{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tutorial A13 – Solutions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__1__ Modify the coinflip section from lesson A13 to simulate throwing a dice. Throw the dice 100 times and save the outcomes $X_i$ with $i = 1, ... , N$ in a list. Plot the result as a histogram."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import random\n",
    "\n",
    "\n",
    "mpl.rc_file(\n",
    "    \"../../matplotlibrc\",\n",
    "    use_default_template=False\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'counts')"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x741 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "random.seed(1)\n",
    "\n",
    "def throw_n_times(n):\n",
    "    \"\"\"Throw a dice n times\n",
    "    \n",
    "    Returns:\n",
    "        List of outcomes\n",
    "    \"\"\"\n",
    "\n",
    "    throws = []  # Outcomes\n",
    "    for _ in range(n):        \n",
    "        # Draw a random number\n",
    "        random_number = random.random()\n",
    "\n",
    "        # We want all outcomes to be equally likely \n",
    "        # The following lines assign the random number to either outcome\n",
    "\n",
    "        # Integer just truncated after the decimal point is used like the ceil function here\n",
    "        outcome = int(random_number * 6 + 1)\n",
    "        \n",
    "        # Finally, store the outcome\n",
    "        throws.append(outcome)\n",
    "    return throws\n",
    "\n",
    "throws = throw_n_times(100)\n",
    "plt.hist(throws, bins=[0.5, 1.5, 2.5, 3.5, 4.5, 5.5, 6.5], density=True, edgecolor='k')\n",
    "plt.xticks((1, 2, 3, 4, 5, 6))\n",
    "plt.xlabel('outcome')\n",
    "plt.ylabel('counts')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__2__ Modify the code further to throw  $N = 10, 100, 1000$ dice and store the mean values $S_N = \\frac{1}{N}\\sum_{i=1}^N X_i =  \\langle X \\rangle$ in a list. For each $N$ repeat the experiment 5000 times and plot the resulting distributions of mean values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x741 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "random.seed(2020)\n",
    "\n",
    "plt.figure()\n",
    "random.seed(2020)\n",
    "\n",
    "for n in [10, 100, 1000]:   \n",
    "    mean_values = []\n",
    "    \n",
    "    for t in range(5000):\n",
    "        throws = throw_n_times(n)\n",
    "        m = sum(throws) / n\n",
    "        mean_values.append(m)\n",
    "    \n",
    "    plt.hist(mean_values, 20, label=f'{n} dice', edgecolor='k', linewidth=0.4)\n",
    "    \n",
    "plt.legend()    \n",
    "plt.ylabel('counts')\n",
    "plt.xlabel('average outcome')\n",
    "plt.xticks((1, 2, 3, 4, 5, 6))\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__3__ Repeat the experiment of task __2__ but instead of plotting the distribution of mean values $S_N$, plot the distribution of $\\sqrt{N}(S_N - \\mu)$,\n",
    "where $\\mu$ is the expectation value $\\mu = \\frac{1}{M}\\sum_k^M w_k X_k$, where $\\omega_k$ and $X_k$ are the weights and possible outcomes of the random variables, respectively. In the case of a dice the expectation value is $\\mu = (1 + 2 + 3 + 4 + 5 + 6) / 6 = 3.5$.\n",
    "What do you observe?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1200x741 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "random.seed(2020)\n",
    "\n",
    "plt.figure()\n",
    "\n",
    "for n in [10, 100, 1000][::-1]:   \n",
    "    mean_values = []\n",
    "    \n",
    "    for t in range(5000):\n",
    "        throws = throw_n_times(n)\n",
    "        m = np.sqrt(n) * (sum(throws) / len(throws) - 3.5)\n",
    "        mean_values.append(m)\n",
    "    \n",
    "    plt.hist(mean_values, 20, \n",
    "             label=f'{n} dice',\n",
    "             edgecolor='k', linewidth=0.4)\n",
    "\n",
    "plt.legend()    \n",
    "plt.ylabel('counts')\n",
    "plt.xlabel('outcome')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The distributions converge towards mean-zero normal distributions. This is a manifestation of the central limit theorem, which states that the $\\mu$-shifted average values of an increasing sample size converge towards a normal distribution with variance $\\sigma^2 =  \\langle (X-\\mu)^2 \\rangle$ \n",
    " $$ \\lim_{N->\\infty}\\sqrt{N}(S_N-\\mu)=\\mathcal{N}(0,\\sigma^2) $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.9166666666666665"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "((np.arange(1, 7) - 3.5)**2).mean()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
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    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.10"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
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   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
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   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
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 "nbformat": 4,
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