03-variable-aleatoria-categorica.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# V.A Categorica"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Cada una de las N posibles salidas tiene un valor de probabilidad específico\n",
    "- La forma mas usual de definirla es a través de un histograma\n",
    "- Este tipo de representación se llama no paramétrica debido a que la V.A no queda definida con unos pocos parámetros sino que hay que definirla explicitamente"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ejemplos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Usaremos un diccionario en python para definirla\n",
    "X = {1: 0.1, 2: 0.3, 3: 0.5, 4:0.1}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Verificamos que la suma sea 1\n",
    "sum(X.values())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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6JDXi/wCr//k7mLx9CwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.bar(X.keys(), X.values())\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3862943611198906"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.log(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cálculo de momentos y entropía de una V.A categórica"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mean(X):\n",
    "    m = 0\n",
    "    for x, p in X.items():\n",
    "        m = m + x*p\n",
    "    return m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.6"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def variance(X):\n",
    "    m = mean(X)\n",
    "    v = 0\n",
    "    for x, p in X.items():\n",
    "        v = v + (x-m)**2*p\n",
    "    return v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "variance(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def entropy(X, normalize = True):\n",
    "    e = 0\n",
    "    for _, p in X.items():\n",
    "        e = e - np.log(p)* p\n",
    "    if normalize:\n",
    "        e = e/np.log(len(X))\n",
    "    else:\n",
    "        e = e/np.log(2)\n",
    "    return e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6079067132126817"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "entropy(X, normalize=True)/np.log(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Que idea intuitiva nos da la varianza o el desvio estandard? y la entropía?\n",
    "### Cual es mejor medida para la incertidumbre?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def analize_VA(X, normalize=True):\n",
    "    #assert sum(X.values()) == 1\n",
    "    plt.bar(X.keys(), X.values())\n",
    "    plt.show()\n",
    "    print('Media:', mean(X))\n",
    "    if normalize:\n",
    "        print('Entropía normalizada:', entropy(X, normalize=normalize))\n",
    "    else:\n",
    "        print('Entropía:', entropy(X, normalize=normalize))\n",
    "    print('Varianza:', variance(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Media: 2.02\n",
      "Entropía normalizada: 0.3087715616560074\n",
      "Varianza: 0.15960000000000002\n"
     ]
    }
   ],
   "source": [
    "X_1 = {1: 0.05, 2: 0.9, 3: 0.03, 4:0.02}\n",
    "analize_VA(X_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Media: 2.5\n",
      "Entropía normalizada: 1.0\n",
      "Varianza: 1.25\n"
     ]
    }
   ],
   "source": [
    "X_2 = {1: 0.25, 2: 0.25, 3: 0.25, 4:0.25}\n",
    "analize_VA(X_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Media: 1.0449999999999997\n",
      "Entropía normalizada: 0.030891008405092145\n",
      "Varianza: 0.282975\n"
     ]
    }
   ],
   "source": [
    "X_3 = {1: 0.991, 2: 0.001, 3: 0.001, 4:0.001, 5:0.001, 6:0.001, 7:0.001, 8:0.001, 9:0.001, 10:0.001}\n",
    "analize_VA(X_3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Media: 5.500000000000001\n",
      "Entropía normalizada: 0.9999999999999998\n",
      "Varianza: 8.25\n"
     ]
    }
   ],
   "source": [
    "X_4 = {1: 0.1, 2: 0.1, 3: 0.1, 4:0.1, 5:0.1, 6:0.1, 7:0.1, 8:0.1, 9:0.1, 10:0.1}\n",
    "analize_VA(X_4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Media: 5.4910000000000005\n",
      "Entropía normalizada: 0.32608130132741736\n",
      "Varianza: 20.129919\n"
     ]
    }
   ],
   "source": [
    "X_5 = {1: 0.497, 2: 0.001, 3: 0.001, 4:0.001, 5:0.001, 6:0.001, 7:0.001, 8:0.001, 9:0.001, 10:0.495}\n",
    "analize_VA(X_5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Intuición de la entropía"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Media: 2.5\n",
      "Entropía: 2.0\n",
      "Varianza: 1.25\n"
     ]
    }
   ],
   "source": [
    "X = {1: 0.25, 2: 0.25, 3: 0.25, 4:0.25}\n",
    "analize_VA(X, normalize=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dado que realicé el experimento y tengo que adivinar cual fue la observación:\n",
    "\n",
    "¿Cúal es la cantidad de preguntas promedio que deberia hacer para adivinar la salida?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Es mayor a 2.5?  \n",
    "- si -> Es 3?  \n",
    "- No -> Es 1?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Con dos preguntas encuentro resultado"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Media: 4.5\n",
      "Entropía: 3.0\n",
      "Varianza: 5.25\n"
     ]
    }
   ],
   "source": [
    "X = {1: 0.125, 2: 0.125, 3: 0.125, 4:0.125, 5: 0.125, 6: 0.125, 7: 0.125, 8:0.125}\n",
    "analize_VA(X, normalize=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Es mayor a 4.5?\n",
    "- si -> Es mayor a 6.5?:\n",
    "    - Si -> es 7?\n",
    "    - No -> es 5?\n",
    "- no -> Es menor a 2.5?:\n",
    "    - Si -> es 1?\n",
    "    - No -> es 3?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD8CAYAAACMwORRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAADj9JREFUeJzt3X+s3fVdx/HnixacERyJvUZCW4qxS6xkCt5UDImiw6Qw0/4hmpLMyYJrouI0LBqmplP8R7fEmSmKVcl+6GAVzaxYUn+MZcYIUsYPKbXmWlFuSkLHGHPBDatv/zgHPDuc2/O9957e790nz0dyku+PT8958bmcV7/3e87321QVkqS2nNd3AEnS7FnuktQgy12SGmS5S1KDLHdJapDlLkkNstwlqUGWuyQ1yHKXpAZt7OuFN23aVNu2bevr5SXpq9Kjjz762aqamzaut3Lftm0bR48e7evlJemrUpJ/7zLO0zKS1CDLXZIaZLlLUoMsd0lqkOUuSQ2aWu5J7k7yfJKnltifJB9MspDkySRXzT6mJGk5uhy5fwjYdZb91wPbh499wO+uPpYkaTWmlntVfRr43FmG7AE+UgMPARcnuWRWASVJyzeLc+6XAs+OrC8Ot0mSejKLK1QzYdvEf3U7yT4Gp27YunXril9w2+1/ueI/24Jnfu2tfUeQtM7N4sh9Edgysr4ZODVpYFUdqKr5qpqfm5t6awRJ0grNotwPAW8ffmvmauClqnpuBs8rSVqhqadlktwDXAtsSrIIvBc4H6Cq7gIOAzcAC8DLwDvOVVhJUjdTy72qbpqyv4CfmlkiSdKqeYWqJDXIcpekBlnuktQgy12SGmS5S1KDLHdJapDlLkkNstwlqUGWuyQ1yHKXpAZZ7pLUIMtdkhpkuUtSgyx3SWqQ5S5JDbLcJalBlrskNchyl6QGWe6S1CDLXZIaZLlLUoMsd0lqkOUuSQ2y3CWpQZa7JDXIcpekBlnuktQgy12SGmS5S1KDLHdJapDlLkkNstwlqUGdyj3JriQnkiwkuX3C/q1JHkzyWJInk9ww+6iSpK6mlnuSDcCdwPXADuCmJDvGhv0ScLCqrgT2Ar8z66CSpO66HLnvBBaq6mRVvQLcC+wZG1PA1w+X3wicml1ESdJybeww5lLg2ZH1ReC7xsb8MvBXSX4a+DrgupmkkyStSJcj90zYVmPrNwEfqqrNwA3AR5O87rmT7EtyNMnR06dPLz+tJKmTLuW+CGwZWd/M60+73AIcBKiqfwDeAGwaf6KqOlBV81U1Pzc3t7LEkqSpupT7I8D2JJcnuYDBB6aHxsb8B/AWgCTfyqDcPTSXpJ5MLfeqOgPcChwBjjP4VsyxJHck2T0c9m7gnUmeAO4Bbq6q8VM3kqQ10uUDVarqMHB4bNv+keWngWtmG02StFJeoSpJDbLcJalBlrskNchyl6QGWe6S1CDLXZIaZLlLUoMsd0lqkOUuSQ2y3CWpQZa7JDXIcpekBlnuktQgy12SGmS5S1KDLHdJapDlLkkNstwlqUGWuyQ1yHKXpAZZ7pLUIMtdkhpkuUtSgyx3SWqQ5S5JDbLcJalBlrskNchyl6QGWe6S1CDLXZIaZLlLUoMsd0lqkOUuSQ3qVO5JdiU5kWQhye1LjPmRJE8nOZbkY7ONKUlajo3TBiTZANwJ/ACwCDyS5FBVPT0yZjvwHuCaqnoxyTeeq8CSpOm6HLnvBBaq6mRVvQLcC+wZG/NO4M6qehGgqp6fbUxJ0nJ0KfdLgWdH1heH20a9CXhTkr9P8lCSXbMKKElavqmnZYBM2FYTnmc7cC2wGfi7JFdU1ee/4omSfcA+gK1bty47rCSpmy5H7ovAlpH1zcCpCWP+vKr+u6r+DTjBoOy/QlUdqKr5qpqfm5tbaWZJ0hRdyv0RYHuSy5NcAOwFDo2N+QTwfQBJNjE4TXNylkElSd1NLfeqOgPcChwBjgMHq+pYkjuS7B4OOwK8kORp4EHg56rqhXMVWpJ0dl3OuVNVh4HDY9v2jywXcNvwIUnqmVeoSlKDLHdJapDlLkkNstwlqUGWuyQ1yHKXpAZZ7pLUIMtdkhpkuUtSgyx3SWqQ5S5JDbLcJalBlrskNchyl6QGWe6S1CDLXZIaZLlLUoMsd0lqkOUuSQ2y3CWpQZa7JDXIcpekBlnuktQgy12SGmS5S1KDLHdJapDlLkkNstwlqUGWuyQ1yHKXpAZZ7pLUIMtdkhrUqdyT7EpyIslCktvPMu7GJJVkfnYRJUnLNbXck2wA7gSuB3YANyXZMWHcRcC7gIdnHVKStDxdjtx3AgtVdbKqXgHuBfZMGPerwPuAL80wnyRpBbqU+6XAsyPri8Ntr0lyJbClqu6fYTZJ0gp1KfdM2Fav7UzOAz4AvHvqEyX7khxNcvT06dPdU0qSlqVLuS8CW0bWNwOnRtYvAq4APpXkGeBq4NCkD1Wr6kBVzVfV/Nzc3MpTS5LOqku5PwJsT3J5kguAvcChV3dW1UtVtamqtlXVNuAhYHdVHT0niSVJU00t96o6A9wKHAGOAwer6liSO5LsPtcBJUnLt7HLoKo6DBwe27Z/ibHXrj6WJGk1vEJVkhpkuUtSgyx3SWqQ5S5JDbLcJalBlrskNchyl6QGWe6S1CDLXZIaZLlLUoMsd0lqkOUuSQ2y3CWpQZa7JDXIcpekBlnuktQgy12SGmS5S1KDLHdJapDlLkkNstwlqUGWuyQ1yHKXpAZZ7pLUIMtdkhpkuUtSgyx3SWqQ5S5JDbLcJalBlrskNchyl6QGWe6S1CDLXZIa1Knck+xKciLJQpLbJ+y/LcnTSZ5M8rdJLpt9VElSV1PLPckG4E7gemAHcFOSHWPDHgPmq+rNwH3A+2YdVJLUXZcj953AQlWdrKpXgHuBPaMDqurBqnp5uPoQsHm2MSVJy9Gl3C8Fnh1ZXxxuW8otwAOTdiTZl+RokqOnT5/unlKStCxdyj0TttXEgcnbgHng/ZP2V9WBqpqvqvm5ubnuKSVJy7Kxw5hFYMvI+mbg1PigJNcBvwh8b1V9eTbxJEkr0eXI/RFge5LLk1wA7AUOjQ5IciXwe8Duqnp+9jElScsxtdyr6gxwK3AEOA4crKpjSe5Isns47P3AhcCfJHk8yaElnk6StAa6nJahqg4Dh8e27R9Zvm7GuSRJq+AVqpLUIMtdkhpkuUtSgyx3SWqQ5S5JDbLcJalBlrskNchyl6QGWe6S1CDLXZIaZLlLUoMsd0lqkOUuSQ2y3CWpQZa7JDXIcpekBlnuktQgy12SGmS5S1KDLHdJapDlLkkNstwlqUGWuyQ1yHKXpAZZ7pLUIMtdkhpkuUtSgyx3SWqQ5S5JDbLcJalBlrskNchyl6QGdSr3JLuSnEiykOT2Cfu/JsnHh/sfTrJt1kElSd1NLfckG4A7geuBHcBNSXaMDbsFeLGqvgX4APDrsw4qSequy5H7TmChqk5W1SvAvcCesTF7gA8Pl+8D3pIks4spSVqOLuV+KfDsyPricNvEMVV1BngJ+IZZBJQkLd/GDmMmHYHXCsaQZB+wb7j6xSQnlnjNTcBnO2TrS6/5Mv2kl/O3Ous9H6z/jOZbnbPlu6zLE3Qp90Vgy8j6ZuDUEmMWk2wE3gh8bvyJquoAcGDaCyY5WlXzHbL1wnyrY77VW+8Zzbc6s8jX5bTMI8D2JJcnuQDYCxwaG3MI+LHh8o3AJ6vqdUfukqS1MfXIvarOJLkVOAJsAO6uqmNJ7gCOVtUh4A+BjyZZYHDEvvdchpYknV2X0zJU1WHg8Ni2/SPLXwJ+eIa5pp666Zn5Vsd8q7feM5pvdVadL549kaT2ePsBSWpQr+Xe4bYGNyc5neTx4ePH1zjf3UmeT/LUEvuT5IPD/E8muWqd5bs2yUsj87d/0rhzlG1LkgeTHE9yLMnPTBjT2/x1zNfn/L0hyT8meWKY71cmjOntth8d8/X6/h1m2JDksST3T9jX+21TpuRb3fxVVS8PBh/O/ivwzcAFwBPAjrExNwO/3WPG7wGuAp5aYv8NwAMMvud/NfDwOst3LXB/T3N3CXDVcPki4F8m/Hx7m7+O+fqcvwAXDpfPBx4Grh4b85PAXcPlvcDH11m+Xt+/wwy3AR+b9HPsc/465lvV/PV55N7ltga9qqpPM+H7+iP2AB+pgYeAi5NcsjbpOuXrTVU9V1WfGS7/J3Cc11/Z3Nv8dczXm+GcfHG4ev7wMf4BWW+3/eiYr1dJNgNvBf5giSG93jalQ75V6bPcu9zWAOCHhr+y35dky4T9fer639Cn7x7+6vxAkm/rI8Dw190rGRzdjVoX83eWfNDj/A1/ZX8ceB7466pacv6qh9t+dMgH/b5/fxP4eeB/l9jf921TpuWDVcxfn+Xe5ZYFfwFsq6o3A3/D//8tu150uu1Cjz4DXFZV3w78FvCJtQ6Q5ELgT4GfraovjO+e8EfWdP6m5Ot1/qrqf6rqOxhcFb4zyRVjQ3qdvw75env/JvlB4PmqevRswyZsW5P565hvVfPXZ7lPva1BVb1QVV8erv4+8J1rlK2rLrdm6E1VfeHVX51rcK3C+Uk2rdXrJzmfQXH+cVX92YQhvc7ftHx9z99Ijs8DnwJ2je16bf5yltt+nGtL5ev5/XsNsDvJMwxO+X5/kj8aG9Pn/E3Nt9r567Pcp97WYOz8624G50XXk0PA24ff+rgaeKmqnus71KuSfNOr5xCT7GTw835hjV47DK5cPl5Vv7HEsN7mr0u+nudvLsnFw+WvBa4D/nlsWG+3/eiSr8/3b1W9p6o2V9U2Bt3yyap629iw3uavS77Vzl+nK1TPhep2W4N3JdkNnGHwN+rNa5kxyT0MvjGxKcki8F4GHxxRVXcxuGr3BmABeBl4xzrLdyPwE0nOAP8F7F2r/3kZHJn8KPBPw/OyAL8AbB3J1+f8dcnX5/xdAnw4g38s5zzgYFXdn/Vz248u+Xp9/06yjuZvolnOn1eoSlKDvEJVkhpkuUtSgyx3SWqQ5S5JDbLcJalBlrskNchyl6QGWe6S1KD/A68IDYVZXy6VAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Media: 1.0000001385\n",
      "Entropía: 1.0205288417267646e-06\n",
      "Varianza: 3.134999890169505e-07\n"
     ]
    }
   ],
   "source": [
    "# Caso extremo:\n",
    "X = {1: 0.99999999, 2: 0.0000000033, 3: 0.0000000033, 4: 0.000000033}\n",
    "analize_VA(X, normalize=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cuantas preguntas necesito hacer para adivinar?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Media: 1.875\n",
      "Entropía: 1.75\n",
      "Varianza: 1.109375\n"
     ]
    }
   ],
   "source": [
    "X = {1: 0.5, 2: 0.25, 3: 0.125, 4:0.125}\n",
    "analize_VA(X, normalize=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Es 1?\n",
    "- Si -> Resuelto\n",
    "- No -> Es 2?\n",
    "    - Si -> Resuelto\n",
    "    - No -> Es 3?\n",
    "        - Si o No Resuelto"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.75"
      ]
     },
     "execution_count": 202,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 * 0.5 + 2 * 0.25 + 3 * 0.125 + 3 * 0.125"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modelo generador de una V.A Categórica"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = {1: 0.1, 2: 0.3, 3: 0.5, 4:0.1}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(dict_keys([1, 2, 3, 4]), dict_values([0.1, 0.3, 0.5, 0.1]))"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.keys(), X.values()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "observaciones = np.random.choice(list(X.keys()), size = 1000, p = list(X.values()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 3, 3, 2, 4, 3, 1, 2, 3, 2, 1, 4, 2, 2, 2, 3, 1, 2, 3, 3, 3, 2,\n",
       "       3, 3, 4, 3, 4, 3, 3, 3, 3, 1, 4, 3, 1, 2, 3, 3, 3, 4, 4, 3, 3, 3,\n",
       "       3, 3, 1, 1, 3, 2, 4, 2, 2, 3, 3, 3, 3, 3, 1, 2, 3, 3, 3, 4, 3, 1,\n",
       "       3, 3, 2, 2, 3, 2, 3, 1, 3, 3, 3, 2, 2, 3, 2, 2, 3, 3, 3, 2, 1, 1,\n",
       "       1, 2, 3, 3, 3, 2, 3, 2, 2, 3, 3, 3, 4, 3, 3, 3, 3, 2, 3, 3, 3, 2,\n",
       "       3, 3, 3, 4, 3, 3, 3, 4, 4, 3, 3, 3, 3, 2, 3, 2, 2, 4, 3, 2, 1, 2,\n",
       "       3, 2, 4, 4, 2, 3, 4, 3, 3, 2, 3, 3, 1, 2, 2, 1, 3, 2, 3, 3, 3, 1,\n",
       "       3, 1, 3, 2, 3, 1, 1, 2, 3, 2, 3, 4, 3, 3, 2, 3, 2, 3, 4, 3, 3, 2,\n",
       "       3, 2, 2, 3, 2, 3, 2, 2, 2, 2, 1, 3, 3, 3, 2, 3, 2, 2, 3, 3, 3, 3,\n",
       "       2, 3, 3, 2, 3, 3, 1, 1, 1, 3, 4, 2, 2, 1, 3, 2, 4, 1, 3, 1, 2, 3,\n",
       "       3, 1, 2, 3, 2, 3, 2, 2, 3, 3, 2, 4, 3, 2, 3, 2, 3, 3, 3, 3, 2, 3,\n",
       "       3, 4, 2, 2, 2, 3, 3, 2, 3, 4, 2, 2, 2, 1, 2, 3, 3, 2, 1, 3, 3, 3,\n",
       "       3, 3, 2, 3, 2, 2, 2, 3, 2, 3, 3, 2, 1, 1, 3, 3, 2, 2, 2, 2, 3, 3,\n",
       "       3, 3, 3, 3, 1, 3, 3, 3, 2, 4, 2, 1, 2, 3, 2, 3, 3, 2, 1, 3, 3, 2,\n",
       "       3, 2, 3, 2, 2, 2, 3, 3, 2, 3, 2, 3, 3, 3, 4, 3, 3, 3, 3, 2, 3, 4,\n",
       "       3, 3, 3, 3, 3, 2, 3, 2, 3, 1, 3, 4, 1, 4, 2, 3, 3, 3, 3, 2, 3, 3,\n",
       "       2, 2, 2, 3, 3, 3, 2, 2, 3, 1, 2, 2, 3, 4, 1, 2, 2, 3, 4, 2, 3, 4,\n",
       "       3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 4, 2, 2, 2, 2, 4, 1, 3, 3, 4, 3,\n",
       "       2, 2, 4, 3, 2, 2, 2, 2, 1, 3, 3, 3, 3, 3, 3, 2, 2, 1, 3, 1, 3, 2,\n",
       "       4, 3, 3, 3, 2, 3, 2, 2, 4, 3, 3, 3, 3, 2, 2, 1, 3, 3, 1, 2, 4, 1,\n",
       "       3, 2, 2, 3, 3, 2, 3, 2, 3, 4, 3, 3, 4, 1, 2, 1, 3, 3, 4, 2, 2, 2,\n",
       "       3, 3, 3, 4, 3, 2, 3, 1, 3, 3, 4, 4, 2, 2, 2, 3, 2, 3, 2, 2, 2, 4,\n",
       "       3, 3, 3, 2, 3, 3, 3, 2, 2, 1, 3, 3, 3, 3, 3, 3, 3, 2, 3, 1, 2, 3,\n",
       "       4, 1, 3, 3, 1, 3, 3, 2, 1, 3, 2, 3, 3, 1, 2, 3, 1, 3, 2, 3, 3, 3,\n",
       "       3, 4, 3, 3, 2, 3, 3, 4, 3, 3, 4, 3, 3, 3, 3, 3, 2, 3, 1, 3, 4, 2,\n",
       "       2, 3, 3, 2, 2, 1, 2, 4, 4, 3, 3, 2, 2, 3, 3, 2, 1, 3, 3, 2, 2, 4,\n",
       "       3, 1, 1, 3, 2, 2, 2, 3, 2, 3, 4, 2, 1, 1, 3, 2, 4, 4, 2, 2, 2, 4,\n",
       "       2, 3, 2, 1, 3, 3, 3, 4, 3, 2, 2, 2, 2, 3, 4, 2, 2, 2, 2, 1, 1, 2,\n",
       "       4, 3, 2, 2, 1, 4, 3, 3, 3, 2, 2, 2, 4, 1, 3, 3, 3, 3, 3, 2, 3, 3,\n",
       "       1, 3, 3, 3, 3, 3, 3, 3, 2, 4, 3, 1, 2, 2, 4, 3, 1, 3, 2, 3, 2, 4,\n",
       "       3, 1, 2, 3, 3, 2, 2, 1, 3, 3, 3, 1, 4, 3, 3, 2, 4, 4, 4, 4, 3, 2,\n",
       "       3, 2, 4, 3, 3, 4, 3, 2, 3, 2, 3, 2, 1, 3, 2, 2, 3, 3, 2, 4, 3, 3,\n",
       "       3, 3, 4, 3, 2, 4, 2, 3, 2, 3, 3, 3, 3, 3, 2, 3, 1, 3, 2, 2, 3, 3,\n",
       "       2, 2, 1, 3, 1, 3, 2, 3, 3, 4, 3, 2, 3, 3, 3, 2, 1, 1, 3, 2, 3, 2,\n",
       "       3, 2, 2, 4, 3, 2, 3, 2, 2, 3, 2, 3, 3, 3, 4, 4, 1, 4, 2, 3, 1, 3,\n",
       "       2, 4, 4, 3, 1, 1, 3, 3, 2, 3, 4, 3, 1, 3, 1, 3, 1, 4, 3, 3, 3, 2,\n",
       "       1, 3, 3, 4, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 4, 2,\n",
       "       2, 3, 1, 3, 2, 3, 3, 3, 3, 2, 2, 2, 1, 3, 2, 2, 4, 2, 2, 2, 2, 2,\n",
       "       2, 4, 1, 2, 3, 3, 3, 1, 2, 2, 2, 3, 3, 2, 2, 2, 3, 1, 3, 3, 3, 3,\n",
       "       3, 2, 4, 4, 3, 2, 3, 2, 3, 3, 3, 2, 4, 3, 3, 4, 3, 2, 3, 3, 3, 1,\n",
       "       3, 3, 3, 3, 3, 3, 1, 2, 2, 3, 1, 3, 3, 2, 2, 3, 4, 2, 3, 2, 3, 4,\n",
       "       3, 1, 2, 3, 2, 2, 3, 3, 1, 2, 2, 3, 2, 3, 2, 4, 3, 3, 4, 3, 2, 3,\n",
       "       3, 4, 3, 3, 3, 2, 3, 4, 1, 3, 2, 3, 3, 1, 2, 3, 2, 3, 2, 1, 1, 2,\n",
       "       1, 1, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 3, 2, 3, 3, 3, 3, 3, 3, 2,\n",
       "       3, 3, 3, 3, 2, 3, 1, 3, 3, 2, 2, 2, 3, 3, 3, 2, 2, 1, 2, 3, 3, 1,\n",
       "       2, 3, 2, 4, 3, 2, 3, 2, 1, 2])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "observaciones"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Estimar la función de masa de probabilidad de las observaciones"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Counter({3: 489, 2: 303, 4: 100, 1: 108})"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from collections import Counter\n",
    "Counter(observaciones)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Histograma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([108, 303, 489, 100]), array([1., 2., 3., 4., 5.]))"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.histogram(observaciones, bins=4, range=[1,5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tener en cuenta que toma como primer intervalo [1, 2), como segundo [2,3), y asi hasta el ultimo [4, 5)\n",
    "\n",
    "donde \"[\" es incluido y \")\" es excluido"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist = plt.hist(observaciones, bins=4, range=[1,5], width=0.9, density=True) # normed='density')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0.108, 0.303, 0.489, 0.1  ]),\n",
       " array([1., 2., 3., 4., 5.]),\n",
       " <a list of 4 Patch objects>)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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6JDXi/wCr//k7mLx9CwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Media: 2.6\n",
      "Entropía normalizada: 0.8427376486136672\n",
      "Varianza: 0.64\n"
     ]
    }
   ],
   "source": [
    "# Esta es la Ground Truth\n",
    "analize_VA(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}