-49c1-a093-1eac2dce120c", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "a2,b2,c2 = params['a_inep'].iloc[1],params['b_inep'].iloc[1],0 # os parâmetros do segundo item\n", "ax = sns.lineplot(x=theta,y=(1-P(theta,a1,b1,c1))*P(theta,a2,b2,c2), label=f\"$(1-P_{1})*P_2$\");\n", "ax.set_xlabel(r\"$\\theta$\");ax.set_ylabel(r\"$\\mathrm{prob}(x_1=0,x_2=1|\\theta$)\");" ] }, { "cell_type": "markdown", "id": "3ac546c6-b781-48df-9fa1-c525aa758d82", "metadata": {}, "source": [ "Vemos que com duas repostas, um erro e outro acerto, já podemos fazer inferências com um pouco mais de confiança. O método de máxima verossimilhança agora estima uma habilidade próximo de 2. Vamos, para finalizar o exemplo, analisar o padrão de resposta $\\{0,1,1,0\\}$. " ] }, { "cell_type": "code", "execution_count": 12, "id": "c1414486-bdbe-4e8d-8bc4-14d4bcd8a8b2", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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dilp+fj6ysrIwYMAAvd739OnTGD58OMzMmv4BoI0u8eXm5uLKlSvNShr0FceCBQtgZWWFPn36wNXVFY899pjOMai0h/dRaWkpFi9ejNWrVzdYT1/vI/rT4Ut5qFEKeLSZG8+G9HWGmViEgxdvtVJkZOqaNYIWEBAAf39/7NixA1OmTIGNjU29dceMGYM5c+YAqE3stm/fjsWLF6OiogLvvfeeblEToXZe0aRJkxAfH1/n2rp161BcXIzi4mIAwM8//4xly5YBAJ544ok6O83ri2rekD4TtOzsbFy8eBHz58/X+V4tje/u3buYOXMmZs+ejT59+jTeQM9xrF+/HrGxsTh58iSOHj3arNMFGtPQ+wgwzHupua/Pe++9hzlz5mgcU/Ugfb6P6E8/puRCLAIe6evcrHZdrCQI9LHH8av5kFfVNGv0jTqGZiVo33//vdYJwo3x9/eHv78/3nvvPS7vJr168cUX8eijjyI5OVljLs9HH32EjIwM9fdHjhzBkSNHAAAeHh4mlaDFxcVBKpVixowZOt+rJfEplUo899xzkEgkdbaxacs4zMzMMHr0aOzcuRMbNmxAVFSUXmIB6n8fAYZ5LzXn9UlOTsaPP/6IpKSkBuvp831EtZRKAb9eLcBD7p1bNI8sqLcTTqQV4ExGIcb0atr8Neo4mvWIsyXJ2f2cnJy4cz7pVUhICAYPHoz169drlKuO29L2pY95ZvV58803IQgCxowZo5f7KZVKbNy4EfPnz0fnzp11vl9z4xMEAXPmzEFubi6+/vprWFhY6BxDS+K4X3V1NdLS0vQSh0p97yPAMO+l5rw+R48eRXp6Ojw9PdG1a1d89NFH+Prrr9V7MwL6fx9RrT9ySlEiv4uRPVu26GLUvXa/XM1vpCZ1RM1eJFBdXY29e/fixIkTyMvLUx+F0qdPH4wYMYJ761CbEolEWL58OSZNmoTFixc3+IjH2FRXV6O6uho1NTWoqamBQqGosyfWV199hZycHCxatMggMc6fPx8pKSn48ccf6+wb2Bby8vJw+PBhTJo0CZaWlvjxxx/xxRdf6P08SVN+H82bN09ja6CPPvoI6enp2LBhg7rM0O+j9upEWm1iNbKHQ4va93O1hZ2VBX5lgkZaNCtBu3HjBkJDQ3HliuZBr/dv4tq9e3fMnDkTCxcu5FJuahPjx483ycUny5Ytw/vvv6/+fufOnXX2xAoLC1MfF9bWMjIysGnTJkilUnTt2lVdvmnTJsycObNNYhCJRNiwYQNefvllKJVKeHl54eOPP9Y42UNfTPV9ZGVlBSsrK/X3nTp1gkwm0zi/05Dvo/bsRFoBLMxEGOLVvBMdVMRiEUb2dMT+CzkoKq+CnbVEzxGSKWvWI87IyEhcuXIFr732GhISEpCamorff/8dEREREAQBzz77LO7cuYN//OMf8PHxqXP+JBH9acmSJXUemdW3+a0heHl5QRAEKBQK3LlzR/3VVskZUDst4tixYyguLkZpaSkuXLiAF198sc36N0VLlizRukkt6dfdGiVOXS+Ev6edThP8R/d0hCAAJ68V6DE6ag+alaD9/PPPeOaZZ/DRRx9h6NCh6NGjB/r16wcPDw+IRCLs3LkT2dnZOHjwIIYMGYK//vWvWLBgQWvFTkREZBDnM0tQUVWDEd1b9nhTRfV49GQaEzTS1KwEzcLCAm5ubg3WEYlEGD9+PI4cOYJ//OMf2LRpE3bt2qVTkERERMbkbEbtqQzDfFr2eFPF094KTjZSnMnQ30kW1D40K0F7+OGH8dVXX6G8vLxJ9d999108/PDD+Pjjj1sSGxERkVE6e6MIYhEwqFsXne4jEokwxMsOl2+VokxxVz/BUbvQrARt6dKlyMvLw4QJEzT2BWpIQEAA/vjjjxYFR0REZGwEQcDZG0Xo7WKDTlKdjrQGAAR42UEpAMk3i3UPjtqNZiVovr6+2LdvH37//Xf4+vpi5syZ+O677+odUauoqMD+/fu5mtMA7l9ZS0TUEvx3RLvsEgVySysx2MtOL/cb4l37mPRMOh9z0p+anfo/8sgjuHDhAt58803s2bMHu3fvVl+LiIhA165dIZFIkJeXh3379iEnJ0d9LAq1HZFIBLFYjOrqap67R0TNcvfuXfXB9FRX4r35YoM99ZOg9XO1hdRcrL4vEdCCBA2oPd5k9+7dyMjIwO7du3Ho0CGcOnUKO3bs0Kjn7OyMf/7zn3j77bf1ESs1g0gkglQqRVlZmV7PLSSi9q+kpASdOnViglaPs+oErYte7icxF2NQty5IulGEGqUAMzFfd2phgqbi5eWF6OhoREdHAwAyMzORk5ODu3fvwsnJCT179uRfcANydnbGzZs3IZVKNTayJCLS5u7duygpKUFxcTE8PT0NHY7RSr5ZjC5WFvBxtNbbPf09u+DU9UKk3b6D3i42ersvmS7dZzfex8PDw6SOSGnvrKys4OTkhFu3bqG6utrQ4RCRkROJROjUqRM8PT0NcrSXKaiuUSIlpxTDfOz1OgAx0L0LAODczWImaARAzwkaGR97e3vY2dmpd6onItJGNeeMTz0advX2HVRWKzHAXb+Hzg/0qL3fhawSPD2km17vTaaJCVoHwH90iYj040JmCQDgIT0naB52lrCzssC5e/cnalaC5uPjo7cP+r/+9a+IiorSy72IiIjawu9ZrZOgiUQiDPTogpPXClBVrYTEvFm7YFE71KwELSgoSG8Jmre3t17uQ0RE1FYuZJWgs6UFPOz0P0dvkEdnHLtyG1dyy/T+CJVMT7MStAe30SAiIuooapQC/sgpRYCXXatMG3nIowsA4FxmMRM0at5JAkRERB1V2u07UNzV/wIBFdVj04vZpa1yfzItOi0SuHTpEo4fP460tDSUlNQ+l+/cuTN69OiBMWPGoE+fPnoJkoiIyNBScmoTp36utq1yfxdbKeysLNT9UMfWogQtKSkJkZGRSEhIqHfrBpFIhMDAQKxfvx5+fn66xEhERGRwl26VAQD6tlKCJhKJ0NfVFsk3i6FUChDzRIEOrdkJ2vnz5zFmzBgolUo8//zzCAkJQY8ePWBrW/uGLS0tRVpaGg4dOoQ9e/Zg9OjROHnyJB566CG9B09ERNRWLuWUwsJMpNcTBB7U19UWJ9IKkFFY0ar9kPFrdoK2aNEiSKVSHD9+HP369dNaZ9iwYXj22Wfx5ptvYvTo0Vi0aBH+97//6RwsERGRoVy+VYYeTp1gYdZ607dVo3MpOaVM0Dq4Zr/Lfv31V8yYMaPe5Ox+/fr1w4wZM3D8+PEWBadSXV2NpUuXwsfHBzKZDH379sX69eub3P7w4cMYNWqU+uijiIgI5Ofna60bFxcHf39/yGQyuLu74/XXX0d5eblGnfT0dMyYMQO9e/eGjY0NbG1t4e/vj9jYWFRVVdWpe/8O3fd/LVu2rPkvBhERtbkS+V1klyjQp2vrHsPU17X2/pyHRs0eQaupqWnW8mKRSASlUtncbjTMnz8fW7duxbx58zBkyBDEx8cjMjISxcXFWLRoUYNtjx07htDQUPj5+WH16tXIzc3FqlWrkJiYiISEBMhkMnXdXbt2ITw8HCEhIYiNjUVqaio+/vhjXLx4EQcPHlTXy8nJwa1btxAWFoZu3bqhpqYGv/76K1599VUcO3YMX331VZ04pk6dimnTpmmUcW4eEZFpuJJbO/+sTyvNP1Pp6dwJ5mIREzQChGYKCgoSHBwchNTU1EbrXr58WbC3txeCg4Ob241aUlKSAECIjo7WKA8LCxNkMpmQm5vbYHs/Pz/Bx8dHKC8vV5ft379fACCsXbtWXVZZWSm4uLgII0aMEGpqatTl69evFwAI+/btazTWyMhIAYBw9epVddn169cFAEJMTEyj7ZsqMTFRACAkJibq7Z5ERFS//55MF7yivxMOX2r4M0cfQtccE0b+86dW74faXnM+v5v9iHPx4sUoLi6Gv78/IiMj8fXXXyM5ORnXrl3DtWvXkJycjK+//hoLFixAQEAASktLERMT0+IEMi4uDgDqHAsVFRUFhUKBvXv31tv2ypUrSE5Oxty5c2FlZaUunzhxInr27Indu3ery44ePYrc3FwsXLgQYvGfL0tERASsra016tZHdTpCcXGx1utyuRwKhaLR+xARkXG5dG9Eq7UfcQK189CyiuUoqbjb6n2R8Wr2I86HH34Y//d//4f58+djw4YN2Lhxo9Z6giDAw8MDGzZsQHBwcIsDPHPmDDw8PODm5qZRPnToUIjFYiQmJuLFF1+sty0ABAYG1rkWGBiIb775BkqlEmKxuN66UqkUfn5+SExMrHMPuVyO8vJyVFRU4NSpU1i5ciVcXV3Rv3//OnVXrVqF999/H0Dt3LxFixZh5syZDf7sOTk5yMnJqVOekpLSYDsiItKvy7fKYCszR1dbWeOVddTX1QbfJgEpt0oxvLtDq/dHxqlF+6BNmjQJoaGhOHToEI4fP46rV6+itLT2twtbW1v07NkTY8aMQUhICCQSiU4BZmdn10nOAEAikcDBwQFZWVkNtgWgtb2bmxvkcjmKiorg4ODQaN1z587VKf/3v/+Nd955R/39kCFD8Mknn2jMaxOLxRg/fjymTJmCbt264ebNm1i3bh3Cw8NRUFDQ4IHxmzZtUid1RERkGIIg4HJuGfq62rbKEU8Pun8lJxO0jqvFJwlYWFjgsccew2OPPabPeOqQy+Wwt7fXek0mk0EulzfYFqgdBdPW9v46jdXV1s+zzz6LIUOGoKioCEeOHMG5c+fUiaqKp6cn4uPjNcrmzJkDf39/vPvuu3j++efVe8g96KWXXsITTzxRpzwlJQXh4eFa2xARkX5llyhQpqhuk8ebgGaCRh2XTkc9tQVLS0tUVlZqvaZQKGBpadlgWwBa26vmgqnq3F/3wXvW14+Xlxe8vLwAAE8//TRiY2Mxfvx4nDt3rsFjrqRSKaKiojB//nycPHkSoaGhWuu5urrC1dW13vsQEVHru3yrNlHybaMEzbGTFE42UvXJBdQxGf1h6W5uburHj/erqqpCQUGB1keS97cFoLV9dnY2LC0tYWdn16S6DfWjMmPGDFRVVeGzzz5rtK6npycAoKCgoNG6RERkOKpEqa1G0ACgt0snXM27A6VS+3GK1P4ZfYIWEBCAzMzMOnPNTp8+DaVSiYCAgAbbAkBCQkKdawkJCfDz81Ov2KyvbmVlJZKTkxvsR0U1KldUVNRo3bS0NACAk5NTo3WJiMhwrubeAQD0cmm7BK2Xsw0qqmqQVVz/NB5q34w+QQsLCwMAxMbGapSvXbsWMpkMkydPBgBUVFTg0qVLGicE+Pr6YtCgQdiyZQsqKirU5QcOHMDVq1cxffp0dVlwcDCcnZ2xbt06jY11t23bhvLyco26eXl5WmNVrWgdNmxYg3VLS0uxZs0adOnSBSNHjmz8RSAiIoNJu30HzjZS2Mos2qzPXi6dAABX8+60WZ9kXIx+Dpq/vz8iIiKwYsUKlJSUqE8SiIuLw9KlS+Hi4gIAOHXqFMaNG4eYmBgsWbJE3X7NmjUYP348goKCMGfOHOTl5WHVqlUYMGAA5s2bp64nlUqxcuVKzJ49GxMmTEBYWBhSU1OxZs0ahISEaEzWf/vtt5GSkoLx48fDy8sLJSUl+PHHH3Hw4EGMHDlSY/uM6OhoXLlyBePHj4e7uzuysrKwdetWZGVlYdu2bbC25llrRETGShAEpN0ux0Pundu0317OtaN1V3LLMK6Pc5v2TcbB6BM0oHZkytPTE9u3b8e2bdvg7e2N2NhYREZGNtp23Lhx+OGHH/Dee+/htddeg7W1NaZOnYoVK1bUmfg/a9YsSCQSLF++HAsXLoSdnR0WLFiAZcuWaSytnjZtGjZv3ozt27fj9u3bkEgk8PX1xfLly/Hqq6/CwuLP37IeffRRXL9+HRs2bEBhYSFsbGwwbNgw7NixA4888oj+XiQiItK7W6UK3KmsRk/nTm3ab+97I2ipHEHrsESCIOg8A3Hv3r3Yu3cvtm3bpvV70q+zZ88iICAAiYmJGDx4sKHDISJqt35JzUf41gS8/0R/zB7p3aZ9D/3gR7h1lmHvwtFt2i+1nuZ8futlDlpycjI+/fTTer8nIiIyRVfzaldwtvUIGgD0cu6E1Lw70MM4Cpkgo18kQEREZChXb9c+Yuzh1PYJWm8XruTsyJigERER1SMtrxydpOZwsa17ykxrU43acR5ax8QEjYiIqB5Xb99BD+dObXIG54N639t3LTWXJwp0REzQiIiItCiR38Xtskr0cDLMdki9VCNouRxB64iYoBEREWmRdm/+mSEWCACAnbUEjp2kuMJHnB0SEzQiIiItVLv49zTAAgGVXs6dcDW3jCs5OyAmaERERFqoRtB6GGgEDag98qm8qga3ShUGi4EMgwkaERGRFml5d2BhJoKXvZXBYujuWDv/7drtcoPFQIbBBI2IiEiLa7fL4WlvBXMzw31Udr/3ePXabc5D62j08q4TBEHj+fiD3xMREZmS6holbhRWwMfRcI83AaD7vRWkaRxB63D0kqAtWbIESqWy3u+JiIhMSVaxHNVKAT6Ohnu8CQBunS0hsxCr58NRx8FHnERERA+4ll87YmXoETSxWAQfx06cg9YBMUEjIiJ6QPq9BM3bwCNoQO1jzuwSOeRVNYYOhdoQEzQiIqIHXFePoBnmFIH79XC0hiD8GRN1DEzQiIiIHnA9vxyWFmZwsZEZOhT1PmzX8jkPrSNhgkZERPSA6/nl8HKwgljc9oekP6i7o2qrDY6gdSRtlqC98cYbKCkpaavuiIiIWqSyugbZxXKjeLwJAD5Oqs1qOYLWkZjr+4Y///yz1vJt27Zh1KhRcHR0xNixY/XdLRERkV7cLKyAUjCO+WcA0Elqjq62Mu6F1sHoPUELDg6GSCTSulHtU089BZFIhJoarkQhIiLjpHqU6G0kCRpQu5Lz3M1iCIIAkcjwj12p9en9EeeUKVPwyCOPID09HUqlUv3l4OCAzMxMJmdERGTU0guMZwWnSncna5RX1SCvrNLQoVAb0XuC9s0332D27NkICgrChg0b9H17IiKiVmVMW2yoqBYKpOVxHlpH0SqLBGbOnIkTJ07ghx9+QHBwMNLS0jgkS0REJuF6fjlspOZwsJYYOhQ11VYbadwLrcPQ+xw0FVdXV+zduxeffvopxo4dyxWcRERkEtLzK+DtaG1UAwvdHbmSs6PRaQStKQeiz549G2fOnEFcXBwcHR116Y6IiKhVVVRV41apwqgebwKAexdLSM3F3AutA9EpQZs0aRIqKioarefq6orJkydDIjGe4WIiIqIHpefXfqYZ0wpOQHVoujXSOILWYeiUoB06dAijR49GTk5Og/XS09N16YaIiKhNqBYIdDeyBA0Aejh1QlaxHIq73A2hI9ApQdu3bx/S0tIwfPhwXLhwoc71zMxMvPzyy/D19dWlGyIiojah2mLD2EbQAMDb0QqCANwobPzJFZk+nRK0iRMn4vjx41AqlRg9ejTi4+MBALm5uYiKikKvXr2wefNmDBo0SKcgq6ursXTpUvj4+EAmk6Fv375Yv359k9sfPnwYo0aNgpWVFZycnBAREYH8/HytdePi4uDv7w+ZTAZ3d3e8/vrrKC/XfOafnp6OGTNmoHfv3rCxsYGtrS38/f0RGxuLqqoqvcdPRERtQzXHy8fBCBO0ezFd50rODkHnVZwDBw5EQkIC/vKXv2DSpEl46qmnsG/fPlRUVCAwMBCLFy/GxIkTdepj/vz52Lp1K+bNm4chQ4YgPj4ekZGRKC4uxqJFixpse+zYMYSGhsLPzw+rV69Gbm4uVq1ahcTERCQkJEAmk6nr7tq1C+Hh4QgJCUFsbCxSU1Px8ccf4+LFizh48KC6Xk5ODm7duoWwsDB069YNNTU1+PXXX/Hqq6/i2LFj+Oqrr/QWPxERtZ30gnLYWVmgs5WFoUOpQ7VwIZ0JWscg6EFJSYnw9ttvCyKRSBCLxULXrl2F+Ph4fdxaSEpKEgAI0dHRGuVhYWGCTCYTcnNzG2zv5+cn+Pj4COXl5eqy/fv3CwCEtWvXqssqKysFFxcXYcSIEUJNTY26fP369QIAYd++fY3GGhkZKQAQrl69qrf4tUlMTBQACImJic1uS0RE9QtYekiYvO4XQ4eh1e0yheAV/Z3wt6/PGToUaqHmfH7r9IizqKgIMTEx8Pb2xkcffYQBAwZg3LhxyM3NVT/u1FVcXBwAICoqSqM8KioKCoUCe/furbftlStXkJycjLlz58LKykpdPnHiRPTs2RO7d+9Wlx09ehS5ublYuHAhxOI/X5aIiAhYW1tr1K2Pt7c3AKC4uFgv8RMRUdspr6xG/p1KeDlYNV7ZABysJbCRmvMRZweh0yNOLy8vlJeXo3fv3tiwYQPCwsIgCAIiIyOxatUqXL9+HTt37tR4jNhcZ86cgYeHB9zc3DTKhw4dCrFYjMTERLz44ov1tgWAwMDAOtcCAwPxzTffQKlUQiwW11tXKpXCz88PiYmJde4hl8tRXl6OiooKnDp1CitXroSrqyv69++vl/hzcnK0rpBNSUnRWp+IiFpONfney944EzSRSARvR2v1ViDUvumUoDk7O2Px4sUIDw9XjzqJRCJs2LAB3bt3x9/+9jcEBwdj3759cHZ2blEf2dnZdZIbAJBIJHBwcEBWVlaDbQFobe/m5ga5XI6ioiI4ODg0WvfcuXN1yv/973/jnXfeUX8/ZMgQfPLJJxoJqS7xb9q0Ce+//36914mISH8yCmoTH08jXCCg4u1ojQtZJZBX1cBSYmbocKgV6ZSgXb58GWZm2t8gb731Fnx8fDBr1iwMHz4c165da1Efcrkc9vb2Wq/JZDLI5fIG2wK1o2Da2t5fp7G62vp59tlnMWTIEBQVFeHIkSM4d+4cSktL9Rb/Sy+9hCeeeKJOeUpKCsLDw+ttR0REzXejsPbRobE+4gQAn3uxpReUo6+rrYGjodakU4JWX3Km8tRTT8Hd3R1TpkxpcR+WlpaorKzUek2hUMDS0rLBtgC0tlcoFBp17q/74D3r68fLywteXl4AgKeffhqxsbEYP348zp07hz59+ugcv6urK1xdXeu9TkRE+qMeQTPSR5zAn/uzZTBBa/d0WiTQFCNGjMBvv/3W4vZubm7qx4/3q6qqQkFBgdbHh/e3BaC1fXZ2NiwtLWFnZ9ekug31ozJjxgxUVVXhs88+00v8RETUdm4UVkBmIYazTd0nKcbCS70XGuehtXetnqABgI+PT4vbBgQEIDMzs85crdOnT0OpVCIgIKDBtgCQkJBQ51pCQgL8/PzUc+fqq1tZWYnk5OQG+1FRjcoVFRXpJX4iImo7Nwor4GlvBZFIZOhQ6sW90DqONknQdBEWFgYAiI2N1Shfu3YtZDIZJk+eDACoqKjApUuXNE4I8PX1xaBBg7BlyxaNQ90PHDiAq1evYvr06eqy4OBgODs7Y926dVAqlerybdu2oby8XKNuXl6e1lg3btwIABg2bFiz4yciIsOprlEiq0gOT3vjXSAAAHZWFrCVmeN6ARO09k7nkwRam7+/PyIiIrBixQqUlJSod+KPi4vD0qVL4eLiAgA4deoUxo0bh5iYGCxZskTdfs2aNRg/fjyCgoIwZ84c5OXlYdWqVRgwYADmzZunrieVSrFy5UrMnj0bEyZMQFhYGFJTU7FmzRqEhIRoTNZ/++23kZKSgvHjx8PLywslJSX48ccfcfDgQYwcORIzZ85sdvxERGQ42cUKVCsFo14gANTulODjaM0RtA7A6BM0oHZkytPTE9u3b8e2bdvg7e2N2NhYREZGNtp23Lhx+OGHH/Dee+/htddeg7W1NaZOnYoVK1bUmaA/a9YsSCQSLF++HAsXLoSdnR0WLFiAZcuWaQx5T5s2DZs3b8b27dtx+/ZtSCQS+Pr6Yvny5Xj11VdhYaF5RIgu8RMRUevLMIEVnCrejtY4l1mC8spqWEtN4mOcWkAkCIJg6CCoec6ePYuAgAAkJiZi8ODBhg6HiMjk7fwtA3//v9+x44WhCPZt2b6dbWXNoSv490+p+D5qNPq7dTZ0ONQMzfn8btU5aGZmZpBIJJgxY4Z6p34iIiJjoz5FwIg3qVX5c6EAV3K2Z62aoHXr1g1ubm6Ii4tDYGAgxo4d25rdERERtUhGQTnEIsC9S/17UxoL1V5o6Vwo0K616sPr9PR0AEBZWRlOnDiBEydOtGZ3RERELZJRUAG3LpaQmBv95gbwUe+FxgStPWuT2YU2NjYIDQ1FaGhoW3RHRETUZIIg4EZhBfw9uxg6lCbpbGUBOysLruRs54z/VwUiIqJWlH+nChVVNUa/B9r9vB2t+YiznWv1BK2wsBA3btxo7W6IiIhaRLVAwJjP4HyQj4M18u9UoUxx19ChUCtp9QTtjTfeQPfu3Vu7GyIioha5YUJ7oKn8eWg6V3K2V23yiJNbrRERkbFSJTmmNIKmStC4UKD9avYigfvPqWwKJmdERGTMbhSo9kAzoQTtXqxcKNB+NTtBe/AYIyIiIlOWUVgBe2sJbGSm8/mmHkHjQoF2q0XbbHTp0gUDBw5sUt1Lly4hLy+vJd0QERG1uoyCCpN6vAkAtjILOFhLOILWjjU7QevduzcqKytx5MiRJtV/4YUX8N///rfZgREREbW28spq5N+pxKieDoYOpdm8Ha05B60da/YigaFDhyIjIwOFhYWtEQ8REVGbUZ/BaWIjaADg7WCNwvIqlMi51UZ71OwEbciQIRAEAadPn25S/T59+vAMTiIiMkrqFZwmcEj6g3wcuVCgPWt2ghYVFQWlUtnkY5uio6Ob/DiUiIioLZniHmgqPDS9feNRT0RE1GGpRtBM9REnwL3Q2ismaERE1GHdKKyAzEIMJxupoUNpNh+eJtCuMUEjIqIO60Zh7RYbIpHI0KE0m7XUHE42Uo6gtVNM0IiIqEOqrlEiq0gOT3vTWyCg4uNgzTlo7RQTNCIi6pCyixWoVgomuUBAxcvBCsUVd1FcUWXoUEjPmKAREVGHlGHCKzhVeGh6+6WXBG3v3r2IiIio93siIiJjo94DzQRXcKr4cKuNdksvCVpycjI+/fTTer8nIiIyNupTBExwk1oV1VYb6flcydne8BEnERF1SBkF5RCLAPculoYOpcW8VacJcASt3WGCRkREHVJGQQXculhCYm66H4VWEnM420h53FM7ZLrvSiIiohYSBAE3CitMeoGAirejNa7nl0MQBEOHQnrEBI2IiDqcgvIqVFTVmPQCARUfB2uUKqpRVHHX0KGQHjFBIyKiDufPFZymu0BAhYemt08mkaBVV1dj6dKl8PHxgUwmQ9++fbF+/fomtz98+DBGjRoFKysrODk5ISIiAvn5+VrrxsXFwd/fHzKZDO7u7nj99ddRXq75pr9y5QoWLVqEIUOGoEuXLnBwcMCoUaPw1Vdf1blfeno6RCKR1q9ly5Y174UgIiK9uNEO9kBT8VEtFOA8tHbF3NABNMX8+fOxdetWzJs3D0OGDEF8fDwiIyNRXFyMRYsWNdj22LFjCA0NhZ+fH1avXo3c3FysWrUKiYmJSEhIgEwmU9fdtWsXwsPDERISgtjYWKSmpuLjjz/GxYsXcfDgQXW9bdu2Yf369ZgyZQoiIiJQU1ODL7/8Ek8//TQWLVqEDz74oE4cU6dOxbRp0zTK/Pz8dHthiIioRdrDHmgqXuqtNpigtSuCHixZskQQi8X1fq+LpKQkAYAQHR2tUR4WFibIZDIhNze3wfZ+fn6Cj4+PUF5eri7bv3+/AEBYu3atuqyyslJwcXERRowYIdTU1KjL169fLwAQ9u3bpy47c+aMUFJSotGPUqkUgoODBXNzc6GgoEBdfv36dQGAEBMT06yfuyGJiYkCACExMVFv9yQi6khe25MkeEV/J5TIqwwdis4qKqsFr+jvhIWfnzV0KNSI5nx+G/0jzri4OABAVFSURnlUVBQUCgX27t1bb9srV64gOTkZc+fOhZXVn78lTZw4ET179sTu3bvVZUePHkVubi4WLlwIsfjPlyUiIgLW1tYadQMCAmBra6vRl0gkwrRp01BdXY0rV65ojUcul0OhUDThpyYiotZ0o6ACdlYWsJVZGDoUnVlKzNDVVsYRtHZGLwmaIAgay3sf/F4XZ86cgYeHB9zc3DTKhw4dCrFYjMTExAbbAkBgYGCda4GBgUhKSoJSqWywrlQqhZ+fX4P9qGRnZwMAnJyc6lxbtWoVrKysYGlpif79+2PXrl2N3i8nJwdnz56t85WSktJoWyIiql9GYQU8TfgEgQd5O1ohvYBbbbQneknQlixZok50tH2vi+zs7DrJGQBIJBI4ODggKyurwbYAtLZ3c3ODXC5HUVFRk+o21A8A5OXl4ZNPPsGwYcPQo0cPdblYLMb48ePxr3/9C/v27cN//vMfCIKA8PBwrF27tsF7btq0CQEBAXW+wsPDG2xHRET1k1fV4HZZJbzawfwzFR9Ha5QpqlFYXmXoUEhPjH6RgFwuh729vdZrMpkMcrm8wbZA7SiYtrb312msbkP93L17F2FhYSgrK8OGDRs0rnl6eiI+Pl6jbM6cOfD398e7776L559/vs7jUpWXXnoJTzzxRJ3ylJQUJmlERC305xmc7SdBUy8UKCiHQ6e6n2Nkeow+QbO0tERlZaXWawqFApaW9Z+hprqmrb1qLpiqzv11H7xnQ/0olUqEh4fj+PHj+PzzzzF48OBGfqLaJDAqKgrz58/HyZMnERoaqrWeq6srXF1dG70fERE1Xca9/cK6taMRNNWh6dfzKxDgpX1Qg0yL0S8ScHNzUz9+vF9VVRUKCgq0PpK8vy0Are2zs7NhaWkJOzu7JtXV1o8gCJg7dy7i4uKwfv16TJ8+vWk/FGpH1gCgoKCgyW2IiEh36hG0dpSg+Thyq432xugTtICAAGRmZtaZA3b69GkolUoEBAQ02BYAEhIS6lxLSEiAn5+fesVmfXUrKyuRnJystZ9XXnkF27dvx4oVK/DSSy816+dKS0sDoH1BARERtZ4/H3G2n0UCqse113maQLth9AlaWFgYACA2NlajfO3atZDJZJg8eTIAoKKiApcuXdI4IcDX1xeDBg3Cli1bUFFRoS4/cOAArl69qjHiFRwcDGdnZ6xbt05jgcO2bdtQXl5eZ3QsOjoa//nPf/Duu+/irbfeqjf+vLy8OmWlpaVYs2YNunTpgpEjRzblZSAiIj3JKKiA1FwMZ5v2M1dLZmEGt84y9eNbMn1tMgetsLAQmZmZ6NevH8zNm9elv78/IiIisGLFCpSUlKhPEoiLi8PSpUvh4uICADh16hTGjRuHmJgYLFmyRN1+zZo1GD9+PIKCgjBnzhzk5eVh1apVGDBgAObNm6euJ5VKsXLlSsyePRsTJkxAWFgYUlNTsWbNGoSEhGhM1l+7di1WrFiBfv36oU+fPti5c6dGzOPHj1fHFR0djStXrmD8+PFwd3dHVlYWtm7diqysLGzbtg3W1u3nNzgiIlNwo7AC3eytIBaLDB2KXnk5WONCVgkEQYBI1L5+to5I7wlaRkaGOrlZtmwZ+vfvj0mTJqG8vBze3t44dOiQxjYUTbFx40Z4enpi+/bt2LZtG7y9vREbG4vIyMhG244bNw4//PAD3nvvPbz22muwtrbG1KlTsWLFijoT/2fNmgWJRILly5dj4cKFsLOzw4IFC7Bs2TKNN/vZs2cBAH/88Qeee+65On0eOXJEnaA9+uijuH79OjZs2IDCwkLY2Nhg2LBh2LFjBx555JFmvQ5ERKSbGqWAzKIKjO3V/qaXeDta4+S1AuTfqYJTOxod7KhEgp53tXv66afh6ekJMzMz/Pvf/8aSJUswd+5c3L17F5GRkbCysmrSJq1Uv7NnzyIgIACJiYlNWjVKRES1MosqMPpfR/DCKG/E/KW/ocPRq80/p+HD/Zfw5csjMNSbKzmNUXM+v/U+gnb8+HGkp6dDqVTio48+wpw5c9QT4WNjYzFixAh9d0lERNQkNwra3wpOlT+32ihngtYO6D1BUygU6k1gbW1t4ezsrL7m4eGB4uJifXdJRETUJBn3VnB6tqNNalVUW21woUD7oPdVnPb29igrKwOAOrvq5+fnc1I8EREZjGqLDU/79vdZ1M3eCiIRkJ5f0XhlMnp6T9BmzJiBnJwcAMCzzz6rce3LL79scN8yIiKi1nSjoAIiEdDNvv5TaExV7VYblrjOzWrbBZ0SNG0Hoi9btgy9e/fWWv/FF1/Evn37dOmSiIioxTIKy+FqK4PU3MzQobQKb0crpBeUQ8/r/8gAdErQJk2apLEBbGPMzc1hZtY+/1IQEZFxEwQBGQUV7eoMzgd5O1ijoqoGt8u0n2FNpkOnBO3QoUMYPXq0+pFmfdLT03XphoiISGcl8rsoU1Srj0Vqj9RnchZwHpqp0ylB27dvH9LS0jB8+HBcuHChzvXMzEy8/PLL8PX11aUbIiIinWUUtL8zOB+k+tl4aLrp0ylBmzhxIo4fPw6lUonRo0cjPj4eAJCbm4uoqCj06tULmzdvxqBBg/QSLBERUUupt9hox484fRx5aHp7ofMqzoEDByIhIQE9e/bEpEmTMGPGDPTo0QPr1q2Dn58fvv/+e5w6dUofsRIREbXYjXtJS3tO0LrZW0Es4ghae6CXbTY6deqEkJAQVFdXY8+ePbCxscHBgwdx8uRJTJw4UR9dEBER6US1B1p7noMmNTeDWxdutdEe6JSgFRUVISYmBt7e3vjoo48wYMAAjBs3Drm5uerHnURERMYgo6ACtjJzdLGSGDqUVuXjaI2MggputWHidDrqycvLC+Xl5ejduzc2bNiAsLAwCIKAyMhIrFq1CtevX8fOnTvVRz8REREZyo3Cina9QEDFy8EKx1PzkVdWCRdbfv6aKp1G0JydnbF9+3ZcvHgR06dPh0gkglgsxoYNG/Cvf/0L3377LYKDg5GXl6eveImIiJpNcbcGt0oV7Xr+mcr9h6aT6dJpBO3y5cv1bjz71ltvwcfHB7NmzcLw4cNx7do1XboiIiJqscwiOQShfR6S/iD1Xmj55Rje3cHA0VBL6TSC1tipAE899RR++uknlJcziyciIsO5UVj7OeTVEUbQ7iVo3GrDtOn9sPQHjRgxAr/99ltrd0NERFQv1Sa1HWEErZsdt9poD1o9QQMAHx+ftuiGiIhIqxsdYJNaFYm5GB52VuqklExTmyRoREREhnSjoAIWZiK4drY0dChtwsvBCukF5VAqudWGqWKCRkRE7V5GYQW62VnBTCwydChtwsfRGoq7SuSWKQwdCrUQEzQiImrXlEoBNworOsT8MxVutWH6mKAREVG7lldWiapqZYeYf6ai2mqDCZrpatUEzczMDBKJBDNmzMCZM2dasysiIiKtMjrAIekP6uHUCQBw7TYTNFPVqglat27d4Obmhri4OAQGBmLs2LGt2R0REVEdqtWMHeGYJxV3O0tIzMW4dvuOoUOhFtLpJIHGpKenAwDKyspw4sQJnDhxojW7IyIiqkO1YauPY8cZQTMTi+DtYIU0jqCZrFZN0FRsbGwQGhqK0NDQtuiOiIhILaOgHGIR0K0DPeIEgO6OnRD/xy1UVtdAat7wyT9kfLhIgIiI2rXr+RVw62LZ4ZKUHs7WUArghrUmqtUTtMLCQty4caO1uyEiIqpDEARkFJSrVzV2JN0dVQsFOA/NFLV6gvbGG2+ge/fuOt2juroaS5cuhY+PD2QyGfr27Yv169c3uf3hw4cxatQoWFlZwcnJCREREcjPz9daNy4uDv7+/pDJZHB3d8frr79e57D3K1euYNGiRRgyZAi6dOkCBwcHjBo1Cl999VWrxE9ERC2TV1aJiqoaeHWgPdBUujvVJqWch2aa2uQRpyDodtTE/PnzERMTg9DQUKxbtw4PPfQQIiMj8eGHHzba9tixYwgNDUVVVRVWr16NhQsX4quvvsIjjzwChUJzh+Vdu3Zh+vTpcHR0RGxsLGbOnIl169Zh2rRpGvW2bduGdevWoV+/fvjwww+xZMkSmJmZ4emnn8a7776r1/iJiKjlVAeGe3egFZwq3e9ttZHGETTTJDRTTU1Ns75mz54tiMXi5najlpSUJAAQoqOjNcrDwsIEmUwm5ObmNtjez89P8PHxEcrLy9Vl+/fvFwAIa9euVZdVVlYKLi4uwogRI4Samhp1+fr16wUAwr59+9RlZ86cEUpKSjT6USqVQnBwsGBubi4UFBToLX5tEhMTBQBCYmJis9sSEXUku09lCF7R3wk//nHL0KEYRMDSQ8Lkdb8YOgy6pzmf380eQbOwsGjW12effaZTAhkXFwcAiIqK0iiPioqCQqHA3r1762175coVJCcnY+7cubCy+nN4e+LEiejZsyd2796tLjt69Chyc3OxcOFCiMV/viwRERGwtrbWqBsQEABbW1uNvkQiEaZNm4bq6mpcuXJFL/ETEZFurud3vD3Q7tfdyRrXbt/R+UkWtb0WbbPRpUsXDBw4sEl1L126hLy8vJZ0AwA4c+YMPDw84ObmplE+dOhQiMViJCYm4sUXX6y3LQAEBgbWuRYYGIhvvvkGSqUSYrG43rpSqRR+fn5ITExsNNbs7GwAgJOTk17iz8nJQU5OTp3ylJSURmMhIqLaR5xiUcc6ReB+PZyscep6IQrKq+DYSWrocKgZmp2g9e7dG5WVlThy5EiT6r/wwgv473//2+zAVLKzs+skNwAgkUjg4OCArKysBtsC0Nrezc0NcrkcRUVFcHBwaLTuuXPnGowzLy8Pn3zyCYYNG4YePXroJf5Nmzbh/fffb7BfIiKqX3pBuXpX/Y5ItZIzLe8OEzQT0+x37NChQ5GRkYHCwsLWiKcOuVwOqVT7m0omk0EulzfYFoDW9jKZTKNOY3Ub6ufu3bsICwtDWVkZNmzYoLf4X3rpJSQmJtb52rlzZ71tiIioliAIyCio6JALBFR6ONf+7Nd4aLrJafYI2pAhQ7Bz506cPn26SScD9OnTR6czOC0tLVFZWan1mkKhgKWlZYNtAWhtr1rBqapzf90H79lQP0qlEuHh4Th+/Dg+//xzDB48WG/xu7q6wtXVtd7rRERUv9zSSsjv1nToBI17oZmuZo+gRUVFQalUNvnYpujo6CY/DtXGzc1N/fjxflVVVSgoKND6+PD+tgC0ts/OzoalpSXs7OyaVFdbP4IgYO7cuYiLi8P69esxffp0vcZPREQtd121xUYH3KRWxcPOEhZmIlzjXmgmx+gfygcEBCAzM7POXK3Tp09DqVQiICCgwbYAkJCQUOdaQkIC/Pz81Cs266tbWVmJ5ORkrf288sor2L59O1asWIGXXnpJ7/ETEVHLZXTAQ9IfZG4mhpeDNR9xmiCjT9DCwsIAALGxsRrla9euhUwmw+TJkwEAFRUVuHTpksYJAb6+vhg0aBC2bNmCioo/zyI7cOAArl69qjHiFRwcDGdnZ6xbtw5KpVJdvm3bNpSXl9cZHYuOjsZ//vMfvPvuu3jrrbd0jp+IiPTr+r0EraNusaHS3dEaNworUFWtbLwyGY0WbbPRlvz9/REREYEVK1agpKQEQ4YMQXx8POLi4rB06VK4uLgAAE6dOoVx48YhJiYGS5YsUbdfs2YNxo8fj6CgIMyZMwd5eXlYtWoVBgwYgHnz5qnrSaVSrFy5ErNnz8aECRMQFhaG1NRUrFmzBiEhIXjiiSfUddeuXYsVK1agX79+6NOnT51J++PHj1fH1dT4iYhIv1RbbHSz67gjaADQw7kT4v/IxY3CcvR0tjF0ONRERp+gAcDGjRvh6emJ7du3Y9u2bfD29kZsbCwiIyMbbTtu3Dj88MMPeO+99/Daa6/B2toaU6dOxYoVK+pM0J81axYkEgmWL1+OhQsXws7ODgsWLMCyZcsgEonU9c6ePQsA+OOPP/Dcc8/V6fPIkSMaiZcu8RMRUcuk51fAw86qw26xodLd8c8zOZmgmQ6RwO2FTc7Zs2cREBCAxMTEOqtGiYgIUCoF9Iv5AcN8HPDfiGGGDsegEjOK8OSGE4ie0Afzg3s03oBaTXM+vzv2rxVERNQu5ZYpoLirhLdDx368CdSeJgBwqw1To5cEbe/evYiIiKj3eyIiorak3mKjgy8QAIAuVhI4WEuQxgTNpOglQUtOTsann35a7/dERERtKaOgduW+TwfeA+1+3Z241Yap4SNOIiJqd9K5Sa2G7o6dUFxxFwV3tJ9sQ8aHCRoREbU71/PLYSYWwcOu/uP0OpJeLrVHPl3N42NOU8EEjYiI2p30gvJ7xxzxYw4AejrXJmipTNBMBt+5RETUriiVAjIKKrhA4D69XGr3P+MImulggkZERO1KTqkCldXcYuN+bp1lsJaYITWvzNChUBMxQSMionZFtd9Xj3uP9QgQiUTo6dwJV3I5gmYqmKAREVG7knbvMV4PJyZo9+vpbIPbZZUorqgydCjUBEzQiIioXVHt99XdiXPQ7seVnKaFCRoREbUrabfvwEpihq62MkOHYlR6cSWnSdFLgiYIAu4/c/3B74mIiNrKtdvl6O5kDZFIZOhQjErveys5UzkPzSToJUFbsmQJlEplvd8TERG1hfLKauSUKNDdkfPPHuTexRIyCzFXcpoIPuIkIqJ2Q3VIOhcI1CUW167k5Bw008AEjYiI2o20e1tscIGAdr2cbZBTokCp4q6hQ6FGMEEjIqJ2I+02R9AaojryiaNoxo8JGhERtRuqTWp9HDmCpo1qJedVLhQwekzQiIio3Ui7XQ73LpawlJgZOhSjpDqTkwsFjF+bJ2iZmZlt3SUREXUASqWA6/l3OP+sAd3sLCExF3MvNBOg9wStqKgIkydPRpcuXRAUFIRz585pXO/Xr5++uyQiIkJOqQKKu0rOP2uAuZkY3R2tuReaCdB7ghYdHQ2FQoFdu3Zh8ODBGDt2LH755Rf1dW5gS0REreHPMzg5gtaQ3i42yCqW405ltaFDoQaY6/uGBw4cQFJSEhwdHfH4449jxIgRmDJlCg4cOIChQ4dyZ2ciImoV19RbbHAErSG9753JmZpbBn9POwNHQ/XRe4JWUlICO7s//8DDwsKgVCrx2GOPIT4+Xt/dERERAeAWG03Vp6stAODSLSZoxkzvCZqnpyd+//13DBo0SF32zDPPoLy8HI8++igqKyv13SURERGu5d+BtcQMLrZSQ4di1Hy71q7kvHyLKzmNmd7noE2aNAlffvllnfI5c+bgvffew9273L2YiIj0Ly2vHN2dOnEqTSM87CzRSWqOlJxSQ4dCDdApQdN2IPry5cuxbNkyrfWjoqJ4iDoREeldeWU1bpUquMVGE4hEIvTpaoNLt8q4cM+I6ZSgTZo0CRUVFfqKpV7V1dVYunQpfHx8IJPJ0LdvX6xfv77J7Q8fPoxRo0bBysoKTk5OiIiIQH5+vta6cXFx8Pf3h0wmg7u7O15//XWUl5fXqffhhx9iypQpcHd3h0gkwvPPP19v/yKRSOvX3Llzm/wzEBFR/VRHF/Xk/LMm8e1qgxL5XeSWctqRsdJpDtqhQ4cwevRofP/993B1da23Xnp6Ory9vVvcz/z587F161bMmzcPQ4YMQXx8PCIjI1FcXIxFixY12PbYsWMIDQ2Fn58fVq9ejdzcXKxatQqJiYlISEiATCZT1921axfCw8MREhKC2NhYpKam4uOPP8bFixdx8OBBjfu+++67cHZ2xrBhw5Cdnd3ozzBmzBjMmzdPo6xnz57NeBWIiKg+V3Jr51OpdsqnhvVxrV0okHKrFF07yxqpTQYh6GD//v2Cra2t4OnpKZw/f77O9Zs3bwovvfSSIJFIWtxHUlKSAECIjo7WKA8LCxNkMpmQm5vbYHs/Pz/Bx8dHKC8v14gbgLB27Vp1WWVlpeDi4iKMGDFCqKmpUZevX79eACDs27dP477Xrl1T/z8AYfbs2fXG0Nj15kpMTBQACImJiXq7JxGRKfvg+z8Er+jvhLS8MkOHYhJOXy8QvKK/EzYcvWroUDqU5nx+6/SIc+LEiTh+/DiUSiVGjx6t3kYjNzcXUVFR6NWrFzZv3qyxorO54uLiANTOX7tfVFQUFAoF9u7dW2/bK1euIDk5GXPnzoWVlZVG3D179sTu3bvVZUePHkVubi4WLlwIsfjPlyUiIgLW1tYadQHAx8en2T9LZWVlmzwSJiLqaK7klkFiJoanvVXjlQm9763kvMSFAkZL51WcAwcOREJCAnr27IlJkyZhxowZ6NGjB9atWwc/Pz98//33OHXqVIvvf+bMGXh4eMDNzU2jfOjQoRCLxUhMTGywLQAEBgbWuRYYGIikpCT1ooX66kqlUvj5+TXYT1N8+eWXsLKygrW1NXx8fPDxxx9zciYRkZ6k5taewWlu1uZHTJskW5kF3LtY4hK32jBaetkHrVOnTggJCUFSUhL27NkDZ2dnfPvttxg/frzO987Ozq6TnAGARCKBg4MDsrKyGmwLQGt7Nzc3yOVyFBUVwcHBodG6D54p2hzDhw/H9OnT0b17d+Tm5mL79u147bXXcOPGDaxevbredjk5OcjJyalTnpKS0uJYiIjamzuV1cgqluOJQXX//ab69elqg59Tb6OqWgmJORNbY6NTglZUVISPP/4YsbGxKCkpwYABA+Ds7IzDhw8jPj5eLwmaXC6Hvb291msymQxyubzBtkDtKJi2tvfXaaxuQ/005uTJkxrfz5kzB6Ghofj3v/+NBQsW1LtYYNOmTXj//fdb3C8RUUegWsGpOsKImqaPqw1+upSHa/l31KcLkPHQKUHz8vJCeXk5evfujQ0bNiAsLAyCICAyMhKrVq3C9evXsXPnTo2Vks1laWlZ7+kDCoUClpaWDbYFoLW9QqHQqHN/3Qfv2Vg/zSUWi/HGG2/gxx9/xE8//VRvgvbSSy/hiSeeqFOekpKC8PBwvcVDRGTKuIKzZVRJ2eVbZUzQjJBOCZqzszMWL16M8PBw9cR6kUiEDRs2oHv37vjb3/6G4OBg7Nu3D87Ozi3qw83NTesjvaqqKhQUFGh9JHl/W6D2UWffvn01rmVnZ8PS0lJ9buj9dXv06FGnbkP9tISnpycAoKCgoN46rq6uDW5fQkREtYd+A0BvJmjN0ufeQoGUnDJM9jNsLFSXTg+dL1++jFmzZmmselR56623sGfPHpw/fx7Dhw9vcR8BAQHIzMysM9fs9OnTUCqVCAgIaLAtACQkJNS5lpCQAD8/P3Xs9dWtrKxEcnJyg/20RFpaGgDAyclJr/clIuporuTegcScKziby8fRGhIzMS7d4kpOY6RTgmZmZtbg9aeeego//fST1p34myosLAwAEBsbq1G+du1ayGQyTJ48GQBQUVGBS5cuaZwQ4Ovri0GDBmHLli0a21scOHAAV69exfTp09VlwcHBcHZ2xrp16zSOo9q2bRvKy8s16jbH7du365RVVVXhn//8J8zNzfHoo4+26L5ERFQrNbcMPZw6wUzMMzibw9xMjF4unXhoupHSyyrOhowYMQK//fZbi9v7+/sjIiICK1asQElJifokgbi4OCxduhQuLi4AgFOnTmHcuHGIiYnBkiVL1O3XrFmD8ePHIygoCHPmzEFeXh5WrVqFAQMGaOzsL5VKsXLlSsyePRsTJkxAWFgYUlNTsWbNGoSEhNSZC/bZZ58hIyND/f358+fVZ5COHTsWY8eOBQD85z//wTfffIMnnngCnp6euH37Nnbt2oWUlBS8//778PLyavFrQ0TU0ZUp7iK7RIGhPtoXk1HDfLva4JuzWSiuqEIXK4mhw6H7tHqCBrRsU9f7bdy4EZ6enti+fTu2bdsGb29vxMbGIjIystG248aNww8//ID33nsPr732GqytrTF16lSsWLGizsT/WbNmQSKRYPny5Vi4cCHs7OywYMECLFu2DCKR5m9mW7duxbFjx9TfJyUlISkpCQAQExOjTtBGjRqF3377Ddu2bUNBQYF6X7W4uDg8/fTTOr0uREQdXap6BSfnn7VEP1dbfIMs/JFdipE9HQ0dDt1HJHC3VJNz9uxZBAQEIDExEYMHDzZ0OEREBrPn9A1Ef30Bm58LwKP9uxo6HJPz27UCPLP5Nyx6rA/mje3ReAPSSXM+v7kzHRERmazUXI6g6aKfW+32Gr9ncaGAsWGCRkREJutK3h1IzcXoxhWcLWIrs4C3gxV+zy4xdCj0ACZoRERksriCU3f93Tvjen457lRWGzoUuk+rJmhmZmaQSCSYMWOG+jByIiIifShV3EVOiYJHPOlogFtnCAKQksPHnMakVRO0bt26wc3NDXFxcQgMDFSvbCQiItKVav8uXx5TpJMB7qp5aHzMaUxadZuN9PR0AEBZWRlOnDiBEydOtGZ3RETUgVy6N+LT15ULBHTR360zAC4UMDZtsg+ajY0NQkNDERoa2hbdERFRB/BHTu0IWl9XjqDpwt5aAvculrjIhQJGhYsEiIjIJF26VQp7awmcbaSGDsXk9XezRWreHSju1hg6FLpHpxG0S5cu4fjx40hLS0NJSW3m3blzZ/To0QNjxoxBnz599BIkERHR/ZRKAZdvlcGvW5c6J71Q8w1w74z4P3Jx6d5rSobXogQtKSkJkZGRSEhIQH0HEYhEIgQGBmL9+vXw8/PTJUYiIiINGYUVqKiq4eNNPbl/oQATNOPQ7ATt/PnzGDNmDJRKJZ5//nmEhISgR48esLWt/cMtLS1FWloaDh06hD179mD06NE4efIkHnroIb0HT0REHdOfCwSYoOnDgHsLBTgPzXg0O0FbtGgRpFIpjh8/jn79+mmtM2zYMDz77LN48803MXr0aCxatAj/+9//dA6WiIgI+HPPrj5duYJTH5xtZXCykXIlpxFp9iKBX3/9FTNmzKg3Obtfv379MGPGDBw/frxFwREREWmTcqsM5mIRenGTWr0Z4GaLy7fKUFWtNHQohBYkaDU1Nc2akCkSiaBU8g+biIj0JyWnFD2cOkFqbmboUNqNh9w7o6pGiSu5ZYYOhdCCBG3w4MH4/PPPcfXq1UbrXrlyBZ9//jkCAgJaFBwREdGDShV3kVkkRx9uUKtXg+4tDki6WWzQOKhWs+egLV68GI8++ij8/f0xa9YsPPzww1oXCfz000/47LPPoFAoEBMTo/fAiYioY1Id8cQFAvqlStDO3SzGc8O9DBsMNT9Be/jhh/F///d/mD9/PjZs2ICNGzdqrScIAjw8PLBhwwYEBwfrGicREREA4I9sruBsDY6dpPCws0QyR9CMQov2QZs0aRJCQ0Nx6NAhHD9+HFevXkVpae1fGFtbW/Ts2RNjxoxBSEgIJBKJXgMmIqKO7cK9Q70HuDFB0ze/bl3w/YUclCruwlZmYehwOrQWnyRgYWGBxx57DI899pg+4yEiImrQ71klcOssg0MnHvGkb37duuC78zk4f7MEo3s5GjqcDo1ncRIRkclQ3K1Bat4dDHDvbOhQ2iXVKQLJN4sMGwgxQSMiItORklOKGqXABK2VDHDvDHOxCMk3eaKAoTFBIyIik/H7vQUCDzFBaxUyCzP0cbVB8s3ies/aprbBBI2IiEzG75m1Izv93blAoLUM8uiC/DuVyCqWGzqUDo0JGhERmYwLWSVwsZXC2UZm6FDarT/noRUbNI6OTi8J2t69exEREVHv90RERLqqrK7BldwyPt5sZYO97AAAiRlcKGBIeknQkpOT8emnn9b7PRERka4u3ypDtVJAfzcmaK2pu6M17K0lOJPOBM2Q+IiTiIhMwu9ZXCDQFkQiEQK87PBHTinKK6sNHU6HxQSNiIhMgvoEASZorW6otx1qlALnoRmQSSRo1dXVWLp0KXx8fCCTydC3b1+sX7++ye0PHz6MUaNGwcrKCk5OToiIiEB+fr7WunFxcfD394dMJoO7uztef/11lJeX16n34YcfYsqUKXB3d4dIJMLzzz/fYAzr169H3759IZPJ4OPjg2XLlqG6mr+ZEBE1VfLNYrjYStG1MxcItLYAL3sA4GNOAzKJBG3+/PmIiYlBaGgo1q1bh4ceegiRkZH48MMPG2177NgxhIaGoqqqCqtXr8bChQvx1Vdf4ZFHHoFCodCou2vXLkyfPh2Ojo6IjY3FzJkzsW7dOkybNq3Ofd99912cPHkSgwcPbjSGDz74AJGRkRg4cCDWrVuH0NBQLF68GAsWLGj6i0BE1IFVVFXj8q1S9QpDal0D3G0hNRfjTEahoUPpsFp8FmdbSU5OxpYtWxAdHY3ly5cDAObOnYvp06dj6dKlmDt3Lpydnett/9e//hXdunXDsWPHYGVlBQAYNmwYHnvsMXzyySd45ZVXAABVVVV44403MGLECBw8eBBicW3u6uPjgwULFuB///sf/vKXv6jve+3aNfj4+ACofV5fn9zcXCxbtgzTp0/H7t271fF37twZK1euxMKFCzFw4EAdXiEiovbvfGYJlALg183O0KF0CFJzMwzy6IKkG8WoUQowE9f/OUetw+hH0OLi4gAAUVFRGuVRUVFQKBTYu3dvvW2vXLmC5ORkzJ07V52cAcDEiRPRs2dPdcIEAEePHkVubi4WLlyoTs4AICIiAtbW1hp1AaiTs8bs3bsXCoWiTvyvvPIKBEHAnj17mnQfIqKOTDUXyt+zi0Hj6EgCvO1wp7Ial26VGjqUDsnoR9DOnDkDDw8PuLm5aZQPHToUYrEYiYmJePHFF+ttCwCBgYF1rgUGBuKbb76BUqmEWCyut65UKoWfnx8SExNbHL9YLMaQIUM0yj08PODu7t7gfXNycpCTk1OnPCUlpUWxEBGZquQbxRCLuIKzLQ31tsMG1M5D49Ymbc/oE7Ts7Ow6yRkASCQSODg4ICsrq8G2ALS2d3Nzg1wuR1FRERwcHBqte+7cuRbH7+joCIlEovW+DcW/adMmvP/++y3ql4ioPUm+WYzeLjawlhr9x1a7EeBpD5EIOJVeiNkjvQ0dTodj9O90uVwOe3t7rddkMhnk8vrPClNdk0qlWtveX6exug310xC5XK71nqr7FhbWPwHzpZdewhNPPFGnPCUlBeHh4S2Kh4jI1OSUyHGrVIFxfZwMHUqH0tnKAn262iLhWiEEQWhwvjXpn14SNEEQNE69f/B7XVhaWqKyslLrNYVCAUtLywbbAtDaXrWCU1Xn/roP3rOxfhqiS/yurq5wdXVtUb9ERO1F8o1iAOAKTgMY0d0B2369jqt5d9DLxcbQ4XQoelkksGTJEiiVynq/14Wbm5v68eP9qqqqUFBQoPWR5P1tAWhtn52dDUtLS9jZ2TWpbkP9NBZ/fn4+qqqq9HpfIqKO4s8FAlzB2dZG9HAAAJy8VmDgSDoeo1/FGRAQgMzMzDpztU6fPg2lUomAgIAG2wJAQkJCnWsJCQnw8/NTr9isr25lZSWSk5Mb7Kex+JVKpXoRgorqZ2rpfYmIOoqkm8XoJDVHD6dOhg6lwxnmYw+xCDiZxgStrRl9ghYWFgYAiI2N1Shfu3YtZDIZJk+eDACoqKjApUuXNE4I8PX1xaBBg7BlyxZUVFSoyw8cOICrV69i+vTp6rLg4GA4Oztj3bp1GqN/27ZtQ3l5uUbd5pg8eTKkUinWrl2rUa76eVQ/HxER1VVVrcT5zGIM6taZe3EZQGdLC/R364zfrhVAqdTP1CVqGqNfJODv74+IiAisWLECJSUlGDJkCOLj4xEXF4elS5fCxcUFAHDq1CmMGzcOMTExWLJkibr9mjVrMH78eAQFBWHOnDnIy8vDqlWrMGDAAMybN09dTyqVYuXKlZg9ezYmTJiAsLAwpKamYs2aNQgJCakzWf+zzz5DRkaG+vvz589j2bJlAICxY8di7NixAICuXbvi3XffxeLFiyEIAh599FGcPn0amzdvxpw5c+Dn59dKrxwRken7PbsEirtKDPXWvliMWt+IHg7Y/HMJLueWoa+rraHD6TgEE1BVVSUsWbJE8PLyEiQSidC7d28hNjZWUCqV6jpHjhwRAAgxMTF12h86dEgYPny4IJPJBAcHB2H27NlCbm6u1r6++OILYdCgQYJUKhW6du0qvPrqq0JZWVmdekFBQQIArV8PxqBUKoXY2Fihd+/egkQiEby8vIQlS5YIVVVVLXo9EhMTBQBCYmJii9oTEZmKjUevCl7R3wm/pt42dCgd1uGUXMEr+jth6/Frhg7F5DXn81skCHpabklt5uzZswgICEBiYmKTzgIlIjJVcz89g6OX83B+yaOwkhj9Q5926U5lNQa9H4+H+zjjk1lDGm9A9WrO57fRz0EjIqKOSakUcCajEP3dOzM5M6BOUnMM9Kidh1Zdo58dGqhxbZ6g3bhxo627JCIiE3T19h0UV9zFMG9ur2FoY3o6okxRjXOZxYYOpcNo0wStsrKyyYeMExFRx3bqeu1JK0O4QMDggnxrT3E4diW/kZqkL20+gsYpb0RE1BRn0msTNK7gNLxBHl1gIzPHz1duGzqUDkPvD/XNzMwavM6zvIiIqClOpxehp3Mn2FtLDB1Kh2duJsbono744eItFJVXwY5/Jq1O7wlap06d8PHHH6N79+51rlVWVmLixIn67pKIiNqZzKIKZBXL8eywboYOhe4Z29sJB36/hV+u5uMvg3hMYWvTe4I2aNAgWFlZISgoqM61yspKPuIkIqJGnbh3tNDw7g4GjoRUxvaunYf285XbTNDagN7noEVGRsLeXvt8AQsLC2zfvl3fXRIRUTtz4mrtZPSRPRwNHAmpuHexRA8na/ycepuDLW1ApwTt/jMrVaZPn47x48dr70wsxuzZs3XpkoiI2jlBEPBrWgH6dLWBk43U0OHQfYJ6OyO3tBIpOWWGDqXd0ylBmzRpksYh5ERERLpKzbuD22WVHD0zQo/0dQYA/JSSa+BI2j+dErRDhw5h9OjRyMnJabBeenq6Lt0QEVEH8uu9x5ujenL+mbEZ5mMPG5k5DjFBa3U6JWj79u1DWloahg8fjgsXLtS5npmZiZdffhm+vr66dENERB3Ir1cLYCYWYZgP9z8zNhZmYozzdcb5zBLcKlEYOpx2TacEbeLEiTh+/DiUSiVGjx6N+Ph4AEBubi6ioqLQq1cvbN68GYMGDdJLsERE1L5V1yiRcK0Agzw6w0ZmYehwSIvx/VwAAD9yFK1V6byKc+DAgUhISEDPnj0xadIkzJgxAz169MC6devg5+eH77//HqdOndJHrERE1M6dzypBWWU1RvXk/DNjFeTrBAszERO0VqaXbTY6deqEkJAQVFdXY8+ePbCxscHBgwdx8uRJbkxLRERNdvyKav4ZEzRjZSuzwPDuDjhxtQB3KqsNHU67pVOCVlRUhJiYGHh7e+Ojjz7CgAEDMG7cOOTm5qofdxIRETXV4ct5sJGZI8DLztChUAPG93NBVY2SZ3O2Ip0SNC8vLyxbtgwuLi74/PPPce7cOcTHx+Oll17CqlWr8NRTT0Gh4CRCIiJqXP6dSpzPLMbYXk6wMNP7PuqkR6p5aN9faHgXB2o5nf4GODs7Y/v27bh48SKmT58OkUgEsViMDRs24F//+he+/fZbBAcHIy8vT1/xEhFRO3X08m0IAjCuj7OhQ6FGuHa2xBAvOxxOyUNFFR9ztgadErTLly9j1qxZEIvr3uatt97Cnj17cP78eQwfPlyXboiIqAM4crn2l/mge2c+knGbNNAV8rs1+CmFgzCtQacEzczMrMHrTz31FH766SeUl5fr0g0REbVzd+/NZxrk0ZnHO5mIxx5yhUgEfHc+29ChtEut/pB/xIgR+O2331q7GyIiMmGJGUUoU1Tz8aYJcbaVIdDHHkcu30aZ4q6hw2l3mpWgvfnmmy2aT+bj4wOg9uSBr776qtntiYiofTtyqfaz5WEmaCZl0kA3VFUruSdaK2hWgrZnzx54e3sjIiIC8fHxUCqVjbbJzMzEqlWrMHDgQEybNg0lJSUtDpaIiNofQRBw8OItONtIMcCts6HDoWaYOKArzMQi7EvmY059M29O5atXr2Lt2rVYsWIFPv30U3Tq1AkBAQHw9/eHs7Mz7OzsoFAoUFhYiNTUVJw5cwZpaWlQKpUIDQ3Fp59+Cn9//9b6WYiIyARdulWG9IIKzB7hBbFYZOhwqBkcOkkR1NsJRy/nIa9UAWdbmaFDajealaBJpVK89dZbePXVV/Htt9/is88+wy+//IKjR4/WqSsSidCnTx+8+eabiIiIQO/evfUVMxERtSMH7u2lNWGAq4EjoZZ4OsADhy/l4dukLLwU1MPQ4bQbzUrQVCQSCaZPn47p06dDEAT88ccfyMzMRGFhISwtLeHk5IR+/frBzo47QRMRUcMO/H4LDtYSDPOxN3Qo1AIP93VGFysLfJWYiXlju0Mk4iioPrQoQbufSCRC//790b9/f33EQ0REHUhqbhlS8+5gRqAnzPh40yRJzc0wxc8dO06k41xmCfy6dTF0SO0Cz9IgIiKDOfD7LQC1k83JdD0V4AEA+CrxpoEjaT/0kqAdOXIEc+bMwdChQ+Hr64uhQ4di7ty5OHLkiD5uj+rqaixduhQ+Pj6QyWTo27cv1q9f3+T2hw8fxqhRo2BlZQUnJydEREQgPz9fa924uDj4+/tDJpPB3d0dr7/+er0b7a5fvx59+/aFTCaDj48Pli1bhupqzSMv0tPTIRKJtH4tW7as6S8CEVE7tP9CDrpYWWB4dwdDh0I66O9miz5dbbA3ORvyqhpDh9Mu6PSIs7q6Gi+88AI+//xzCIIAsVgMe3t7pKWlITExEdu3b8eMGTOwY8eORk8daMj8+fOxdetWzJs3D0OGDEF8fDwiIyNRXFyMRYsWNdj22LFjCA0NhZ+fH1avXo3c3FysWrUKiYmJSEhIgEz254qTXbt2ITw8HCEhIYiNjUVqaio+/vhjXLx4EQcPHtS47wcffIC///3vCAsLwxtvvIEzZ85g8eLFuHHjBjZv3lwnjqlTp2LatGkaZX5+fi1+TYiITN2lW6W4dKsMzw7rxsPRTZxIJMLMQE+8t/ci9iZn4ZlhnoYOyfQJOoiJiRFEIpHwyCOPCL/88otQXV0tCIIgVFdXC8ePHxcefvhhQSwWC++//36L+0hKShIACNHR0RrlYWFhgkwmE3Jzcxts7+fnJ/j4+Ajl5eXqsv379wsAhLVr16rLKisrBRcXF2HEiBFCTU2Nunz9+vUCAGHfvn3qslu3bgkymUyYPn26Rl9vv/22IBKJhHPnzqnLrl+/LgAQYmJimvVzNyQxMVEAICQmJurtnkREbe3D7/8QvKK/E05dLzB0KKQHZYq7Qv/FPwgTPv5ZUCqVhg7HKDXn81unX1l27NiBgQMHIj4+HqNGjVKPkpmZmWH06NGIj49H//79sXXr1hb3ERcXBwCIiorSKI+KioJCocDevXvrbXvlyhUkJydj7ty5sLKyUpdPnDgRPXv2xO7du9VlR48eRW5uLhYuXKhx+HtERASsra016u7duxcKhaJOTK+88goEQcCePXu0xiOXy6FQKJrwUxMRtW81SgHfJmWhm70lhnhxxX970ElqjmmD3ZGSU4ozGUWGDsfk6ZSg5ebmYuLEiRoJzf3MzMzw+OOP4/bt2y3u48yZM/Dw8ICbm5tG+dChQyEWi5GYmNhgWwAIDAyscy0wMBBJSUnq0xDqqyuVSuHn56fRz5kzZyAWizFkyBCNuh4eHnB3d9ca06pVq2BlZQVLS0v0798fu3btaujHBgDk5OTg7Nmzdb5SUlIabUtEZMx+vZqPvLJKTPP34LYM7cisEV4AgP+ezDBwJKZPpzlovr6+yM1t+PytW7duwdfXt8V9ZGdn10nOgNq92BwcHJCVldVgWwBa27u5uUEul6OoqAgODg6N1j137pzGfR0dHSGRSLTWvT8msViM8ePHY8qUKejWrRtu3ryJdevWITw8HAUFBXVG4e63adMmvP/++/VeJyIyVd+czQQATBvsbuBISJ96OttgZA8HHLiQg9zH+8KFJwu0mE4J2jvvvIMXXngBERERGD16dJ3rx48fx+7du/Hpp5+2uA+5XA57e+2bF8pkMsjl8gbbArWjYNra3l+nsbr39yOXy7XWU9UtLCxUf+/p6Yn4+HiNOnPmzIG/vz/effddPP/887C1tdV6r5deeglPPPFEnfKUlBSEh4drbUNEZOzKFHfxw8VbGOJlBy8Ha0OHQ3r2wigfnEgrwLZfr+OdiX0NHY7JalaC9t///rdO2bhx4xAUFIQJEyZg1KhRcHJywu3bt/HLL7/g4MGDmDhxok7zriwtLVFZWan1mkKhgKWlZYNtAWhtr4pJVef+ug/e88F+dIkJqE0Co6KiMH/+fJw8eRKhoaFa67m6usLVlUefEFH78n/J2VDcVeLJe3tnUfvySB9n9HTuhF2/3cCC4J7obGlh6JBMUrMStOeffx4ikQiCINS5duDAARw4cKBO+f79+3HgwAHMmjWrRQG6ublpnXNVVVWFgoICrY8k728L1D6S7NtXM4vPzs6GpaWl+jiq++v26NGjTt37+3Fzc0N+fj6qqqrqPObMzs5u0qkKnp61S5ALCgoarUtE1F4IgoCdJzNgIzXHZL/6//0m0yUWi/ByUA+8+eU57PwtA5Hjeho6JJPUrARNXxvPNkdAQAAOHTqErKwsuLv/OVfh9OnTUCqVCAgIaLAtACQkJOCRRx7RuJaQkAA/Pz/1Aof7696foFVWViI5OVnjUWNAQAA++eQTnDlzBiNHjlSXZ2ZmIisrq0nJaFpaGgDAycmp0bpERO3FqeuFuJxbhudHesNKovNpg2SkJvu5YXX8ZWz/9TrmjPaBzKLle6F2WK2954euzp492+A+aLdu3RIEQRDKy8uFlJQU4fbt2xr1Bg0aVO8+aB9//LG6TKFQCM7OzvXug/Z///d/6rKcnBxBKpVq3QcNgJCUlKQu07ZPW0lJieDj4yN06dJFuHPnTjNejVrcB42ITFXkrkTBK/o7ITW3zNChUCvb9ss1wSv6O2H7L9cMHYrRaM7nt95+fbl58ybOnz+P0tJS2NraYuDAgejWrZvO9/X390dERARWrFiBkpIS9UkCcXFxWLp0KVxcXAAAp06dwrhx4xATE4MlS5ao269Zswbjx49HUFAQ5syZg7y8PKxatQoDBgzAvHnz1PWkUilWrlyJ2bNnY8KECQgLC0NqairWrFmDkJAQjRG0rl274t1338XixYshCAIeffRRnD59Gps3b8acOXM0TgiIjo7GlStXMH78eLi7uyMrKwtbt25FVlYWtm3bBmtrTpAloo4hr0yBH36/hZE9HNDTuZOhw6FW9sxQT6w/moZ1R9IQNrQbR0ybS9ds8PfffxfGjh0riMXiOl9BQUHCxYsXde1CqKqqEpYsWSJ4eXkJEolE6N27txAbG6uxU/GRI0fq3bH/0KFDwvDhwwWZTCY4ODgIs2fPrvcEgi+++EIYNGiQIJVKha5duwqvvvqqUFZW9zc9pVIpxMbGCr179xYkEong5eUlLFmyRKiqqtKo9/nnnwtBQUGCs7OzYG5uLtjZ2QmhoaHCjz/+2OLXgyNoRGSKVsVfFryivxP2n882dCjURj49cV3wiv5O+M+RVEOHYhSa8/ktEgQtM/6bKDU1FcOGDUNJSQnGjBmDoKAguLi4IDc3Fz///DN+/vln2NnZ4bfffkOvXr30llR2dGfPnkVAQAASExMxePBgQ4dDRNSo8spqjFx+GJ0tLXD4jSCY8+zNDqGqWomHVx1Fqfwujkc/3OFXdDbn81un8cbFixejvLwc//vf//D444/Xub5//35MnToVMTEx+Pzzz3XpioiITNgXp26gRH4Xb0/wZXLWgUjMxXgtpDfe+PIcNh1Lw9sT+hg6JJOh09+Sw4cPY/r06VqTMwB47LHH8PTTT+PHH3/UpRsiIjJhVdVKbDl+HU42Ujw5mHufdTRT/N3h62KDLb9cx42CCkOHYzJ0StBKSkoaXQjg6emJsrIyXbohIiIT9n9JWbhVquB2Cx2UmViEmCf6oapaiaXf/2HocEyGTgmat7c3fvrppwbrHD58GF5eXrp0Q0REJqqqWonYI6mwlZljZqCnocMhAxnZwxGPP+SKQ3/k4tiV24YOxyTolKA9++yzOH36NMLDw5GRoXlyfUZGBp577jmcPn0aM2bM0ClIIiIyTZ8nZOBmoRwvB/eAjaxjTxDv6BY93hcyCzHe33cRirs1hg7H6OmUoP3tb39DcHAwPv/8c/Ts2RPe3t4IDAyEt7c3evbsiV27diE4OBjR0dH6ipeIiEzEncpqxB6+ChdbKV4Y6WPocMjA3LtYIuqRXriWX46Pf0w1dDhGT6cETSqV4scff8TGjRsxcuRIlJaW4uzZsygtLcWoUaOwadMmHDp0CFKpVF/xEhGRidhy/BoKyqvw15DesJRw7hkB88Z0x0PunbH55zScu1ls6HCMms7b+orFYsybN09jV34iIurYsovl2PzzNXR3ssbTAVy5SbXMzcT46OlBmBR7HG9+eQ7/e2U0F47UQ6cRtGnTpmH58uX6ioWIiNqJpd/9gYqqGiye1I/7npEG3642ePWRXkjNu4N/7k8xdDhGS6e/NQcPHkRJSYm+YiEionbgyOU8HPj9Fh57qCuCfZ0NHQ4ZofnBPTG8uz0+PZmB/RdyDB2OUdIpQevfvz+uX7+ur1iIiMjEyatqELP3IqwlZnhvUj9Dh0NGykwswr+f8YeDtQTRX51HRkG5oUMyOjolaG+99Rb27t2LkydP6iseIiIyYcsPpOBGYQVeG98brp0tDR0OGTEXWxnWTPfDnapqzP30DEoVdw0dklHRaZGAXC5HUFAQgoKCMG3aNAQEBMDZ2RkikahO3VmzZunSFRERGbkjl/Pw6ckMBPrY44VR3FaDGje2txPemdgHH+6/hIWfJ2Hb7CGcs3iPTgna888/r/7/uLg4xMXFaa0nEomYoBERtWOF5VV4+6vzsJGZY/V0P5iJ6/6iTqTNi2O649rtcuw+fROL913EB1MGaB3o6Wh0StCOHDmirziIiMhEVdcoEfVFEm6XVeLj6X5w78JHm9R0IpEI/5g8AJlFcnyecAM2UnP8bWKfDp+k6ZSgBQUF6SsOIiIyUf88cAm/XM3HzEBPTPF3N3Q4ZIIk5mJsei4As7adwqafr0FmYYbXxvc2dFgGpZcHvUeOHMGcOXMwdOhQ+Pr6YujQoZg7dy5H2IiI2rmvEjOx9ZfrGOpth5i/9Dd0OGTCrKXm2P7CUDzk3hn//ikV/9yfAkEQDB2WweiUoFVXV+O5555DSEgItm/fjqSkJBQVFSEpKQnbtm1DSEgInnvuOdTU8FBUIqL25sc/chH99Xm4dZZh/cwASMw5uZt0YyuzwM45gQjwssOmn68h+uvzqK5RGjosg9Dpb9OyZcuwa9cujBs3DsePH0dlZSXy8vJQWVmJn3/+WX2Q+gcffKCveImIyAicTCvAgs/PooulBf47JxBONjxzmfSjs1Vtkhbs64S4M5mYte0UisqrDB1Wm9MpQduxYwcGDhyI+Ph4jBo1CmZmtedpmZmZYfTo0YiPj0f//v2xdetWvQRLRESGdzz1NuZ8ehpSMzE+jRiGns6dDB0StTOWEjN8MmsInhvuhRNpBXjiP7/gYnbHOrlIpwQtNzcXEydOhFis/TZmZmZ4/PHHcfv2bV26ISIiI/Hd+WxE7DgNc7EIOyKGYYB7Z0OHRO2UhZkYS6cMwIdTH8KtEgWm/OdXbDyWhhplx5iXplOC5uvri9zc3Abr3Lp1C76+vrp0Q0REBqZUCvjPkat45Ysk2FlJ8OXLIxHgZWfosKgDmBHoiW/mj4KnvRWWH7iEZz/5DTcKKgwdVqvTKUF75513sHv3bvzyyy9arx8/fhy7d+/GO++8o0s3RERkQKWKu3h5ZyJWHrwMXxcbfD1/JHy72hg6LOpAHvLojO9eGYNZI7xw6nohQtYcw6r4y5BXtd9FiDrtg1ZZWYlx48YhKCgIEyZMwKhRo+Dk5ITbt2/jl19+wcGDBzFx4kQoFAr897//1WjLkwWIiIzfL6n5ePurc8guUeAvg9zwrycfgpVEp48OohaxlJjhH5MHYOIAVyzZdxGxh6/i68RMvP6oL6b4ubW7I6JEgg6bjNQ396zRTkUibr2hg7NnzyIgIACJiYkYPHiwocMhonao4E4lPoq/jC9O3YSVxAyLHuuLmYGeHX53dzIO1TVK7Eq4gVXxl1GqqIaXgxUix/XEVH93WBhxotacz28e9URERGoVVdXY9dsNrD2cijJFNYZ3t8eKJwfB08HK0KERqZmbiTF7pDem+Ltjx6/p2PrLNbz91Xl8dPAynhnmiWeHdYNrZ9M+coxHPREREUoVd/HZyQxs/eU6Csur4N7FEsunDcRjD3XlqBkZrc6WFng1pBciRntj5283sPO3DKz9KRX/OXIVo3s64i+D3PBofxfYyiwMHWqzcSIBEVEHJQgCzt4owp7TN/Hd+RxUVNXAvYsl/jG5P8KGdIPMwszQIRI1iY3MAvODe2De2O44cikPuxIycDw1H8eu3IbkGzHG9nZEsK8zxvZyMpnRYON9UHuf6upqLF26FD4+PpDJZOjbty/Wr1/f5PaHDx/GqFGjYGVlBScnJ0RERCA/P19r3bi4OPj7+0Mmk8Hd3R2vv/46ysvLtdZdv349+vbtC5lMBh8fHyxbtgzV1dV6j5+ISF9qlAJOpxfiw/0pGPfRUTy54STizmSil3MnrHxqII6+FYxZI7yZnJFJMhOLENLPBdtfGIbT74Zg+bSHMMzHHocv5eHv//c7xq48grErjuCdb84j7vRNXL5VZrT7qpnECNr8+fOxdetWzJs3D0OGDEF8fDwiIyNRXFyMRYsWNdj22LFjCA0NhZ+fH1avXo3c3FysWrUKiYmJSEhIgEwmU9fdtWsXwsPDERISgtjYWKSmpuLjjz/GxYsXcfDgQY37fvDBB/j73/+OsLAwvPHGGzhz5gwWL16MGzduYPPmzXqLn4hIF4q7NbiYXYLT6UU4fb0QZzKKUCK/CwBwsZXihVHemD60G/p0tTVwpET6ZWctwTPDPPHMME+UVNzFibR8HL+aj+Opt/HFqZv44tRNAICVxAwPuXdGX1db9HaxQS+XTujl3AldrCQGjV+nVZxtITk5Gf7+/oiOjsby5cvV5dOnT8e+ffuQkZEBZ2fnetv7+/ujpKQEv//+O6ysaoc1Dxw4gMceewxr167FK6+8AgCoqqqCp6cnunfvjl9++UW9QnXDhg1YsGAB9u3bh7/85S8Aak9Q8Pb2xuTJk7F79251X9HR0Vi5ciWSk5MxcOBAvcSvDVdxEtH9lEoB+XcqcbNIjsyiCqTnV+BKbhku3SpFekGFeoTAXCzCQx6dMbqnI8b3c8EAt84Qizm/jDqe7GI5zmcWI+lmMc7dLMaFzBKUP7Cn2gdTB2BmoJde+22zVZxtIS4uDgAQFRWlUR4VFYW4uDjs3bsXL774ota2V65cQXJyMj744AN1cgYAEydORM+ePbF79251gnb06FHk5uZi9erVGtuHRERE4K233sLu3bvVCdrevXuhUCjqxPTKK69gxYoV2LNnjzpB0yV+Imr/BEFAtVJAdY2AqmolKu5Wo6KqBhWVNaiouvf/VTUor6pGcUUVCsqrUFRehcLy2v8vLK9CTokCVdVKjfuKRICXvRVC+jqjv1tnDPW2h1+3LrCU8NElkVsXS7h1scSEAa4Aan/JySqW42reHaTmlSE19w4GuBn2GDOjT9DOnDkDDw8PuLm5aZQPHToUYrEYiYmJ9SY4Z86cAQAEBgbWuRYYGIhvvvkGSqUSYrG43rpSqRR+fn5ITEzUuK9YLMaQIUM06np4eMDd3b1O3ZbGn5OTg5ycnDrlKSkpWuvr6trtO1jyvz/qva7rYGtjzQU0XKGh9q1579r2jTBg/439uTQWu+4/e+v1r/PrpuPPput7vkYpoEYp4K5SieoaAXdrBFTf+/8//9uyPizMRLCzksDeWoJRPRzgYWcFDztLeNhZwdPeCj2dOzEZI2oisViEbvZW6GZvhXF9mvdUq7UYfYKWnZ1dJ7kBAIlEAgcHB2RlZTXYFoDW9m5ubpDL5SgqKoKDg0Ojdc+dO6dxX0dHR0gkdZ9Pu7m5acSkS/ybNm3C+++/X+91fauoqsHZjKIG6zTpYUgjlRq7R2NL+htb8a/r/Zt2D93uoPvP0Fj/gKjVY9Dt0ViTfoZGYzTsz9iUPyeJuRiWYjOYm4lhIRbB3EwECzMxzMWi2jIzEczFYpibiSAxE8NKYg4riRmspGawsjCDldQc1vfKOltZwN5KAvtOEthIzbn9BVE7ZvQJmlwuh729vdZrMpkMcrm8wbZA7SiYtrb312ms7v39yOVyrfVUdQsLC/US/0svvYQnnniiTnlKSgrCw8PrbddSA9w74/f3Q/V+XyIiImoeo0/QLC0tUVlZqfWaQqGApWX9OwWrrmlrr1AoNOrcX/fBez7YT3Ni0iV+V1dXuLq61nudiIiI2iej3wfNzc1N/fjxflVVVSgoKND6+PD+tgC0ts/OzoalpSXs7OyaVPf+ftzc3JCfn4+qqqom1W1p/ERERNQxGX2CFhAQgMzMzDpztU6fPg2lUomAgIAG2wJAQkJCnWsJCQnw8/NTr9isr25lZSWSk5M1+gkICIBSqVQvLFBRxflg3ZbGT0RERB2T0SdoYWFhAIDY2FiN8rVr10Imk2Hy5MkAgIqKCly6dEnjhABfX18MGjQIW7ZsQUVFhbr8wIEDuHr1KqZPn64uCw4OhrOzM9atWwel8s/l6tu2bUN5eblG3cmTJ0MqlWLt2rUaMaliVMXcnPiJiIiIVIx+Dpq/vz8iIiKwYsUKlJSUqHfij4uLw9KlS+Hi4gIAOHXqFMaNG4eYmBgsWbJE3X7NmjUYP348goKCMGfOHOTl5WHVqlUYMGAA5s2bp64nlUqxcuVKzJ49GxMmTEBYWBhSU1OxZs0ahISEaEzW79q1K959910sXrwYgiDg0UcfxenTp7F582bMmTMHfn5+zY6fiIiISE0wAVVVVcKSJUsELy8vQSKRCL179xZiY2MFpVKprnPkyBEBgBATE1On/aFDh4Thw4cLMplMcHBwEGbPni3k5uZq7euLL74QBg0aJEilUqFr167Cq6++KpSVldWpp1QqhdjYWKF3796CRCIRvLy8hCVLlghVVVUtir85EhMTBQBCYmJii9oTERFR22vO57fRH/VEdfGoJyIiItPTnM9vo5+DRkRERNTRMEEjIiIiMjJM0IiIiIiMDBM0IiIiIiPDBI2IiIjIyDBBIyIiIjIyTNCIiIiIjIzRnyRAdcnlcgBASkqKgSMhIiKiplJ9bqs+xxvCBM0EpaenAwDCw8MNGwgRERE1W3p6OkaNGtVgHZ4kYILy8/Nx8OBBeHt7w9LSUq/3TklJQXh4OHbu3Im+ffvq9d7tDV+rpuNr1XR8rZqHr1fT8bVqutZ6reRyOdLT0xEaGgpHR8cG63IEzQQ5Ojpi5syZrdpH3759eYxUE/G1ajq+Vk3H16p5+Ho1HV+rpmuN16qxkTMVLhIgIiIiMjJM0IiIiIiMDBM0IiIiIiPDBI2IiIjIyDBBIw2urq6IiYmBq6uroUMxenytmo6vVdPxtWoevl5Nx9eq6YzhteI2G0RERERGhiNoREREREaGCRoRERGRkWGCRkRERGRkmKARERERGRkmaNSgl19+Gf7+/rC3t4elpSV8fX3x+uuv4/bt24YOzagUFRVh9erVePjhh9G1a1d06tQJgwYNwr/+9S8oFApDh2d09uzZg1mzZqFPnz4Qi8Xw9vY2dEgGV11djaVLl8LHxwcymQx9+/bF+vXrDR2WUbpz5w5iYmLw2GOPwcnJCSKRCEuWLDF0WEYpMTERf/3rXzFw4EDY2Niga9euCAkJweHDhw0dmtE5e/YsnnzySXTv3h1WVlawt7fH8OHD8dlnn8EQ6yl5Fic16PTp0wgKClK/Yf/44w9s2bIFe/fuRVJSEmxtbQ0dolFISEjA22+/jUcffRRvvvkmbG1tcfz4cbzzzjv4/vvvcfToUYjF/H1IZcOGDThz5gwCAgJQUlJi6HCMwvz587F161bMmzcPQ4YMQXx8PCIjI1FcXIxFixYZOjyjkp+fj3/84x/w8PCAv78/Dh06ZOiQjNbKlSvx008/4cknn8TChQtx584d7NixA4888gg2b96MF1980dAhGo1r165BLpdj9uzZcHNzg0KhwA8//IBZs2bh3Llz+Oijj9o2IIGomb788ksBgLBlyxZDh2I0rl+/LqSlpdUpj4mJEQAIe/fuNUBUxuvGjRtCdXW1IAiCEBQUJHh5eRk2IANLSkoSAAjR0dEa5WFhYYJMJhNyc3MNFJlxUigUQlZWliAItX/3AAgxMTGGDcpI/frrr4JcLtcok8vlgq+vr+Do6CjU1NQYKDLT8fjjjwsSiUSoqKho0375Kz01m+pxVHFxsUHjMCbe3t7o3r17nfInn3wSAPDHH3+0dUhGrVu3bjAzMzN0GEYjLi4OABAVFaVRHhUVBYVCgb179xoiLKMllUrh5uZm6DBMwsiRIyGTyTTKZDIZHn/8ceTn5yMvL89AkZkOb29vVFVVoaKiok375SNOalR1dTWKi4tx9+5dXLlyBX/7298gEonwyCOPGDo0o5ednQ0AcHJyMnAkZMzOnDkDDw+POknH0KFDIRaLkZiYyEdRpFfZ2dmwsLBA586dDR2K0SkvL4dcLkdpaSmOHj2K7du3w9/fHw4ODm0aBxM0atSZM2cwYsQI9ffdunXDrl274OfnZ7igTIBSqcQ///lPWFtb44knnjB0OGTEsrOztY4ISSQSODg4ICsrywBRUXuVkpKCb775BlOnToWlpaWhwzE6b7zxBjZt2qT+/uGHH8bWrVvbPA4maB2EIAiorKxsUl1zc3OYm//51ujXrx8OHToEuVyO5ORkfPvttygtLW2tUA1Ol9fqfn//+99x7NgxrFu3rt2OoOnrtero5HI57O3ttV6TyWSQy+VtHBG1VyUlJXjyySdhbW3d9pPeTcRf//pXPPXUU8jLy8P+/fuRk5OD8vLytg+kTWe8kcGcPHlSANCkr8Ym2549e1YwMzMTtm3b1jbBtzF9vFaxsbECAGHBggVtG3wb08drxUUCgtC/f39h2LBhWq85OTkJkyZNauOITAcXCTRdRUWFMGbMGMHS0lI4duyYocMxGa+//rpgb28v3L59u0375a+zHUSPHj2wffv2JtVt7NGlv78/+vbtiy1btuCFF17QQ3TGRdfXaseOHYiKisLMmTOxbt06PUdnXPT5vurI3NzckJKSUqe8qqoKBQUFnBBPOquqqsLUqVPx22+/4dtvv8XYsWMNHZLJmDFjBlavXo1vv/22TeeCMkHrIJycnPD888/r7X4KhQI1NTV6u58x0eW12rNnD+bMmYO//OUv2LFjB0QikX6DMzL6fl91VAEBATh06BCysrLg7u6uLj99+jSUSiUCAgIMGB2ZuurqaoSFheHQoUPYtWsXHn/8cUOHZFJUm40XFRW1ab/cZoPqVVhYqDUJO3ToENLS0jBs2DADRGW89u3bh/DwcIwbNw5xcXGcb0VNFhYWBgCIjY3VKF+7di1kMhkmT55siLCoHVAqlZg1axb27t2LjRs34plnnjF0SEarvi1HNm7cCABt/pnHTxCq1759+xATE4Mnn3wSPXr0gCAIOHv2LHbt2gUnJyfExMQYOkSjcfr0aYSFhcHS0hJPP/00vvzyS43rAwcOxMCBAw0UnfH5+eef8fPPPwMAMjIyUFJSgmXLlgEAvLy88NxzzxkyvDbn7++PiIgIrFixAiUlJeqTBOLi4rB06VK4uLgYOkSjs27dOhQXF6v3Y/z555/V76EnnniCf9/uefPNN/HFF18gKCgIlpaW2Llzp8b1qVOnwtra2kDRGZfp06fDzMwMo0ePhoeHB/Lz87F371789ttvePrppxEcHNy2AbXpjDcyKb///rsQHh4u9OjRQ7CyshIkEonQq1cvYeHChepdvKnW9u3bdVp40dGoTljQ9hUUFGTo8AyiqqpKWLJkieDl5SVIJBKhd+/eQmxsrKBUKg0dmlHy8vKq9z20fft2Q4dnNIKCghr8t+n69euGDtFobNu2TXjkkUcEFxcXwdzcXLC1tRVGjhwpbNiwQX3ySVsSCYIBTgAlIiIionpxDhoRERGRkWGCRkRERGRkmKARERERGRkmaERERERGhgkaERERkZFhgkZERERkZJigERERERkZJmhERERERoYJGhEREZGRYYJGRGRELl26hLCwMDg4OMDW1haTJk1CRkaGocMiojbGo56IiIzETz/9hL/85S9wcnLCU089hezsbOzZswe9evXChQsXIJFIDB0iEbURc0MHQEREwM2bN/Hkk0/Cz88PBw8ehI2NDQDAzc0Nq1evxt69e/H0008bOEoiait8xElEZATeeustVFRUYOfOnerkDACmT58OADhx4oShQiMiA2CCRkRkYOnp6fjyyy8xbdo0dO/eXeOavb09ACAvL88QoRGRgTBBIyIysD179kCpVGLGjBl1rlVWVgIApFJpW4dFRAbEOWhERAYWHx8PADh+/DjOnj2rcS0zMxNA7Vw0Iuo4mKARERmQIAg4deoUAOCjjz6qt16fPn3aKiQiMgJ8xElEZECZmZm4c+cOZs2aBUEQ6nypHnuOGDHCwJESUVtigkZEZEA5OTkAAFdX1zrXlEolfvrpJ3Tv3h09evRo69CIyICYoBERGdDdu3cBQOsmtD/99BNyc3O1Lh4govaNCRoRkQE5OTkB0L6NxocffggrKyu88sorbR0WERkYEzQiIgPq2bMnnJ2dsW/fPty5c0dd/sEHH+Do0aP44IMP4OzsbMAIicgQeBYnEZGB/etf/8Lf/vY3DBgwAI899hjOnj2LH3/8EfPmzcPGjRshEokMHSIRtTEmaEREBiYIAj788ENs3LgR+fn56NevH1599VXMmjXL0KERkYEwQSMiIiIyMpyDRkRERGRkmKARERERGRkmaERERERGhgkaERERkZFhgkZERERkZJigERERERkZJmhERERERoYJGhEREZGRYYJGREREZGSYoBEREREZGSZoREREREaGCRoRERGRkfl/iPB6lB+WBL4AAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "a3,b3,c3 = params['a_inep'].iloc[2],params['b_inep'].iloc[2],0 # os parâmetros do terceiro item\n", "a4,b4,c4 = params['a_inep'].iloc[3],params['b_inep'].iloc[3],0 # os parâmetros do quarto item\n", "\n", "ax = sns.lineplot(x=theta,y=(1-P(theta,a1,b1,c1))*P(theta,a2,b2,c2)*P(theta,a3,b3,c3)*(1-P(theta,a4,b4,c4)), label=f\"$(1-P_{1})*P_2*P_3*(1-P_4)$\");\n", "ax.set_xlabel(r\"$\\theta$\");ax.set_ylabel(r\"$\\mathrm{prob}(x_1=0,x_2=1,x_3=1,x_4=0|\\theta$)\");" ] }, { "cell_type": "markdown", "id": "aea954ed-b138-4657-9987-5c7307cabc5a", "metadata": {}, "source": [ "Vemos que na medida que temos mais informação (respostas aos itens), podemos estimar a habilidade $\\theta$ para qual a probabilidade de obter esta padrão é máxima fica cada vez mais estreita, correspondendo a uma incerteza na estimativa menor. " ] }, { "cell_type": "markdown", "id": "c1873eb6-9d44-4e31-b479-5309898bbad7", "metadata": {}, "source": [ "Finalmente, veja um vídeo com uma animação como a probabilidade do padrão de acerto evolua analisamos os acertos e erros um por um de alguém que em total acertou 30 dos 45 questões. O ponto principal a observar é que mesmo após 45 questões, a largura do pico de probabilidade é considerável. Não podemos distinguir a habilidade com a de um outro candidato com um padrão de resposta levando a uma uma habilidade próxima suficiente (no caso do vídeo, da ordem de 0.2 desvios padrão, ou 20 pontos na escala ENEM). Isto é uma consequência inerente e inevitável da limitação ao número de questões que podemos usar num único exame.\n", "\n", "" ] }, { "cell_type": "markdown", "id": "ef01406b-0a91-4f48-aea3-8520ad0f9ccb", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "### Estimar $\\theta$ por métodos Bayesianos\n", "Uma das desvantagens do método de inferência ML explicado acima é que para candidatos com muito poucos ou muitos acertos as estimativas de $\\theta$ ficam instáveis. O ENEM usa um método de estimação da nota chamado \"Expected a Posteriori\" (EAP), que usa o teorema de Bayes para inverter o modelo para a probabilidade das padrões e a habilidade $\\theta$:\n", "\n", "$$ \\text{prob}(\\theta|\\vec{x}) = \\frac{\\text{prob}(\\vec{x}|\\theta)\\text{prob}(\\theta)}{\\text{prob}{(\\vec{x})}} $$" ] }, { "cell_type": "markdown", "id": "dcde1a82-2830-477e-ab84-2380002b2fee", "metadata": {}, "source": [ "Na prática, o termo $\\text{prob}{(\\vec{x})}$ é só um fator de normalização para que o posterior $\\text{prob}(\\theta|\\vec{x})$ é uma probabilidade. O que importa na expressão acima é a multiplicação pelo \"prior\" $\\text{prob}(\\theta)$, uma premissa sobre como as habilidades são distribuídas na população. Multiplicando o prior com a modelo $\\text{prob}(\\vec{x}|\\theta)$ resulta no posterior que pode ser interpretado como a distribuição da probabilidade de um certo $\\theta$, dado a evidência: o padrão de respostas $\\vec{x}$.\n", "\n", "Tendo o posterior para $\\theta$, podemos resumir o resultado de várias formas. A estimativa EAP é o valor esperado do $\\theta$\n", "\n", "$$ \\theta_{\\text{EAP}} = \\int \\theta \\text{prob}(\\theta|\\vec{x}) d\\theta $$\n", "\n", "e uma estimativa para sua incerteza é o desvio padrão do posterior. \n", "\n", "No cálculo da nota do ENEM o prior é uma normal com desvio padrão 1. Calcular o posterior é surpreendemente simples na prática. É somente usar o cálculo da verossimilhança que fizeram acima, multiplacado pela função gaussiana $N(0,1)$. O resultado não é normalizado (não é uma probabilidade), mas para fins de cálculo do valor esperado podemos simplesmente usar a posterior não-normalizada como peso." ] }, { "cell_type": "markdown", "id": "48fdebb7-f35a-424c-b66a-06dede1bfea0", "metadata": {}, "source": [ "Vamos usar um determinado padrão de respostas e tentar reproduzir a nota que o INEP forneceu, com os parâmetros das questões, também fornecidos pelo INEP. " ] }, { "cell_type": "code", "execution_count": 13, "id": "61ab14f1-9486-4164-a876-8fe572025ed8", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [], "source": [ "def displaypadr(df):\n", " info = df.iloc[:,-3:]\n", " df = df.iloc[:,:-3]\n", " checkmap = {1: '✔',0: '✖'} \n", " df = df.map(lambda x: checkmap[x])\n", " if len(df) == 1:\n", " return \"\".join(list(df.values[0])) + f\"\\n acertos {info.iloc[0,0]}, nota inep {info.iloc[0,2]}\"\n", " return df\n" ] }, { "cell_type": "code", "execution_count": 14, "id": "34f4d827-e23a-4baa-9733-99a71f3715bf", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Um candidato de 2023, MT:\n", " ✖✖✖✔✖✖✔✔✖✖✖✖✖✖✖✔✖✖✖✖✔✖✖✔✖✔✖✔✖✖✖✖✖✖✖✖✖✖✔✖✖✔✖\n", " acertos 10, nota inep 435.3 \n", "\n", "Os primeiros cinco parâmetros das questões:\n" ] }, { "data": { "text/html": [ "
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a_inepb_inepc_inepu
CO_ITEM
817421.634181.344750.139561
289322.394341.983950.115081
374413.013042.671850.084551
867833.586093.000880.192421
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\n", "
" ], "text/plain": [ " a_inep b_inep c_inep u\n", "CO_ITEM \n", "81742 1.63418 1.34475 0.13956 1\n", "28932 2.39434 1.98395 0.11508 1\n", "37441 3.01304 2.67185 0.08455 1\n", "86783 3.58609 3.00088 0.19242 1\n", "14410 2.38237 1.88674 0.10321 1" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ano = 2023\n", "area = 'MT'\n", "padr = load_acertos(ano,area,1)\n", "print(f\"Um candidato de {ano}, {area}:\\n\",displaypadr(padr),'\\n')\n", "params = params_inep(ano,area) # os parâmetros TRI fornecidos pelo INEP\n", "print(\"Os primeiros cinco parâmetros das questões:\")\n", "params[:5]" ] }, { "cell_type": "markdown", "id": "9417ba4f-c5f2-4f50-a4bc-ee4fc919e72b", "metadata": {}, "source": [ "A conta para reproduzir a nota a partir destas informações não é complexo. Abre a célula abaixo se quiser ver os detalhes. Calculamos o array `lh`(\"likelihood\"), de \\$theta = -3$ até 3, multiplando 45 vezes pelo $P_i(a_i,b_i,c_i;\\theta)$ ou $1-P_i(a_i,b_i,c_i;\\theta)$, conforme se o candidato acertou ou errou, respectivamente. Depois de ter a curva `lh`, a nota é simplesmente o valor onde este é um máximo (`lh.argmax()`). Se usar o método EAP (Bayesiano), multiplica pelo a priori, uma curva normal no nosso caso, e calculo o valor esperado de $\\theta$. Nenhum bixo de sete cabeças, abrimos a caixa opaca da nota ENEM calculado pelo TRI!" ] }, { "cell_type": "code", "execution_count": 26, "id": "e339e07c-0641-488e-a20a-8baf0f6e1816", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "params = params.join(padr.reset_index().T).rename(columns={0:'acertou'})\n", "theta = np.arange(-3,3,0.01)\n", "\n", "def P(theta,a=1,b=0,c=0):\n", " 'O modelo 3PL'\n", " return c + (1-c)*1/(1+np.exp(a*(b-theta)))\n", "\n", "\n", "lh = np.ones(len(theta))\n", "for item,value in params.iterrows(): \n", " acertou = int(value.iloc[-1])\n", " if acertou:\n", " lh = lh*P(theta,a=value['a_inep'],b=value['b_inep'],c=value['c_inep'])\n", " else:\n", " lh = lh*(1-P(theta,a=value['a_inep'],b=value['b_inep'],c=value['c_inep']))\n", "\n", " nota_ml = (-3+lh.argmax()*0.01)\n", " posterior = lh*norm.pdf(theta)\n", " nota_eap = np.average(theta, weights=posterior)\n", "\n", "\n", "\n", "with sns.axes_style(\"whitegrid\"):\n", " fig,axs = plt.subplots(1,2,sharex=True,figsize = (16,6))\n", " ax1 = axs[0]; ax2 = axs[1]\n", " sns.lineplot(x=theta,y=lh,ax=ax1);\n", " ax1.set_xlabel(r\"$\\theta$\");ax.set_ylabel(r\"$\\mathrm{prob}(\\vec{x_i}|\\theta)$\");\n", " ax1.set_title(f\"Máxima verossimilhança: nota = {nota_ml:.2f} ({notas_to_enem_scale(nota_ml,area):.1f})\");\n", " ax1.grid(axis='y')\n", " sns.lineplot(x=theta,y=posterior,ax=ax2);\n", " ax2.set_xlabel(r\"$\\theta$\");ax.set_ylabel(r\"Posterior\");\n", " ax2.set_title(f\"Expected a Posteriori: nota = {nota_eap:.2f} ({notas_to_enem_scale(nota_eap,area):.1f})\");\n", " ax2.grid(axis='y')\n" ] }, { "cell_type": "markdown", "id": "18eaec63-570f-4782-a6a5-7f3af93ccd13", "metadata": {}, "source": [ "Vemos que o método EAP \"encolhe\" as notas um pouco para a média (0 na escala TRI, 500 na escala ENEM). Este efeito é maior para notas altas (acima de 2 desvios padrão ou 700) e notas baixas. " ] }, { "cell_type": "markdown", "id": "82dc0531-a587-40ea-8d3b-b576326455de", "metadata": {}, "source": [ "## Curiosidades: nota máxima possível e respostas aleatórias\n", "Agora que sabemos calcular notas ENEM a partir de qualquer padrão de respostas, podemos responder algumas perguntas. Por exemplo, o que seria a nota máxima ou mínima possível? É fácil de ver que se usar o método" ] }, { "cell_type": "code", "execution_count": null, "id": "cc0e128b-042f-4efc-8eb8-34731a430007", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.11.2" } }, "nbformat": 4, "nbformat_minor": 5 }