{
 "cells": [
  {
   "cell_type": "markdown",
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   "source": [
    "# IntroStat Week 4 \n",
    "\n",
    "Simulation of the Central Limit Theorem (by examples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data from a uniform distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "n=10\n",
    "k=1000\n",
    "u = stats.uniform.rvs(loc=0, scale=30, size=(n,k))\n",
    "\n",
    "mean_values = u.mean(axis=0)\n",
    "\n",
    "plt.hist(mean_values, density=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now increase n to 2,3,6,30"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data from an exponential distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "n=30\n",
    "k=1000\n",
    "u = stats.expon.rvs(loc=0, scale=30, size=(n,k))\n",
    "mean_values = u.mean(axis=0)\n",
    "\n",
    "plt.hist(mean_values, density=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now increase n to 2,3,6,30"
   ]
  }
 ],
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