Aula 3 - Distribuições de Probabilidade.ipynb

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    "# 03 - Distribuições de Probabilidade\n",
    "\n",
    "Nessa aula, iremos tratar dos seguintes conteúdos:\n",
    "- Tipos de Variáveis Aleatórias\n",
    "- Esperança e Variância\n",
    "- Distribuição de Probabilidade\n",
    "- Distribuição - Bernoulli e Binomial\n",
    "- Distribuição Poisson\n",
    "- Distribuição Exponencial\n",
    "- Distribuição Uniforme"
   ]
  },
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    "<img src = \"https://miro.medium.com/max/450/1*FSuKbxt4bLeqTrlbhg3hQQ.gif\">"
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    "<img src = \"http://storage.ning.com/topology/rest/1.0/file/get/1490420457?profile=original\" width=800>"
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   "source": [
    "## "
   ]
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   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
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   "source": [
    "## Tipos de Variáveis Aleatórias\n",
    "\n",
    "\n",
    "<br>\n",
    "\n",
    "Vimos que uma __variável aleatória__ é uma variável cujo valor depende de fatores não determinísticos, ou melhor dizendo __probabilísticos__. Detalhando um pouco mais sobre as variáveis aleatórias, existem dois tipos mais comuns que vamos trabalhar no nosso curso, sendo elas:\n",
    "\n",
    "- __Discreta:__ são as variáveis aleatórias que a distribuição de probabilidade assume apenas valores enumeráveis;\n",
    "\n",
    "- __Contínua:__ são as variáveis aleatórias que a distribuição de probabilidade assume valores contínuos dentro de um intervalo pré-determinado.\n",
    "\n",
    "Mas para realmente entendermos a diferença entre cada uma delas, precisamos definir o que são __distribuições de probabilidade__."
   ]
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   "source": [
    "## "
   ]
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   "source": [
    "## Distribuições de Probabilidade\n",
    "\n",
    "<br>\n",
    "\n",
    "Uma **distribuição de probabilidade** é uma função que descreve o comportamento aleatório de um fenômeno dependente do acaso.\n",
    "\n",
    "A distribuição de probabilidade pode **modelar incertezas** e descrever fenômenos físicos, biológicos, econômicos, entre outros.\n",
    "\n",
    "A representação matemática para a distribuição de probabilidade é feita utilizando o que chamamos de __função de densidade de probabilidade__. Para cada um dos casos de variáveis aleatórias temos uma definição de densidade de probabilidade, conforme veremos agora:\n",
    "\n",
    "- __Discretas:__ Para o caso das variáveis aleatórias discretas a definição matemática para a função de densidade de probabilidade, pode ser dada da seguinte forma:\n",
    "\n",
    "$$ P(X = x) = F(X) $$\n",
    "\n",
    "Ou seja, para o caso discreto, a variável aleatória assume é uma função que assume um valor real para cada elemento do espaço amostral. Partir das definições gerais para probabilidade, são conhecidas as seguintes são sempre válidas:\n",
    "\n",
    "- $ 0 \\leq P(X = x) \\leq 1 $;\n",
    "\n",
    "<br>\n",
    "\n",
    "- $ P(X = x) \\geq 0 $;\n",
    "\n",
    "<br>\n",
    "\n",
    "- $ \\sum_{i=1}^{\\infty} P(X = x_{i}) = 1 $ ;\n",
    "\n",
    "<br>\n",
    "\n",
    "- $ P(a \\leq X \\leq b) = \\sum_{x = a}^{x = b} P(X = x)$;"
   ]
  },
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   "metadata": {},
   "source": [
    "## "
   ]
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   "source": [
    "- __Contínuas:__ Para o caso das variáveis aleatórias contínuas a definição matemática para a função de densidade de probabilidade, pode ser dada da seguinte forma:\n",
    "\n",
    "$$ P(X) = \\int p(x) \\,dx $$\n",
    "\n",
    "Da mesma forma que para o caso discreto, vamos definir algumas relações conhecidas as v. a. contínuas:\n",
    "\n",
    "- $ p(x) \\geq 0, \\forall x \\in \\mathbb{R}$;\n",
    "\n",
    "<br>\n",
    "\n",
    "- $ \\int_{-\\infty}^{\\infty} p(x) \\,dx = 1 $ ;\n",
    "\n",
    "<br>\n",
    "\n",
    "- $ P(a \\leq X \\leq b) = \\int_{a}^{b} p(x) \\,dx$;\n",
    "\n",
    "<br>\n",
    "\n",
    "Uma outra forma de interpretarmos a probabilidade de uma dada distribuição entre o intervalo $a$ e $b$, seria como a área abaixo ao gráfico da função de densidade de probabilidade:\n",
    "\n",
    "<img src=\"https://work.thaslwanter.at/Stats/html/_images/PDF.png\" width=400>\n"
   ]
  },
  {
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   "metadata": {},
   "source": [
    "## "
   ]
  },
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   "source": [
    "## Valor Esperado (Esperança) e Variância\n",
    "\n",
    "<br>\n",
    "\n",
    "Assim como no caso da Estatística Descritiva, no casos de modelos probabilísticos também existem parâmetros de posição e variabilidade utilizada para caracterizar uma distribuição de probabilidade:\n",
    "\n",
    "- __Valor Esperado (Esperança):__ O valor esperado seria o produto da variável aleatória $x$ e sua respectiva probabilidade, funcionando como se fosse uma média ponderada para as probabilidades. O cálculo do valor esperado é definido da seguinte forma:\n",
    "\n",
    "\n",
    "__Caso Discreto:__  $ E[X] = \\sum xP(X = x) $\n",
    "\n",
    "\n",
    "__Caso Contínuo:__  $ E[X] = \\int xp(x) dx $\n",
    "\n",
    "<br><br>\n",
    "\n",
    "- __Variância:__ A variância é o valor que mede a variabilidade, ou seja o quão dispersão estão as probabilidade em relação ao valor esperado. A variância é definida da seguinte forma:\n",
    "\n",
    "<br>\n",
    "\n",
    "$$ V[X] = \\sigma^{2} = E[(X - E[X])^2] = E[X^2] - E[X]^2$$\n",
    "\n",
    "<br>\n",
    "Onde, $ E[X^2] = \\sum x^2P(X = x)$."
   ]
  },
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   "source": [
    "__Exemplo:__ Seja a variável aleatória X com distribuição abaixo, calcule $E[X]$ e $V[X]$:\n",
    " \n",
    "- P(X = 1) = 0.3\n",
    "- P(X = 2) = 0.4\n",
    "- P(X = 3) = 0.2 \n",
    "- P(X = 4) = 0.1"
   ]
  },
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     "text": [
      "Valor esperado:  2.1\n",
      "Variância:       0.89\n"
     ]
    }
   ],
   "source": [
    "# Vetor de eventos\n",
    "X = [1, 2, 3, 4]\n",
    "\n",
    "# Vetor de probabilidades\n",
    "P = [0.3, 0.4, 0.2, 0.1]\n",
    "\n",
    "# Valor esperado\n",
    "esp = np.dot(X, P)  # dot multiplica\n",
    "\n",
    "# print do valor esperado\n",
    "print(\"Valor esperado: \", np.round(esp, 2))\n",
    "\n",
    "# Variância\n",
    "var = np.round(np.dot(np.power(X, 2), P) - np.power(esp, 2), 2)\n",
    "\n",
    "# print da variância\n",
    "print(\"Variância:      \", var)"
   ]
  },
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   "id": "efd9edc5",
   "metadata": {},
   "source": [
    "__Exemplo:__ A variável X tem função de densidade de probabilidade dada por:\n",
    "\n",
    "- $f(x) = \\frac{x^2}{3}$, se $ -1 \\leq x \\leq 2$, caso contrário seria 0."
   ]
  },
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     "text": [
      "Valor Esperado:  1.25\n",
      "Erro da Integral:  1.5728145305099745e-14\n",
      "Variância:       0.6375000000000002\n",
      "Erro da Integral:  2.4424906541753447e-14\n"
     ]
    }
   ],
   "source": [
    "from scipy.integrate import quad\n",
    "\n",
    "# Função para a equação do valor esperado\n",
    "def f1(x):\n",
    "    return x*(x*x)/3\n",
    "\n",
    "# Calculo da integral e o erro\n",
    "esp, err1 = quad(f1, -1, 2)\n",
    "\n",
    "# Print do Valor esperado\n",
    "print(\"Valor Esperado: \", esp)\n",
    "print(\"Erro da Integral: \", err1)\n",
    "\n",
    "# Função para a equação do valor esperado x^2\n",
    "def f2(x):\n",
    "    return (x*x)*(x*x)/3\n",
    "\n",
    "# Integral de x^2\n",
    "esp_x2, err2 = quad(f2, -1, 2)\n",
    "\n",
    "# Calculo da variância\n",
    "var = esp_x2 - esp*esp\n",
    "\n",
    "# Print da Variância\n",
    "print(\"Variância:      \", var)\n",
    "print(\"Erro da Integral: \", err2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f02e294e",
   "metadata": {},
   "source": [
    "## "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "516ffd12",
   "metadata": {},
   "source": [
    "## Distribuições\n",
    "\n",
    "Nos próximos tópicos, vamos apresentar algumas das principais distribuições utilizadas!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e767ff6",
   "metadata": {},
   "source": [
    "## "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "549ff76a",
   "metadata": {},
   "source": [
    "## Distribuição de Bernoulli/Binomial\n",
    "\n",
    "A distribuição de Bernoulli  é uma distribuição discreta para um espaço amostral $k \\in \\{0, 1\\}$, baseando a probabilidade em __sucessos__ e __falhas__. Onde a probabilidade de sucesso de um evento ($k = 1$) é igual a $p$ e a probabilidade de falha ($k = 0$) seria o valor complementar $1 - p$. A função que descreve a distribuição de Bernoulli pode ser definida como:\n",
    "\n",
    "<br>\n",
    "\n",
    "$$ P(X = k) = p^{k}(1-p)^{(1-k)} $$\n",
    "\n",
    "<br>\n",
    "Os valores para o valor esperado e a variância para a distribuição de Bernoulli serão respectivamente:\n",
    "\n",
    "- __Valor Esperado:__ $ E[X] = p $;\n",
    "\n",
    "- __Variância:__ $ V[X] = p(1-p)$.\n",
    "\n",
    "<br>\n",
    "\n",
    "Mas o caso da distribuição de Bernoulli, tratamos apenas para um evento isolado, como por exemplo o lançamento de uma moeda. Quando trabalhamos com eventos __com repetições__, utiliza-se o caso geral da distribuição de Bernoulli que seria uma __Distribuição Binomial.__\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82bee09e",
   "metadata": {},
   "source": [
    "### Distribuição Binomial\n",
    "\n",
    "Seja a variável aleatória baseado em $n$ repetições de Bernoulli, temos que a definição da distribuição Binomial é dada por:\n",
    "\n",
    "$$ P(X = k) = \\binom{n}{k}p^{k}(1-p)^{(n-k)} = \\frac{n!}{k!(n - k)!}p^{k}(1-p)^{(n-k)}$$\n",
    "\n",
    "<br>\n",
    "Os valores para o valor esperado e a variância para a distribuição Binomial serão respectivamente:\n",
    "\n",
    "- __Valor Esperado:__ $ E[X] = np $;\n",
    "\n",
    "- __Variância:__ $ V[X] = np(1-p)$."
   ]
  },
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "1    0.79958\n",
       "0    0.20042\n",
       "dtype: float64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series(np.random.binomial(1, 0.8, 100000)).value_counts(normalize=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "e008620d",
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "3    0.51386\n",
       "2    0.38361\n",
       "1    0.09473\n",
       "0    0.00780\n",
       "dtype: float64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series(np.random.binomial(3, 0.8, 100000)).value_counts(normalize=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db10e97e",
   "metadata": {},
   "source": [
    "__Exemplo:__ Em uma caixa há 8 bolas brancas e 4 pretas. Retira-se 5 bolas com reposição. Calcule a probabilidade de que:\n",
    "\n",
    "__A)__ saiam duas bolas brancas:"
   ]
  },
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   "execution_count": 12,
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   },
   "outputs": [],
   "source": [
    "from math import factorial\n",
    "\n",
    "\n",
    "def binomial(n, p, k):\n",
    "    C = (factorial(n) / (factorial(n - k) * factorial(k)))\n",
    "    return C * np.power(p, k) * np.power(1 - p, n - k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "3578f47d",
   "metadata": {
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     "end_time": "2023-02-28T00:42:40.337919Z",
     "start_time": "2023-02-28T00:42:40.316123Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A probabilidade será:  0.1646\n"
     ]
    }
   ],
   "source": [
    "# número de retiradas:\n",
    "n = 5\n",
    "\n",
    "# número de bolas brancas\n",
    "k = 2\n",
    "\n",
    "# probabilidade de uma bola branca\n",
    "p = 8/12\n",
    "\n",
    "# print do resultado teorico\n",
    "print(\"A probabilidade será: \", np.round(binomial(n, p, k), 4))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80f9cbe5",
   "metadata": {},
   "source": [
    "__B)__ saiam pelo menos 3 pretas:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "a13122e0",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-28T00:44:28.930919Z",
     "start_time": "2023-02-28T00:44:28.909731Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A probabilidade será:  0.2099\n"
     ]
    }
   ],
   "source": [
    "# numero de retiradas\n",
    "n = 5\n",
    "\n",
    "# probabilidade de uma bola preta\n",
    "p = 4/12\n",
    "\n",
    "# calculando a probabilidade acumulativa\n",
    "prop = 0\n",
    "for k in range(3, 6):\n",
    "    prop += binomial(n, p, k)\n",
    "\n",
    "# PRint da probabilidade\n",
    "print(\"A probabilidade será: \", np.round(prop, 4))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46b0cce8",
   "metadata": {},
   "source": [
    "## "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e5389eb",
   "metadata": {},
   "source": [
    "## Distribuição de Poisson"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "74a28c56",
   "metadata": {},
   "source": [
    "Uma variável aleatória tem distribuição de Poisson quando podemos descrever um evento em relação ao uma taxa/contagem de ocorrência, normalmente chamada de $ \\lambda $, sendo $ \\lambda > 0$. Dessa forma a equação para a distribuição de Poisson será definida como:\n",
    "\n",
    "$$ P(X = k) = \\frac{e^{-\\lambda}\\lambda^{k}}{k!} $$\n",
    "\n",
    "<br>\n",
    "Os valores para o valor esperado e a variância para a distribuição de Poisson serão respectivamente:\n",
    "\n",
    "- __Valor Esperado:__ $ E[X] = \\lambda $;\n",
    "\n",
    "- __Variância:__ $ V[X] = \\lambda$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16712ed5",
   "metadata": {},
   "source": [
    "__Exemplo:__ Em uma central telefônica chegam 300 ligações por hora. Sabendo que segue uma distribuição de Poisson, qual é a probabilidade de que:\n",
    "   \n",
    "__A)__ Em um minuto não ocorra ligações;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "537b7e4a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-28T00:50:01.167542Z",
     "start_time": "2023-02-28T00:50:01.148592Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(k = 0) =  0.006737946999085467\n"
     ]
    }
   ],
   "source": [
    "def Poisson(lbd, k):\n",
    "    return np.exp(-lbd) * (lbd**k) / factorial(k)\n",
    "\n",
    "lbd = 5 # 300 chamadas / 60 minutos = 5 chamadas por minuto\n",
    "\n",
    "# frequência procurada\n",
    "k = 0\n",
    "\n",
    "# print do resultado:\n",
    "print(\"P(k = 0) = \", Poisson(lbd,k))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1ec8942",
   "metadata": {},
   "source": [
    "__B)__ Em 2 minutos ocorram 2 chamadas;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "231db8eb",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-28T00:51:52.183491Z",
     "start_time": "2023-02-28T00:51:52.167299Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(k = 2) =  0.0022699964881242427\n"
     ]
    }
   ],
   "source": [
    "lbd = 10 # número de chamadas no intervalo de tempo de 2 min\n",
    "\n",
    "# frequencia procurada\n",
    "k = 2\n",
    "\n",
    "# print do resultado:\n",
    "print(\"P(k = 2) = \", Poisson(lbd,k))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8824e45e",
   "metadata": {},
   "source": [
    "C) 1 chamada em 1 minuto"
   ]
  },
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   "execution_count": 18,
   "id": "65e48fb9",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-28T00:54:49.965804Z",
     "start_time": "2023-02-28T00:54:49.953696Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(k = 1) =  0.03368973499542734\n"
     ]
    }
   ],
   "source": [
    "lbd = 5 # número de chamadas no intervalo de tempo de 1 min\n",
    "\n",
    "# frequencia procurada\n",
    "k = 1\n",
    "\n",
    "# print do resultado:\n",
    "print(\"P(k = 1) = \", Poisson(lbd,k))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a26860c",
   "metadata": {},
   "source": [
    "## Distribuição Exponencial"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa60e89b",
   "metadata": {},
   "source": [
    "Uma variável aleatória continua tem uma distribuição Exponencial quando queremos avaliar o tempo decorrido entre dois eventos consecutivos, diferente do Poisson que avalia de acordo com uma contagem de ocorrências em um espaço de tempo. A função densidade de probabilidade que descreve a distribuição exponencial pode ser descrita como:\n",
    "\n",
    "$$ f(x) = \\alpha e^{-\\alpha x}, x \\geq 0 $$\n",
    "\n",
    "No caso para $x < 0$, a probabilidade de $f(x) = 0$\n",
    "\n",
    "<br>\n",
    "Os valores para o valor esperado e a variância para a distribuição exponencial serão respectivamente:\n",
    "\n",
    "- __Valor Esperado:__ $ E[X] = \\frac{1}{\\alpha} $;\n",
    "\n",
    "- __Variância:__ $ V[X] = \\frac{1}{\\alpha^2}$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9df7300e",
   "metadata": {},
   "source": [
    "__Exemplo:__ O intervalo de tempo, em minutos, entre emissões consecutivas de uma fonte radioativa é uma variável aleatória contínua que segue uma distribuição exponencial com parâmetro $\\alpha = 0.2$. Qual a probabilidade de que ocorra uma emissão em um intervalo inferior a 2 minutos?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "a829ff2b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-28T00:56:25.780791Z",
     "start_time": "2023-02-28T00:56:25.766250Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Valor teórico da probabilidade é:  0.3297\n"
     ]
    }
   ],
   "source": [
    "# função de densidade exponencial\n",
    "def f3(x):\n",
    "    # Parametro alpha\n",
    "    alpha = 0.2\n",
    "    return alpha * np.exp(-alpha * x)\n",
    "\n",
    "\n",
    "# Integral da função de densidade\n",
    "prop, err2 = quad(f3, 0, 2)\n",
    "\n",
    "# Print da Probabilidade\n",
    "print(\"Valor teórico da probabilidade é: \", np.round(prop, 4))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b5c7e0a",
   "metadata": {},
   "source": [
    "## "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "755be7e4",
   "metadata": {},
   "source": [
    "## Distribuição Uniforme"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7505349e",
   "metadata": {},
   "source": [
    "A distribuição uniforme é uma distribuição bem simples e não possui parâmetros, a única diferença é que só vai haver probabilidade para um determinado exento $x$, se $x \\in [a, b]$. Dessa forma a equação de densidade de probabilidade para a distribuição uniforme é dado por:\n",
    "\n",
    "$$ f(x) = \\frac{1}{b - a}, a \\leq x \\leq b $$\n",
    "\n",
    "E para o caso de $x \\notin [a, b]$, a função de densidade será $f(x) = 0$\n",
    "\n",
    "<br>\n",
    "Os valores para o valor esperado e a variância para a distribuição exponencial serão respectivamente:\n",
    "\n",
    "- __Valor Esperado:__ $ E[X] = \\frac{a + b}{2} $;\n",
    "\n",
    "- __Variância:__ $ V[X] = \\frac{(b - a)^2}{12}$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "a6394f4c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-28T00:57:08.218089Z",
     "start_time": "2023-02-28T00:57:07.740563Z"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 100\n",
    "\n",
    "amostra_uniform = np.random.uniform(0, 1, N)\n",
    "\n",
    "sns.displot(amostra_uniform, kde=True)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "e2f5a01a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-28T00:57:51.423076Z",
     "start_time": "2023-02-28T00:57:50.924284Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 10000\n",
    "\n",
    "amostra_uniform = np.random.uniform(0, 1, N)\n",
    "\n",
    "sns.displot(amostra_uniform, kde=True)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "ac901f1c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-28T00:58:15.910512Z",
     "start_time": "2023-02-28T00:58:08.363055Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 1000000\n",
    "\n",
    "amostra_uniform = np.random.uniform(0, 1, N)\n",
    "\n",
    "sns.displot(amostra_uniform, kde=True)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7fc17e95",
   "metadata": {},
   "source": [
    "## "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84c19815",
   "metadata": {},
   "source": [
    "## Exercícios"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bed5d17d",
   "metadata": {},
   "source": [
    "__1)__ Em uma caixa há 7 bolas brancas, 4 pretas e 5 vermelhas. Retira-se 6 bolas com reposição. Calcule a probabilidade de que:\n",
    "\n",
    "__A)__ saiam 4 bolas vermelhas:\n",
    "\n",
    "__B)__ pelo menos 3 bolas brancas:\n",
    "\n",
    "__C)__ 1 ou 2 bolas pretas."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "840489b6",
   "metadata": {},
   "source": [
    "## "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1753989",
   "metadata": {},
   "source": [
    "__2)__ Em um livro de 800 páginas há 800 erros de impressão. Qual a probabilidade de que uma página contenha pelo menos 3 erros?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ed57c97",
   "metadata": {},
   "source": [
    "## "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1f55925",
   "metadata": {},
   "source": [
    "__3)__ Numa criação de coelhos, 45% são machos. Qual a probabilidade de nascerem pelo menos 5 coelhos machos num dia em que nasceram 15 coelhos?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "acd19444",
   "metadata": {},
   "source": [
    "## "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb5be6f8",
   "metadata": {},
   "source": [
    "__4)__ Numa estrada há 2 acidentes para cada 100 km. Qual a probabilidade de que em:\n",
    "\n",
    "__A)__ 250 km pelo menos 3 acidentes?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b32130a",
   "metadata": {},
   "source": [
    "__B)__ 300 km ocorram 5 acidentes?"
   ]
  }
 ],
 "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": "3.10.9"
  },
  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
    }
   },
   "types_to_exclude": [
    "module",
    "function",
    "builtin_function_or_method",
    "instance",
    "_Feature"
   ],
   "window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}