02-variable_aleatoria_uniforme.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# V.A Uniforme"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$P(X=x_i) = 1/N$\n",
    "\n",
    "N es la cantidad de salidas posibles del experimento"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ejemplo: \n",
    "\n",
    "Tirar un dado. \n",
    "\n",
    "N = 6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Momentos de una V.A uniforme"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\huge \\mu_x = \\frac{A + B}{2}$\n",
    "\n",
    "$\\huge \\sigma_x^2 = \\frac{(B-A + 1)^2 - 1}{12}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modelo de una V.A uniforme"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2, 1, 2, 4, 6, 3, 5, 4, 2, 4, 3, 1, 6, 5, 1, 5, 1, 1, 4, 1, 5, 1,\n",
       "       2, 2, 1, 3, 5, 6, 3, 5, 3, 6, 5, 6, 3, 2, 5, 6, 5, 1, 2, 6, 4, 5,\n",
       "       6, 1, 6, 2, 3, 3, 1, 1, 3, 6, 6, 2, 6, 4, 2, 6, 5, 2, 2, 1, 5, 6,\n",
       "       2, 5, 6, 3, 2, 6, 1, 1, 4, 1, 2, 5, 5, 3, 2, 5, 2, 1, 6, 5, 1, 1,\n",
       "       4, 6, 4, 3, 1, 5, 3, 4, 2, 2, 3, 4, 2, 5, 6, 4, 1, 2, 6, 2, 2, 6,\n",
       "       5, 5, 2, 4, 2, 5, 6, 4, 1, 2, 2, 2, 6, 2, 3, 2, 2, 4, 2, 1, 6, 1,\n",
       "       2, 5, 3, 3, 4, 6, 5, 4, 4, 6, 3, 3, 4, 5, 5, 2, 2, 2, 5, 6, 4, 1,\n",
       "       1, 3, 6, 3, 1, 5, 3, 4, 4, 5, 4, 3, 3, 1, 3, 3, 2, 6, 6, 4, 6, 3,\n",
       "       6, 4, 3, 2, 3, 3, 3, 4, 4, 5, 2, 6, 3, 2, 4, 1, 6, 3, 2, 5, 4, 4,\n",
       "       6, 4, 3, 4, 1, 6, 6, 5, 5, 6, 2, 2, 5, 6, 6, 1, 6, 3, 1, 1, 2, 6,\n",
       "       3, 3, 6, 2, 6, 2, 5, 4, 2, 5, 1, 1, 5, 5, 3, 6, 1, 3, 6, 4, 5, 2,\n",
       "       6, 5, 5, 5, 6, 4, 5, 6, 1, 1, 2, 3, 5, 6, 1, 4, 2, 5, 4, 6, 1, 6,\n",
       "       5, 3, 2, 3, 4, 4, 1, 1, 4, 3, 5, 3, 6, 4, 6, 1, 1, 2, 6, 1, 4, 3,\n",
       "       4, 6, 5, 3, 4, 5, 5, 5, 1, 2, 3, 2, 5, 4, 4, 6, 3, 4, 4, 2, 5, 1,\n",
       "       4, 1, 5, 2, 6, 6, 1, 4, 4, 5, 2, 1, 4, 1, 3, 6, 5, 5, 1, 4, 3, 6,\n",
       "       2, 1, 2, 1, 5, 5, 4, 4, 2, 5, 2, 3, 6, 1, 3, 1, 2, 3, 6, 1, 5, 1,\n",
       "       5, 3, 4, 5, 2, 5, 5, 3, 5, 4, 1, 2, 5, 4, 4, 4, 4, 1, 1, 6, 2, 1,\n",
       "       2, 1, 6, 3, 1, 5, 4, 4, 2, 1, 4, 2, 5, 2, 2, 4, 2, 6, 3, 5, 6, 6,\n",
       "       3, 1, 5, 5, 4, 4, 5, 4, 6, 5, 2, 1, 6, 1, 2, 5, 3, 1, 1, 4, 3, 2,\n",
       "       6, 4, 3, 1, 5, 6, 1, 4, 3, 6, 2, 5, 5, 2, 2, 5, 5, 4, 2, 6, 3, 5,\n",
       "       3, 4, 4, 5, 2, 1, 4, 2, 1, 3, 4, 6, 6, 4, 4, 4, 6, 6, 3, 3, 2, 2,\n",
       "       2, 5, 6, 6, 6, 5, 3, 4, 1, 4, 1, 4, 3, 6, 3, 4, 5, 5, 4, 2, 6, 1,\n",
       "       2, 4, 1, 1, 6, 5, 3, 6, 6, 1, 1, 2, 3, 2, 2, 3, 5, 1, 4, 3, 5, 5,\n",
       "       2, 6, 4, 3, 5, 2, 1, 4, 3, 1, 3, 3, 4, 5, 5, 3, 6, 2, 2, 5, 1, 5,\n",
       "       2, 5, 4, 5, 3, 3, 6, 3, 5, 3, 3, 1, 6, 1, 2, 6, 1, 6, 1, 4, 2, 2,\n",
       "       2, 1, 1, 1, 3, 5, 2, 5, 5, 6, 5, 4, 1, 2, 6, 3, 4, 1, 3, 2, 3, 1,\n",
       "       5, 4, 6, 2, 3, 3, 3, 6, 6, 6, 2, 5, 3, 3, 4, 3, 2, 6, 3, 5, 1, 4,\n",
       "       4, 5, 4, 3, 3, 2, 6, 5, 1, 6, 1, 4, 6, 5, 2, 5, 5, 4, 5, 4, 5, 2,\n",
       "       5, 6, 4, 1, 2, 3, 3, 2, 2, 4, 3, 6, 6, 4, 3, 3, 3, 2, 5, 5, 3, 2,\n",
       "       1, 6, 3, 5, 5, 4, 1, 4, 2, 6, 3, 2, 5, 3, 5, 1, 4, 5, 4, 4, 5, 1,\n",
       "       5, 2, 1, 5, 3, 4, 6, 1, 2, 4, 2, 6, 4, 2, 5, 2, 5, 5, 6, 2, 6, 1,\n",
       "       2, 3, 5, 5, 3, 4, 4, 6, 2, 2, 6, 2, 4, 5, 3, 6, 4, 6, 4, 2, 4, 6,\n",
       "       2, 1, 2, 5, 6, 2, 4, 4, 1, 6, 6, 2, 6, 3, 6, 5, 6, 3, 6, 4, 5, 3,\n",
       "       4, 2, 3, 4, 5, 2, 5, 5, 5, 5, 5, 3, 6, 2, 2, 5, 4, 1, 5, 6, 1, 1,\n",
       "       6, 1, 6, 2, 1, 3, 3, 3, 5, 4, 1, 2, 5, 6, 4, 4, 6, 2, 4, 3, 1, 1,\n",
       "       6, 1, 2, 4, 2, 2, 6, 3, 2, 3, 4, 5, 6, 5, 1, 3, 1, 5, 1, 2, 3, 6,\n",
       "       4, 6, 3, 5, 5, 1, 1, 5, 4, 5, 5, 2, 5, 5, 4, 6, 4, 5, 5, 6, 1, 4,\n",
       "       1, 4, 1, 1, 2, 1, 5, 3, 3, 1, 6, 2, 4, 1, 4, 5, 2, 4, 6, 4, 2, 1,\n",
       "       5, 4, 1, 3, 6, 1, 3, 3, 4, 1, 4, 1, 5, 3, 6, 5, 2, 2, 5, 5, 3, 4,\n",
       "       6, 5, 2, 6, 2, 4, 3, 5, 1, 1, 4, 1, 3, 5, 1, 3, 4, 2, 1, 5, 3, 5,\n",
       "       6, 6, 1, 3, 4, 2, 5, 2, 5, 3, 3, 5, 1, 3, 6, 2, 6, 1, 3, 2, 4, 2,\n",
       "       3, 6, 3, 5, 6, 1, 3, 6, 5, 1, 4, 2, 4, 2, 3, 4, 2, 2, 2, 6, 5, 4,\n",
       "       1, 2, 4, 4, 1, 6, 6, 2, 3, 1, 4, 1, 4, 5, 1, 1, 5, 4, 6, 1, 3, 2,\n",
       "       3, 6, 5, 1, 2, 6, 3, 3, 6, 3, 3, 4, 1, 3, 6, 3, 6, 1, 2, 2, 2, 1,\n",
       "       5, 5, 2, 2, 1, 1, 3, 5, 2, 2, 6, 6, 4, 5, 5, 2, 3, 1, 1, 5, 2, 1,\n",
       "       6, 4, 6, 6, 1, 1, 5, 1, 1, 2])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.randint(1,7, 1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cuando vale la entropia?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$S = - \\sum_{i=1}^N{P_i log(P_i)}$\n",
    "\n",
    "$S = - \\sum_{i=1}^N{1/N log(1/N)} = - log(1/N) = log(N)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si normalizo por logaritmo de la cantidad de salidas posibles N\n",
    "\n",
    "$S_N = 1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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