01-Moedas.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy import stats as ss\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "plt.ion()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1 - Moedas Justa com a Binomial\n",
    "\n",
    "Vamos explorar a probabilidade de uma moeda ser justa usando estatística e amostragem (conceitos não exclusivos).\n",
    "Lembrando, temos um espaço amostral:\n",
    "\n",
    "\\begin{align}\n",
    "\\mathcal{S} &= \\{h, t\\} \\\\\n",
    "P(h) &= 0.5 \\\\\n",
    "P(t) &= 0.5\n",
    "\\end{align}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "p = 0.5 # probabilidade de heads/tails\n",
    "n = 30  # temos 33 jogadas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,\n",
       "       17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(0, 31)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10e950dd8>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10439fc88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = 0.5 # probabilidade de heads/tails\n",
    "n = 30  # temos 33 jogadas\n",
    "x = np.arange(0, 31)\n",
    "prob_binom = ss.distributions.binom.pmf(x, n, p)\n",
    "plt.step(x, prob_binom, 'r-')\n",
    "plt.xlabel('Num Caras - x')\n",
    "plt.ylabel('P(sair x caras)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0080624008551239308"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ss.distributions.binom.pmf(22, n, p) + \\\n",
    "ss.distributions.binom.pmf(23, n, p) + \\\n",
    "ss.distributions.binom.pmf(24, n, p) + \\\n",
    "ss.distributions.binom.pmf(25, n, p) + \\\n",
    "ss.distributions.binom.pmf(26, n, p) + \\\n",
    "ss.distributions.binom.pmf(27, n, p) + \\\n",
    "ss.distributions.binom.pmf(28, n, p) + \\\n",
    "ss.distributions.binom.pmf(29, n, p) + \\\n",
    "ss.distributions.binom.pmf(30, n, p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([22, 23, 24, 25, 26, 27, 28, 29, 30])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_extreme = np.arange(22, 31)\n",
    "x_extreme"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0080624008551239291"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ss.distributions.binom.pmf(x_extreme, n, p).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2 - Moedas Justas Simulando\n",
    "\n",
    "Vamos simular sem se preocupar com uma binomial. Só jogar uma moeda para cima várias vezes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Jogando uma única moeda\n",
    "np.random.randint(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1,\n",
       "       1, 0, 1, 1, 0, 1, 1])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Jogando 30 moedas\n",
    "np.random.randint(2, size=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.00824\n"
     ]
    }
   ],
   "source": [
    "NUM_SIMULACOES = 100000\n",
    "resultados = 0\n",
    "n = 30\n",
    "for i in range(NUM_SIMULACOES):\n",
    "    jogadas = np.random.randint(2, size=n) # joga 30 moedas para cima\n",
    "    n_caras = (jogadas == 1).sum()         # conta quantas foram == 1, caras\n",
    "    if n_caras >= 22:\n",
    "        resultados += 1                    # quantas vezes vi >= 22 caras\n",
    "print(resultados / NUM_SIMULACOES)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3 Caso onde Batman está certo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x111caf2b0>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYwAAAEKCAYAAAAB0GKPAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n8nPQtQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e91ba20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = 0.9 # probabilidade de heads/tails\n",
    "n = 30  # temos 33 jogadas\n",
    "x = np.arange(0, 31)\n",
    "prob_binom = ss.distributions.binom.pmf(x, n, p)\n",
    "plt.step(x, prob_binom, 'r-')\n",
    "plt.xlabel('Num Caras - x')\n",
    "plt.ylabel('P(sair x caras)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.99784\n"
     ]
    }
   ],
   "source": [
    "NUM_SIMULACOES = 100000\n",
    "resultados = 0\n",
    "n = 30\n",
    "for i in range(NUM_SIMULACOES):\n",
    "    jogadas = np.random.rand(30) < 0.9\n",
    "    n_caras = (jogadas == 1).sum()\n",
    "    if n_caras >= 22:\n",
    "        resultados += 1\n",
    "print(resultados / NUM_SIMULACOES)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4 Tem vezes que precisamos testar a coroa também"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x111dd5f98>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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lvaVu+4iqrP4bERGNZEQSERGNJJFEREQjSSQREdFIEklERDSSRBIREY0kkURE\nRCNJJBER0UgSSURENPL/AUdzh4l4XrGYAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111d7b080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = 0.2 # probabilidade de heads/tails\n",
    "n = 30  # temos 33 jogadas\n",
    "x = np.arange(0, 31)\n",
    "prob_binom = ss.distributions.binom.pmf(x, n, p)\n",
    "plt.step(x, prob_binom, 'r-')\n",
    "plt.xlabel('Num Caras - x')\n",
    "plt.ylabel('P(sair x caras)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:anaconda3]",
   "language": "python",
   "name": "conda-env-anaconda3-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}