13_probability_distributions_binomial.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ICS 434: DATA SCIENCE FUNDAMENTALS\n",
    "\n",
    "## Probability Distributions\n",
    "#### The Binomial Distribution\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# !pip install scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "from IPython.display import Image\n",
    "import scipy\n",
    "import numpy as np\n",
    "from scipy.stats import binom\n",
    "#import matplotlib.pyplot as plt\n",
    "import itertools\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import binom\n",
    "import matplotlib.pyplot as plt\n",
    "import itertools"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Probability Models\n",
    "\n",
    "* A way to reason about a probabilistic system from various perspectives\n",
    "\n",
    "* E.g., you want to run an ad campaign through an agency. You may be interested in:\n",
    "    * The average number of new clients that we should expect after the ad campaign?\n",
    "    * Determine the amount of variability you should expect to see in the system\n",
    "      * How large is that number? Ex. a value 300-400 is more informative than 100-1,000\n",
    "    * Compute probability of events\n",
    "      * What is the probability of having more than X new clients after a given ad campaign\n",
    "      \n",
    "Note and remember these three components: \n",
    "  * Some summary information about the experiment.\n",
    "  * Variability (variance) around that statistic.\n",
    "  * Computing probability of certain events."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Probability Models: Example\n",
    "\n",
    "* E.g., you want to run an ad campaign through an agency and are interested in:\n",
    "    1. Average number of new clients after an ad campaign\n",
    "    2. Variability around that number\n",
    "    3. The probability of having at least X participants.\n",
    "\n",
    "* We can repeat the ad campaign a large number of times and answer each of these questions\n",
    "\n",
    "\n",
    "```python\n",
    "    nb_new_participants = [500, 800, 860, 820, 840, 760, 430,...]\n",
    "```\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Probability Models: Example\n",
    "\n",
    "```python\n",
    "    nb_new_participants = [500, 800, 860, 820, 840, 760, 430, ...] \n",
    "```\n",
    "\n",
    "1. Average number of new clients after an ad campaign\n",
    "```python\n",
    "np.mean(nb_new_participants)\n",
    "```\n",
    "2. Variability around that number\n",
    "```python\n",
    "np.var(nb_new_participants)\n",
    "```\n",
    "3. The probability of having at least X participants\n",
    "```python\n",
    "    sum(array(nb_new_participants) > X) / len(nb_new_participants)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Probability Models: Example -- Cont'd\n",
    "\n",
    "* The same information is contained in the visualization of the data\n",
    "  * What does every single bar mean? \n",
    "  * How can you get an idea of the `mean`, `variance`, and probability of at least X participants?\n",
    "\n",
    "  <img src=\"https://www.dropbox.com/scl/fi/pisd9d30dhqs5uosnawos/clients_ad_campaign.png?rlkey=rpwezsicf942wb4buv00o40pj&dl=1\" style=\"width:700px\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Probability Distributions\n",
    "\n",
    "* At the heart of probability models are _probability_ _distributions_ and _random_ _variables_\n",
    "\n",
    "* Consider the loaded die with the following probabilities:\n",
    "```\n",
    "    p(1) = 0.3/6\n",
    "    p(2) = 0.7/6\n",
    "    p(3) =   2/6\n",
    "    p(4) = 0.5/6\n",
    "    p(5) = 0.2/6\n",
    "    p(6) = 2.3/6\n",
    "```\n",
    "\n",
    "* We could think of probabilities above as the values returned by the function that takes as input a value in `(1, 2, 3, 4, 5, 6)` and returns the relavant probability from the list `[0.3/6, 0.7/6, 2/6, 0.5/6, 0.2/6, 2.3/6]`\n",
    "\n",
    "* Example:\n",
    "```python\n",
    "    def loaded_die_distribution (face):\n",
    "        try:\n",
    "            dist = {1: 0.3/6, 2: 0.7/6, 3: 2/6, 4: 0.5/6, 5: 0.2/6, 6: 2.3/6}\n",
    "            return dist[face]\n",
    "        except:\n",
    "            raise(\"%s is not a valid die face %d\" % face)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Probability Distributions -- Cont'd\n",
    "\n",
    "* Such a function is called a probability distribution\n",
    "* In essence, a probability distribution is a numerical function that assigns probabilities (y-axis in [0, 1]) to outcomes in the sample space S (x-axis)\n",
    "  * sample space is the _domain_ (numerical or not) \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def loaded_die_distribution (face):\n",
    "    try:\n",
    "        dist = {1: 0.3/6, 2: 0.7/6, 3: 2/6, 4: 0.5/6, 5: 0.2/6, 6: 2.3/6}\n",
    "        return dist[face]\n",
    "    except:\n",
    "        raise(\"%s is not a valid die face %d\" % face)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample_space = list(range(1, 7))\n",
    "p_x = [loaded_die_distribution(f) for f in sample_space]\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.bar(sample_space, p_x)\n",
    "\n",
    "plt.xlabel('Die face obtained')\n",
    "plt.ylabel('probability');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Sampling from the Biased Die\n",
    "\n",
    "- Given our probability distribution, we are four times more likely to draw a 3 than we are to draw a 4\n",
    "- To sample die rolls, we need to encode our probability distribution to reflect the bias in our die\n",
    "  - This can be easily done using the `choice()` function in `np.random`\n",
    "\n",
    "```python\n",
    "np.random.choice([1, 2, 3, 4, 5, 6], p=[0.3/6, 0.7/6, 2/6, 0.5/6, 0.2/6, 2.3/6])\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6 1 1 4 6 4 3 4 6 3 6 3 6 3 3 1 6 6 3 6 "
     ]
    }
   ],
   "source": [
    "for _ in range(20):\n",
    "    print(np.random.choice([1, 2, 3, 4, 5, 6], \n",
    "                            p=[0.3/6, 0.7/6, 2/6, 0.5/6, 0.2/6, 2.3/6]), \n",
    "          end= ' ')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Random Variables\n",
    "\n",
    "* Using CS thinking, a random variable is merely a variable (a RAM space, or box for a value) that can take values that are variable\n",
    "  * E.g.,\n",
    "    ```c\n",
    "        // Variable in C++\n",
    "        string myString = \"Hello World\";\n",
    "        myString = \"Some other message\";\n",
    "    ```\n",
    "* In probabilistic thinking, a random variable is a variable that can take any value from the sample space of the experiment as determined by the probability distribution.\n",
    "    \n",
    "  * I.e., the value assigned to the variable depends on a random process    \n",
    "  ```python\n",
    "      # randomly select a value according to a probability distribution\n",
    "      dieRollVal = np.random.choice([1, 2, 3, 4, 5, 6], p=[0.3/6, 0.7/6, 2/6, 0.5/6, 0.2/6, 2.3/6]);\n",
    "  ```\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Random Variables\n",
    "\n",
    "* Using CS thinking, a random variable is merely a variable that can take values that are variable (random)\n",
    "\n",
    "* In probabilistic thinking, a random variable is a variable that can take any value from the sample space of the experiment as determined by the probability distribution\n",
    "\n",
    "  * The value assigned to the variable depends on a random process    \n",
    "  \n",
    "  ```python\n",
    "      # randomly select a value according to a probability distribution\n",
    "      dieRollVal = np.random.choice([1, 2, 3, 4, 5, 6], p=[0.3/6, 0.7/6, 2/6, 0.5/6, 0.2/6, 2.3/6]);\n",
    "  ```\n",
    "  \n",
    "* Formally, a random variable is a function from the sample space of an experiment to the set of real numbers. That is, a random variable assigns a real number to each possible outcome."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Random Variables -- Cont'd\n",
    "\n",
    "* In a non-probabilistic program, you can trace the value contained in a variable\n",
    "\n",
    "* In a probabilistic program, you cannot since the value is determined probabilistically\n",
    "  * We don't know what that variable will contain prior to executing the code\n",
    "  * We can however reason about what the value will most likely contain"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "* Take for instance the variable `roll_random_var` in the code below:\n",
    "\n",
    "```python\n",
    "for i in range(10):\n",
    "    roll_random_var = np.random.choice([1, 2, 3, 4, 5, 6], \n",
    "                                       p=[0.3/6, 0.7/6, 2/6, 0.5/6, 0.4/6, 2.1/6])\n",
    "    print (f\"roll_random_var contains the value {roll_random_var}\")\n",
    "```\n",
    "\n",
    "* The variable `roll_random_var` is a _random_ _variable_\n",
    "  * The values assigned to it are determined probabilistically using a probability distribution of the biased die\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "roll_random_var contains the value 1\n",
      "roll_random_var contains the value 6\n",
      "roll_random_var contains the value 3\n"
     ]
    }
   ],
   "source": [
    "for i in range(3):\n",
    "    roll_random_var = np.random.choice([1, 2, 3, 4, 5, 6], \n",
    "                                       p=[0.3/6, 0.7/6, 2/6, 0.5/6, 0.4/6, 2.1/6])\n",
    "    print (\"roll_random_var contains the value %s\" % roll_random_var)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{1: 486, 2: 1104, 3: 3314, 4: 840, 5: 682, 6: 3574}\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA+MAAAFfCAYAAAAlEx33AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjYuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8o6BhiAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAqYUlEQVR4nO3df4xV9Z0//ud8QEalzK2AM8PEUUlLWRV0GzAwtPUXiBCRVpvVlu6s7rqoq2JZJLbYP5bddMG6UexKStQY8QcuZtPSmqijGCtdoiiwOyla6tpUU1gZsO4wA3zJYOn9/rHpTUfUdhDOnbGPR3KSOee87pnX25x4ffqe8z415XK5HAAAAKAw/6/aDQAAAMCfGmEcAAAACiaMAwAAQMGEcQAAACiYMA4AAAAFE8YBAACgYMI4AAAAFGxwtRs4Wn7729/mrbfeyrBhw1JTU1PtdgAAAPiYK5fL2bNnT5qamvL//t+Hz31/bMP4W2+9lebm5mq3AQAAwJ+Ybdu25aSTTvrQmo9tGB82bFiS//uHUFdXV+VuAAAA+Ljr7u5Oc3NzJY9+mI9tGP/dn6bX1dUJ4wAAABTmj3lU2gJuAAAAUDBhHAAAAAomjAMAAEDBhHEAAAAomDAOAAAABRPGAQAAoGDCOAAAABRMGAcAAICCCeMAAABQMGEcAAAACiaMAwAAQMGEcQAAACjY4Go3AAAAcKSd+s0nqt0CR9ibt11c7RaOKDPjAAAAULA+hfEVK1bkzDPPTF1dXerq6tLS0pKnnnqqcv6qq65KTU1Nr23y5Mm9rtHT05N58+Zl5MiRGTp0aGbPnp3t27f3quns7Exra2tKpVJKpVJaW1uze/fuwx8lAAAA9CN9CuMnnXRSbrvttmzatCmbNm3KBRdckC9+8Yt59dVXKzUzZszIjh07KtuTTz7Z6xrz58/PmjVrsnr16qxfvz579+7NrFmzcvDgwUrNnDlz0t7enra2trS1taW9vT2tra0fcagAAADQP/TpmfFLLrmk1/4///M/Z8WKFdmwYUPOOOOMJEltbW0aGxvf9/NdXV25//778/DDD2fatGlJkkceeSTNzc159tlnc9FFF2Xr1q1pa2vLhg0bMmnSpCTJfffdl5aWlrz22msZO3ZsnwcJAAAA/clhPzN+8ODBrF69Ovv27UtLS0vl+PPPP5/6+vp85jOfydy5c7Nr167Kuc2bN+fdd9/N9OnTK8eampoybty4vPDCC0mSF198MaVSqRLEk2Ty5MkplUqVmvfT09OT7u7uXhsAAAD0R30O41u2bMknPvGJ1NbW5rrrrsuaNWty+umnJ0lmzpyZVatW5bnnnssdd9yRjRs35oILLkhPT0+SpKOjI0OGDMkJJ5zQ65oNDQ3p6Oio1NTX1x/ye+vr6ys172fp0qWVZ8xLpVKam5v7OjQAAAAoRJ9fbTZ27Ni0t7dn9+7d+f73v58rr7wy69aty+mnn54rrriiUjdu3LhMnDgxp5xySp544olcdtllH3jNcrmcmpqayv7v//xBNe+1aNGiLFiwoLLf3d0tkAMAANAv9TmMDxkyJJ/+9KeTJBMnTszGjRvz3e9+N/fcc88htaNGjcopp5yS119/PUnS2NiYAwcOpLOzs9fs+K5duzJlypRKzc6dOw+51ttvv52GhoYP7Ku2tja1tbV9HQ4AAAAU7iO/Z7xcLlf+DP293nnnnWzbti2jRo1KkkyYMCHHHHNM1q5dW6nZsWNHXnnllUoYb2lpSVdXV15++eVKzUsvvZSurq5KDQAAAAxkfZoZv/XWWzNz5sw0Nzdnz549Wb16dZ5//vm0tbVl7969Wbx4cb785S9n1KhRefPNN3Prrbdm5MiRufTSS5MkpVIpV199dW6++eaMGDEiw4cPz8KFCzN+/PjK6uqnnXZaZsyYkblz51Zm26+55prMmjXLSuoAAAB8LPQpjO/cuTOtra3ZsWNHSqVSzjzzzLS1teXCCy/M/v37s2XLljz00EPZvXt3Ro0alfPPPz+PPfZYhg0bVrnGsmXLMnjw4Fx++eXZv39/pk6dmpUrV2bQoEGVmlWrVuWmm26qrLo+e/bsLF++/AgNGQAAAKqrplwul6vdxNHQ3d2dUqmUrq6u1NXVVbsdAACgQKd+84lqt8AR9uZtF1e7hT+oLzn0Iz8zDgAAAPSNMA4AAAAFE8YBAACgYMI4AAAAFEwYBwAAgIIJ4wAAAFAwYRwAAAAKJowDAABAwQZXuwEA+o9Tv/lEtVvgCHvztour3QIA8D7MjAMAAEDBhHEAAAAomDAOAAAABRPGAQAAoGDCOAAAABRMGAcAAICCCeMAAABQMGEcAAAACiaMAwAAQMGEcQAAACiYMA4AAAAFE8YBAACgYMI4AAAAFEwYBwAAgIIJ4wAAAFAwYRwAAAAKJowDAABAwYRxAAAAKJgwDgAAAAUTxgEAAKBgwjgAAAAUrE9hfMWKFTnzzDNTV1eXurq6tLS05KmnnqqcL5fLWbx4cZqamnLcccflvPPOy6uvvtrrGj09PZk3b15GjhyZoUOHZvbs2dm+fXuvms7OzrS2tqZUKqVUKqW1tTW7d+8+/FECAABAP9KnMH7SSSfltttuy6ZNm7Jp06ZccMEF+eIXv1gJ3LfffnvuvPPOLF++PBs3bkxjY2MuvPDC7Nmzp3KN+fPnZ82aNVm9enXWr1+fvXv3ZtasWTl48GClZs6cOWlvb09bW1va2trS3t6e1tbWIzRkAAAAqK6acrlc/igXGD58eP7lX/4lf/M3f5OmpqbMnz8/3/jGN5L83yx4Q0NDvvOd7+Taa69NV1dXTjzxxDz88MO54oorkiRvvfVWmpub8+STT+aiiy7K1q1bc/rpp2fDhg2ZNGlSkmTDhg1paWnJz3/+84wdO/aP6qu7uzulUildXV2pq6v7KEME+JNx6jefqHYLHGFv3nZxtVsAqArfaR8/A+E7rS859LCfGT948GBWr16dffv2paWlJW+88UY6Ojoyffr0Sk1tbW3OPffcvPDCC0mSzZs359133+1V09TUlHHjxlVqXnzxxZRKpUoQT5LJkyenVCpVat5PT09Puru7e20AAADQH/U5jG/ZsiWf+MQnUltbm+uuuy5r1qzJ6aefno6OjiRJQ0NDr/qGhobKuY6OjgwZMiQnnHDCh9bU19cf8nvr6+srNe9n6dKllWfMS6VSmpub+zo0AAAAKESfw/jYsWPT3t6eDRs25O/+7u9y5ZVX5mc/+1nlfE1NTa/6crl8yLH3em/N+9X/oessWrQoXV1dlW3btm1/7JAAAACgUH0O40OGDMmnP/3pTJw4MUuXLs1ZZ52V7373u2lsbEySQ2avd+3aVZktb2xszIEDB9LZ2fmhNTt37jzk97799tuHzLr/vtra2soq77/bAAAAoD/6yO8ZL5fL6enpyejRo9PY2Ji1a9dWzh04cCDr1q3LlClTkiQTJkzIMccc06tmx44deeWVVyo1LS0t6erqyssvv1ypeemll9LV1VWpAQAAgIFscF+Kb7311sycOTPNzc3Zs2dPVq9eneeffz5tbW2pqanJ/Pnzs2TJkowZMyZjxozJkiVLcvzxx2fOnDlJklKplKuvvjo333xzRowYkeHDh2fhwoUZP358pk2bliQ57bTTMmPGjMydOzf33HNPkuSaa67JrFmz/uiV1AEAAKA/61MY37lzZ1pbW7Njx46USqWceeaZaWtry4UXXpgkueWWW7J///5cf/316ezszKRJk/LMM89k2LBhlWssW7YsgwcPzuWXX579+/dn6tSpWblyZQYNGlSpWbVqVW666abKquuzZ8/O8uXLj8R4AQAAoOo+8nvG+yvvGQfoO+9k/fgZCO9kBTgafKd9/AyE77RC3jMOAAAAHB5hHAAAAAomjAMAAEDBhHEAAAAomDAOAAAABRPGAQAAoGDCOAAAABRMGAcAAICCCeMAAABQMGEcAAAACiaMAwAAQMGEcQAAACiYMA4AAAAFE8YBAACgYMI4AAAAFEwYBwAAgIIJ4wAAAFAwYRwAAAAKJowDAABAwYRxAAAAKJgwDgAAAAUTxgEAAKBgwjgAAAAUTBgHAACAggnjAAAAUDBhHAAAAAomjAMAAEDBhHEAAAAomDAOAAAABRPGAQAAoGB9CuNLly7N2WefnWHDhqW+vj5f+tKX8tprr/Wqueqqq1JTU9Nrmzx5cq+anp6ezJs3LyNHjszQoUMze/bsbN++vVdNZ2dnWltbUyqVUiqV0tramt27dx/eKAEAAKAf6VMYX7duXW644YZs2LAha9euzW9+85tMnz49+/bt61U3Y8aM7Nixo7I9+eSTvc7Pnz8/a9asyerVq7N+/frs3bs3s2bNysGDBys1c+bMSXt7e9ra2tLW1pb29va0trZ+hKECAABA/zC4L8VtbW299h944IHU19dn8+bNOeeccyrHa2tr09jY+L7X6Orqyv3335+HH34406ZNS5I88sgjaW5uzrPPPpuLLrooW7duTVtbWzZs2JBJkyYlSe677760tLTktddey9ixY/s0SAAAAOhPPtIz411dXUmS4cOH9zr+/PPPp76+Pp/5zGcyd+7c7Nq1q3Ju8+bNeffddzN9+vTKsaampowbNy4vvPBCkuTFF19MqVSqBPEkmTx5ckqlUqXmvXp6etLd3d1rAwAAgP7osMN4uVzOggUL8vnPfz7jxo2rHJ85c2ZWrVqV5557LnfccUc2btyYCy64ID09PUmSjo6ODBkyJCeccEKv6zU0NKSjo6NSU19ff8jvrK+vr9S819KlSyvPl5dKpTQ3Nx/u0AAAAOCo6tOfqf++G2+8MT/96U+zfv36XsevuOKKys/jxo3LxIkTc8opp+SJJ57IZZdd9oHXK5fLqampqez//s8fVPP7Fi1alAULFlT2u7u7BXIAAAD6pcOaGZ83b14ef/zx/PjHP85JJ530obWjRo3KKaecktdffz1J0tjYmAMHDqSzs7NX3a5du9LQ0FCp2blz5yHXevvttys171VbW5u6urpeGwAAAPRHfQrj5XI5N954Y37wgx/kueeey+jRo//gZ955551s27Yto0aNSpJMmDAhxxxzTNauXVup2bFjR1555ZVMmTIlSdLS0pKurq68/PLLlZqXXnopXV1dlRoAAAAYqPr0Z+o33HBDHn300fzoRz/KsGHDKs9vl0qlHHfccdm7d28WL16cL3/5yxk1alTefPPN3HrrrRk5cmQuvfTSSu3VV1+dm2++OSNGjMjw4cOzcOHCjB8/vrK6+mmnnZYZM2Zk7ty5ueeee5Ik11xzTWbNmmUldQAAAAa8PoXxFStWJEnOO++8XscfeOCBXHXVVRk0aFC2bNmShx56KLt3786oUaNy/vnn57HHHsuwYcMq9cuWLcvgwYNz+eWXZ//+/Zk6dWpWrlyZQYMGVWpWrVqVm266qbLq+uzZs7N8+fLDHScAAAD0G30K4+Vy+UPPH3fccXn66af/4HWOPfbY3H333bn77rs/sGb48OF55JFH+tIeAAAADAgf6T3jAAAAQN8J4wAAAFAwYRwAAAAKJowDAABAwYRxAAAAKJgwDgAAAAUTxgEAAKBgwjgAAAAUTBgHAACAggnjAAAAUDBhHAAAAAomjAMAAEDBhHEAAAAomDAOAAAABRPGAQAAoGDCOAAAABRMGAcAAICCCeMAAABQMGEcAAAACiaMAwAAQMGEcQAAACiYMA4AAAAFE8YBAACgYMI4AAAAFEwYBwAAgIIJ4wAAAFAwYRwAAAAKJowDAABAwYRxAAAAKJgwDgAAAAXrUxhfunRpzj777AwbNiz19fX50pe+lNdee61XTblczuLFi9PU1JTjjjsu5513Xl599dVeNT09PZk3b15GjhyZoUOHZvbs2dm+fXuvms7OzrS2tqZUKqVUKqW1tTW7d+8+vFECAABAP9KnML5u3brccMMN2bBhQ9auXZvf/OY3mT59evbt21epuf3223PnnXdm+fLl2bhxYxobG3PhhRdmz549lZr58+dnzZo1Wb16ddavX5+9e/dm1qxZOXjwYKVmzpw5aW9vT1tbW9ra2tLe3p7W1tYjMGQAAACorppyuVw+3A+//fbbqa+vz7p163LOOeekXC6nqakp8+fPzze+8Y0k/zcL3tDQkO985zu59tpr09XVlRNPPDEPP/xwrrjiiiTJW2+9lebm5jz55JO56KKLsnXr1px++unZsGFDJk2alCTZsGFDWlpa8vOf/zxjx479g711d3enVCqlq6srdXV1hztEgD8pp37ziWq3wBH25m0XV7sFgKrwnfbxMxC+0/qSQz/SM+NdXV1JkuHDhydJ3njjjXR0dGT69OmVmtra2px77rl54YUXkiSbN2/Ou+++26umqakp48aNq9S8+OKLKZVKlSCeJJMnT06pVKrUvFdPT0+6u7t7bQAAANAfHXYYL5fLWbBgQT7/+c9n3LhxSZKOjo4kSUNDQ6/ahoaGyrmOjo4MGTIkJ5xwwofW1NfXH/I76+vrKzXvtXTp0srz5aVSKc3NzYc7NAAAADiqDjuM33jjjfnpT3+af/u3fzvkXE1NTa/9crl8yLH3em/N+9V/2HUWLVqUrq6uyrZt27Y/ZhgAAABQuMMK4/Pmzcvjjz+eH//4xznppJMqxxsbG5PkkNnrXbt2VWbLGxsbc+DAgXR2dn5ozc6dOw/5vW+//fYhs+6/U1tbm7q6ul4bAAAA9Ed9CuPlcjk33nhjfvCDH+S5557L6NGje50fPXp0Ghsbs3bt2sqxAwcOZN26dZkyZUqSZMKECTnmmGN61ezYsSOvvPJKpaalpSVdXV15+eWXKzUvvfRSurq6KjUAAAAwUA3uS/ENN9yQRx99ND/60Y8ybNiwygx4qVTKcccdl5qamsyfPz9LlizJmDFjMmbMmCxZsiTHH3985syZU6m9+uqrc/PNN2fEiBEZPnx4Fi5cmPHjx2fatGlJktNOOy0zZszI3Llzc8899yRJrrnmmsyaNeuPWkkdAAAA+rM+hfEVK1YkSc4777xexx944IFcddVVSZJbbrkl+/fvz/XXX5/Ozs5MmjQpzzzzTIYNG1apX7ZsWQYPHpzLL788+/fvz9SpU7Ny5coMGjSoUrNq1arcdNNNlVXXZ8+eneXLlx/OGAEAAKBf+UjvGe/PvGccoO+8k/XjZyC8kxXgaPCd9vEzEL7TCnvPOAAAANB3wjgAAAAUTBgHAACAggnjAAAAUDBhHAAAAAomjAMAAEDBhHEAAAAomDAOAAAABRPGAQAAoGDCOAAAABRMGAcAAICCCeMAAABQMGEcAAAACiaMAwAAQMGEcQAAACiYMA4AAAAFE8YBAACgYMI4AAAAFEwYBwAAgIIJ4wAAAFAwYRwAAAAKJowDAABAwYRxAAAAKJgwDgAAAAUTxgEAAKBgwjgAAAAUTBgHAACAggnjAAAAUDBhHAAAAAomjAMAAEDB+hzGf/KTn+SSSy5JU1NTampq8sMf/rDX+auuuio1NTW9tsmTJ/eq6enpybx58zJy5MgMHTo0s2fPzvbt23vVdHZ2prW1NaVSKaVSKa2trdm9e3efBwgAAAD9TZ/D+L59+3LWWWdl+fLlH1gzY8aM7Nixo7I9+eSTvc7Pnz8/a9asyerVq7N+/frs3bs3s2bNysGDBys1c+bMSXt7e9ra2tLW1pb29va0trb2tV0AAADodwb39QMzZ87MzJkzP7SmtrY2jY2N73uuq6sr999/fx5++OFMmzYtSfLII4+kubk5zz77bC666KJs3bo1bW1t2bBhQyZNmpQkue+++9LS0pLXXnstY8eO7WvbAAAA0G8clWfGn3/++dTX1+czn/lM5s6dm127dlXObd68Oe+++26mT59eOdbU1JRx48blhRdeSJK8+OKLKZVKlSCeJJMnT06pVKrUvFdPT0+6u7t7bQAAANAfHfEwPnPmzKxatSrPPfdc7rjjjmzcuDEXXHBBenp6kiQdHR0ZMmRITjjhhF6fa2hoSEdHR6Wmvr7+kGvX19dXat5r6dKllefLS6VSmpubj/DIAAAA4Mjo85+p/yFXXHFF5edx48Zl4sSJOeWUU/LEE0/ksssu+8DPlcvl1NTUVPZ//+cPqvl9ixYtyoIFCyr73d3dAjkAAAD90lF/tdmoUaNyyimn5PXXX0+SNDY25sCBA+ns7OxVt2vXrjQ0NFRqdu7ceci13n777UrNe9XW1qaurq7XBgAAAP3RUQ/j77zzTrZt25ZRo0YlSSZMmJBjjjkma9eurdTs2LEjr7zySqZMmZIkaWlpSVdXV15++eVKzUsvvZSurq5KDQAAAAxUff4z9b179+YXv/hFZf+NN95Ie3t7hg8fnuHDh2fx4sX58pe/nFGjRuXNN9/MrbfempEjR+bSSy9NkpRKpVx99dW5+eabM2LEiAwfPjwLFy7M+PHjK6urn3baaZkxY0bmzp2be+65J0lyzTXXZNasWVZSBwAAYMDrcxjftGlTzj///Mr+757TvvLKK7NixYps2bIlDz30UHbv3p1Ro0bl/PPPz2OPPZZhw4ZVPrNs2bIMHjw4l19+efbv35+pU6dm5cqVGTRoUKVm1apVuemmmyqrrs+ePftD320OAAAAA0VNuVwuV7uJo6G7uzulUildXV2eHwf4I536zSeq3QJH2Ju3XVztFgCqwnfax89A+E7rSw496s+MAwAAAL0J4wAAAFAwYRwAAAAKJowDAABAwYRxAAAAKJgwDgAAAAUTxgEAAKBgwjgAAAAUTBgHAACAggnjAAAAUDBhHAAAAAomjAMAAEDBhHEAAAAomDAOAAAABRPGAQAAoGDCOAAAABRMGAcAAICCCeMAAABQMGEcAAAACiaMAwAAQMGEcQAAACiYMA4AAAAFE8YBAACgYMI4AAAAFEwYBwAAgIIJ4wAAAFCwwdVuADgyTv3mE9VugSPszdsurnYLAAAcJWbGAQAAoGDCOAAAABRMGAcAAICC9TmM/+QnP8kll1ySpqam1NTU5Ic//GGv8+VyOYsXL05TU1OOO+64nHfeeXn11Vd71fT09GTevHkZOXJkhg4dmtmzZ2f79u29ajo7O9Pa2ppSqZRSqZTW1tbs3r27zwMEAACA/qbPYXzfvn0566yzsnz58vc9f/vtt+fOO+/M8uXLs3HjxjQ2NubCCy/Mnj17KjXz58/PmjVrsnr16qxfvz579+7NrFmzcvDgwUrNnDlz0t7enra2trS1taW9vT2tra2HMUQAAADoX/q8mvrMmTMzc+bM9z1XLpdz11135Vvf+lYuu+yyJMmDDz6YhoaGPProo7n22mvT1dWV+++/Pw8//HCmTZuWJHnkkUfS3NycZ599NhdddFG2bt2atra2bNiwIZMmTUqS3HfffWlpaclrr72WsWPHHu54AQAAoOqO6DPjb7zxRjo6OjJ9+vTKsdra2px77rl54YUXkiSbN2/Ou+++26umqakp48aNq9S8+OKLKZVKlSCeJJMnT06pVKrUvFdPT0+6u7t7bQAAANAfHdEw3tHRkSRpaGjodbyhoaFyrqOjI0OGDMkJJ5zwoTX19fWHXL++vr5S815Lly6tPF9eKpXS3Nz8kccDAAAAR8NRWU29pqam1365XD7k2Hu9t+b96j/sOosWLUpXV1dl27Zt22F0DgAAAEffEQ3jjY2NSXLI7PWuXbsqs+WNjY05cOBAOjs7P7Rm586dh1z/7bffPmTW/Xdqa2tTV1fXawMAAID+6IiG8dGjR6exsTFr166tHDtw4EDWrVuXKVOmJEkmTJiQY445plfNjh078sorr1RqWlpa0tXVlZdffrlS89JLL6Wrq6tSAwAAAANVn1dT37t3b37xi19U9t944420t7dn+PDhOfnkkzN//vwsWbIkY8aMyZgxY7JkyZIcf/zxmTNnTpKkVCrl6quvzs0335wRI0Zk+PDhWbhwYcaPH19ZXf20007LjBkzMnfu3Nxzzz1JkmuuuSazZs2ykjoAAAADXp/D+KZNm3L++edX9hcsWJAkufLKK7Ny5crccsst2b9/f66//vp0dnZm0qRJeeaZZzJs2LDKZ5YtW5bBgwfn8ssvz/79+zN16tSsXLkygwYNqtSsWrUqN910U2XV9dmzZ3/gu80BAABgIKkpl8vlajdxNHR3d6dUKqWrq8vz4/xJOPWbT1S7BY6wN2+7uPDf6T76+KnGfQTQH/hO+/gZCN9pfcmhR2U1dQAAAOCDCeMAAABQMGEcAAAACiaMAwAAQMGEcQAAACiYMA4AAAAF6/N7xgEAPozXCX28DIRXCQEMRGbGAQAAoGDCOAAAABRMGAcAAICCCeMAAABQMGEcAAAACiaMAwAAQMGEcQAAACiYMA4AAAAFE8YBAACgYMI4AAAAFEwYBwAAgIIJ4wAAAFCwwdVuAAAA3uvUbz5R7RY4gt687eJqtwD9jplxAAAAKJgwDgAAAAUTxgEAAKBgwjgAAAAUTBgHAACAggnjAAAAUDBhHAAAAAomjAMAAEDBhHEAAAAomDAOAAAABTviYXzx4sWpqanptTU2NlbOl8vlLF68OE1NTTnuuONy3nnn5dVXX+11jZ6ensybNy8jR47M0KFDM3v27Gzfvv1ItwoAAABVcVRmxs8444zs2LGjsm3ZsqVy7vbbb8+dd96Z5cuXZ+PGjWlsbMyFF16YPXv2VGrmz5+fNWvWZPXq1Vm/fn327t2bWbNm5eDBg0ejXQAAACjU4KNy0cGDe82G/065XM5dd92Vb33rW7nsssuSJA8++GAaGhry6KOP5tprr01XV1fuv//+PPzww5k2bVqS5JFHHklzc3OeffbZXHTRRUejZQAAACjMUZkZf/3119PU1JTRo0fnK1/5Sn75y18mSd544410dHRk+vTpldra2tqce+65eeGFF5IkmzdvzrvvvturpqmpKePGjavUvJ+enp50d3f32gAAAKA/OuJhfNKkSXnooYfy9NNP57777ktHR0emTJmSd955Jx0dHUmShoaGXp9paGionOvo6MiQIUNywgknfGDN+1m6dGlKpVJla25uPsIjAwAAgCPjiP+Z+syZMys/jx8/Pi0tLfnUpz6VBx98MJMnT06S1NTU9PpMuVw+5Nh7/aGaRYsWZcGCBZX97u7uARPIT/3mE9VugSPszdsurnYLAABAP3bUX202dOjQjB8/Pq+//nrlOfL3znDv2rWrMlve2NiYAwcOpLOz8wNr3k9tbW3q6up6bQAAANAfHfUw3tPTk61bt2bUqFEZPXp0Ghsbs3bt2sr5AwcOZN26dZkyZUqSZMKECTnmmGN61ezYsSOvvPJKpQYAAAAGsiP+Z+oLFy7MJZdckpNPPjm7du3Kt7/97XR3d+fKK69MTU1N5s+fnyVLlmTMmDEZM2ZMlixZkuOPPz5z5sxJkpRKpVx99dW5+eabM2LEiAwfPjwLFy7M+PHjK6urAwAAwEB2xMP49u3b89WvfjW//vWvc+KJJ2by5MnZsGFDTjnllCTJLbfckv379+f6669PZ2dnJk2alGeeeSbDhg2rXGPZsmUZPHhwLr/88uzfvz9Tp07NypUrM2jQoCPdLgAAABTuiIfx1atXf+j5mpqaLF68OIsXL/7AmmOPPTZ333137r777iPcHQAAAFTfUX9mHAAAAOhNGAcAAICCCeMAAABQMGEcAAAACiaMAwAAQMGEcQAAACiYMA4AAAAFE8YBAACgYMI4AAAAFEwYBwAAgIIJ4wAAAFAwYRwAAAAKJowDAABAwYRxAAAAKJgwDgAAAAUTxgEAAKBgwjgAAAAUTBgHAACAggnjAAAAUDBhHAAAAAomjAMAAEDBhHEAAAAomDAOAAAABRPGAQAAoGDCOAAAABRMGAcAAICCCeMAAABQMGEcAAAACiaMAwAAQMGEcQAAACiYMA4AAAAF6/dh/Hvf+15Gjx6dY489NhMmTMh//Md/VLslAAAA+Ej6dRh/7LHHMn/+/HzrW9/Kf/3Xf+ULX/hCZs6cmV/96lfVbg0AAAAO2+BqN/Bh7rzzzlx99dX527/92yTJXXfdlaeffjorVqzI0qVLe9X29PSkp6enst/V1ZUk6e7uLq7hw/Tbnv+v2i1whFXjvnMfffy4jzgS3Ed8VNX6byn30ceLfxdxJAyEbPe7Hsvl8h+srSn/MVVVcODAgRx//PH593//91x66aWV41//+tfT3t6edevW9apfvHhx/vEf/7HoNgEAAKCXbdu25aSTTvrQmn47M/7rX/86Bw8eTENDQ6/jDQ0N6ejoOKR+0aJFWbBgQWX/t7/9bf73f/83I0aMSE1NzVHvlz+su7s7zc3N2bZtW+rq6qrdDgOU+4iPyj3EkeA+4khwH3EkuI/6l3K5nD179qSpqekP1vbbMP477w3S5XL5fcN1bW1tamtrex375Cc/eTRb4zDV1dX5FwUfmfuIj8o9xJHgPuJIcB9xJLiP+o9SqfRH1fXbBdxGjhyZQYMGHTILvmvXrkNmywEAAGAg6bdhfMiQIZkwYULWrl3b6/jatWszZcqUKnUFAAAAH12//jP1BQsWpLW1NRMnTkxLS0vuvffe/OpXv8p1111X7dY4DLW1tfmHf/iHQx4ngL5wH/FRuYc4EtxHHAnuI44E99HA1W9XU/+d733ve7n99tuzY8eOjBs3LsuWLcs555xT7bYAAADgsPX7MA4AAAAfN/32mXEAAAD4uBLGAQAAoGDCOAAAABRMGAcAAICCCeMcdT/5yU9yySWXpKmpKTU1NfnhD39Y7ZYYYJYuXZqzzz47w4YNS319fb70pS/ltddeq3ZbDDArVqzImWeembq6utTV1aWlpSVPPfVUtdtiAFu6dGlqamoyf/78arfCALJ48eLU1NT02hobG6vdFgPQ//zP/+Qv//IvM2LEiBx//PH58z//82zevLnabdEHwjhH3b59+3LWWWdl+fLl1W6FAWrdunW54YYbsmHDhqxduza/+c1vMn369Ozbt6/arTGAnHTSSbntttuyadOmbNq0KRdccEG++MUv5tVXX612awxAGzduzL333pszzzyz2q0wAJ1xxhnZsWNHZduyZUu1W2KA6ezszOc+97kcc8wxeeqpp/Kzn/0sd9xxRz75yU9WuzX6YHC1G+Djb+bMmZk5c2a122AAa2tr67X/wAMPpL6+Pps3b84555xTpa4YaC655JJe+//8z/+cFStWZMOGDTnjjDOq1BUD0d69e/O1r30t9913X7797W9Xux0GoMGDB5sN5yP5zne+k+bm5jzwwAOVY6eeemr1GuKwmBkHBpyurq4kyfDhw6vcCQPVwYMHs3r16uzbty8tLS3VbocB5oYbbsjFF1+cadOmVbsVBqjXX389TU1NGT16dL7yla/kl7/8ZbVbYoB5/PHHM3HixPzFX/xF6uvr89nPfjb33Xdftduij4RxYEApl8tZsGBBPv/5z2fcuHHVbocBZsuWLfnEJz6R2traXHfddVmzZk1OP/30arfFALJ69er853/+Z5YuXVrtVhigJk2alIceeihPP/107rvvvnR0dGTKlCl55513qt0aA8gvf/nLrFixImPGjMnTTz+d6667LjfddFMeeuihardGH/gzdWBAufHGG/PTn/4069evr3YrDEBjx45Ne3t7du/ene9///u58sors27dOoGcP8q2bdvy9a9/Pc8880yOPfbYarfDAPX7j+6NHz8+LS0t+dSnPpUHH3wwCxYsqGJnDCS//e1vM3HixCxZsiRJ8tnPfjavvvpqVqxYkb/6q7+qcnf8scyMAwPGvHnz8vjjj+fHP/5xTjrppGq3wwA0ZMiQfPrTn87EiROzdOnSnHXWWfnud79b7bYYIDZv3pxdu3ZlwoQJGTx4cAYPHpx169blX//1XzN48OAcPHiw2i0yAA0dOjTjx4/P66+/Xu1WGEBGjRp1yP9IPu200/KrX/2qSh1xOMyMA/1euVzOvHnzsmbNmjz//PMZPXp0tVviY6JcLqenp6fabTBATJ069ZBVr//6r/86f/Znf5ZvfOMbGTRoUJU6YyDr6enJ1q1b84UvfKHarTCAfO5znzvkNa///d//nVNOOaVKHXE4hHGOur179+YXv/hFZf+NN95Ie3t7hg8fnpNPPrmKnTFQ3HDDDXn00Ufzox/9KMOGDUtHR0eSpFQq5bjjjqtydwwUt956a2bOnJnm5ubs2bMnq1evzvPPP3/Iav3wQYYNG3bIWhVDhw7NiBEjrGHBH23hwoW55JJLcvLJJ2fXrl359re/ne7u7lx55ZXVbo0B5O///u8zZcqULFmyJJdffnlefvnl3Hvvvbn33nur3Rp9IIxz1G3atCnnn39+Zf93z0NdeeWVWblyZZW6YiBZsWJFkuS8887rdfyBBx7IVVddVXxDDEg7d+5Ma2trduzYkVKplDPPPDNtbW258MILq90a8Cdk+/bt+epXv5pf//rXOfHEEzN58uRs2LDBjCZ9cvbZZ2fNmjVZtGhR/umf/imjR4/OXXfdla997WvVbo0+qCmXy+VqNwEAAAB/SizgBgAAAAUTxgEAAKBgwjgAAAAUTBgHAACAggnjAAAAUDBhHAAAAAomjAMAAEDBhHEAAAAomDAOAAAABRPGAQAAoGDCOAAAABTs/wdDt+U7uqW11QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1200x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from collections import Counter\n",
    "\n",
    "roll_random_var_list = []\n",
    "for i in range(10000):\n",
    "    roll_random_var = np.random.choice([1, 2, 3, 4, 5, 6], \n",
    "                                       p=[0.3/6, 0.7/6, 2/6, 0.5/6, 0.4/6, 2.1/6])\n",
    "    roll_random_var_list.append(roll_random_var)\n",
    "\n",
    "counts = Counter(roll_random_var_list)\n",
    "\n",
    "sorted_counts = dict(sorted(counts.items()))\n",
    "print(sorted_counts)\n",
    "\n",
    "plt.figure(figsize=(12, 4))\n",
    "_ = plt.bar(sorted_counts.keys(), sorted_counts.values())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{1: 528, 2: 1106, 3: 3364, 4: 839, 5: 646, 6: 3517}\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1200x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from collections import Counter\n",
    "\n",
    "roll_random_var_list = np.random.choice([1, 2, 3, 4, 5, 6], size=10000,\n",
    "                                        p=[0.3/6, 0.7/6, 2/6, 0.5/6, 0.4/6, 2.1/6])\n",
    "\n",
    "counts = Counter(roll_random_var_list)\n",
    "\n",
    "sorted_counts = dict(sorted(counts.items()))\n",
    "print(sorted_counts)\n",
    "\n",
    "plt.figure(figsize=(12, 4))\n",
    "_ = plt.bar(sorted_counts.keys(), sorted_counts.values())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Two Types of Random Variables\n",
    "\n",
    "  * Discrete (finite or countably infinite)\n",
    "     * Take as input finite countably finite integer values and return probabilities for those events\n",
    "     * Ex. Number of accidents on H1 on any given day, number of customers at lunchtime at Starbucks on campus, number of siblings a student at UH has, etc.\n",
    "     \n",
    "  * Continuous (uncountably infinite)\n",
    "     * Take as input uncountably infinite float value and returns a probability density\n",
    "     * Ex. Height, weight, time, etc..\n",
    "       * The sample space is infinite."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Two Types of Random Variables \n",
    "\n",
    "\n",
    "* Discrete and continuous random variables have commonly occurring distributions\n",
    "  * These distributions are simply functions -- just like the one encoded above -- that give the \"probability\" for each element in the sample space\n",
    "\n",
    "\n",
    "* Perhaps two of the most popular distributions are the binomial (discrete) and the normal (or Gaussian) (continous)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### The Binomial Distribution (The `\"Hello World\"` Probability Distribution)\n",
    "\n",
    "* A binomial distribution is simply the probability of number of SUCCESS outcomes in an experiment that is repeated multiple times. \n",
    "  * $m$ successes in an experiment of $n$ fixed, independent trials.\n",
    "\n",
    "* Each trial has a probability of success $p$ and a probability of failure $1-p$ (heads and tails; 0 and 1; etc.).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "\n",
    "###  Examples of the Binomial Distribution\n",
    "\n",
    "- You flip a fair coin 100 times. What is the probability of observing 27 heads?\n",
    "\n",
    "- Given an ad clickthrough probability of $p=0.1$, what is the probability of having 100 clicks if we show the add 1,000 times?\n",
    "\n",
    "- Given a disease prevalence of $p=0.05$, what is the probability of observing the disease in at least 100 individuals if we survey 5,000 randomly selected individuals from the population? \n",
    "\n",
    "- What are $p$, $n$ and $m$ in each of these experiments?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Simple Probability Distribution\n",
    "\n",
    "* Let $X$ be the random variable representing the obsrved outcomes (Head and Tails) obtained from flipping a fair coin 5 times.  \n",
    "\n",
    "* What is the sample space of this experiment? \n",
    "\n",
    "  - This amounts to computing the Cartesian product $[H,T]^5$, or $[H,T] \\times [H,T] \\times [H,T] \\times [H,T] \\times [H,T]$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('H', 'H')\n",
      "('H', 'T')\n",
      "('T', 'H')\n",
      "('T', 'T')\n"
     ]
    }
   ],
   "source": [
    "for p in itertools.product(['H', 'T'], repeat=2):\n",
    "    print(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample space is of size 32 \n",
      "The sample space is:\n",
      "\n",
      "HHHHH HHHHT HHHTH HHHTT HHTHH HHTHT HHTTH HHTTT HTHHH HTHHT HTHTH HTHTT HTTHH HTTHT HTTTH HTTTT THHHH THHHT THHTH THHTT THTHH THTHT THTTH THTTT TTHHH TTHHT TTHTH TTHTT TTTHH TTTHT TTTTH TTTTT "
     ]
    }
   ],
   "source": [
    "product = list(itertools.product(['H', 'T'], repeat=5))\n",
    "\n",
    "print(\"Sample space is of size %s \" % len(product))\n",
    "print (\"The sample space is:\\n\")\n",
    "for prod in product:    \n",
    "    print(\"\".join(prod), end=\" \")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Manually Deriving the Probability Distribution\n",
    "\n",
    "* Say we are interested in the probability distribution of obtaining `X` heads in 5 coin flips\n",
    "  * _Binomial_ distribution with n=5 and $p=0.5$\n",
    "\n",
    "- Our sample space is [0, 1, 2, 3, 4, 5]\n",
    "\n",
    "- There are $2^5 = 32$ possible scenarios.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Manually Deriving the Probability Distribution\n",
    "\n",
    "* We are interested in the probability distribution of obtaining `X` heads in 5 coin flips\n",
    "  * _Binomial_ distribution with $n=5$ and $p=0.5$\n",
    "\n",
    "- Possible values of `X`: 0, 1, 2, 3, 4, 5\n",
    "\n",
    "- There are $2^5 = 32$ outcomes\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Manually Deriving the Probability Distribution -- Cont'd\n",
    "\n",
    "  * There is 1 way of obtaining 0 heads: TTTTT <br/>\n",
    "     $p(X=0) = 1/32$\n",
    "     \n",
    "  * There 5 ways of obtaining 1 head: HTTTT, THTTT, TTHTT, TTTHT, TTTTH.  <br/>\n",
    "     $p(X=1) = 5/32$\n",
    "     \n",
    "  * Similarly, there are 10 ways of obtaining 2 heads: HHTTT, HTHTT, HTTHT, HTTTH, …, TTTHH <br/>\n",
    "     $p(X=2) = 10/32$\n",
    "     \n",
    "  * ...\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Manually Deriving the Probability Distribution -- Cont'd\n",
    "\n",
    "* In general, the number of ways we can obtain $m$ heads from $n$ flips is given by the binomial cofficient ${n}\\choose{m}$ (read as $n$ choose $m$), which is given by:\n",
    "\n",
    "$$\n",
    "{{n}\\choose{m}} = \\frac{n!}{m!(n-m)!}\n",
    "$$\n",
    "\n",
    "E.g.: the for $n=5$ and $m=2$, we have\n",
    "\n",
    "\\begin{equation} \n",
    "\\begin{split}\n",
    "{{5}\\choose{2}} & = \\frac{5!}{2!(5-2)!} \\\\\n",
    "                & = \\frac{5\\times4\\times3\\times2 \\times 1}{2 \\times 1 \\times 3 \\times 2 \\times 1} \\\\\n",
    "                & = \\frac{5 \\times 4}{2 \\times 1} \\\\\n",
    "                & = 10 \n",
    "\\end{split}\n",
    "\\end{equation}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = [0, 1, 2, 3, 4, 5]\n",
    "p_x = [1.0/32, 5.0/32, 10.0/32, 10.0/32, 5.0/32, 1.0/32]\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.bar(X, p_x, color=\"#3498db\")\n",
    "plt.xlabel('Number of heads in five coin flips')\n",
    "plt.ylabel('Probability');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Binomial with Biased Coin\n",
    "\n",
    "- What if the coin is biased? For example, $p(H) = 0.7$ and $p(T) = 0.3$.\n",
    "\n",
    "- What is the probability of obtaining 1 head in 5 coin flips with this biased coin?\n",
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Bernoulli Distribution\n",
    "\n",
    "\n",
    "- Recall from elementary statistics and discrete math the Bernoulli distribution, which states that:\n",
    "\n",
    "$$\n",
    " Pr(k;p)=p^{k}(1-p)^{1-k}\\quad {\\text{for }}k\\in \\{0,1\\}\n",
    "$$\n",
    "\n",
    "\n",
    "* $k=1$ is head,  $1- k=0$ is tail, and $p$ is the probability of head\n",
    "\n",
    "\n",
    "* Based on the Bernoulli euqation above, the probability of obtaining a head ($k=1$) is: \n",
    "$$Pr(1; p) = p^1 \\times (1-p)^0 = p$$\n",
    "\n",
    "  and the probability of obtaining a tail ($k=0$ and $1-k = 1$) is:\n",
    "\n",
    "$$Pr(0; p) = p^k \\times (1-p)^{1-k} = p^0 \\times (1-p)^1 = 1-p$$ \n",
    "\n",
    "* This matches our intuition about the probability of a coin landing head\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Binomial with Biased Coin -- Cont'd\n",
    "\n",
    "- What if coin is biased? For example, $p(H) = 0.7$ and $p(T) = 0.3$.\n",
    "\n",
    "- What is the probability of obtaining 1 head in 5 coin flips with this biased coin?\n",
    "  \n",
    "  \n",
    "$$\n",
    "p(X=1) ={{5}\\choose{1}}~~~p(H)^1 \\times p(T)^4   \n",
    "$$\n",
    "\n",
    "* The five possible ways to obtain a 1 head and 4 tails: HTTTT, THTTT, TTHTT, TTTHT, TTTTH\n",
    "\n",
    "$$\n",
    "p(X=1) = 5  \\times 0.7 \\times 0.3^4 = 0.02835\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "\n",
    "### The Binomial Distribution -- Cont'd\n",
    "\n",
    "* The equation above can be generalized to any number of trials $n$, any number of successes $m$ and any probability of heads $p(H)$\n",
    "\n",
    "* We will write $p(H)$ as $p$ and $p(T)$ as $(1-p)$\n",
    "  \n",
    "    $p(X=m) ={{n}\\choose{m}} p^m \\times (1-p)^{n-m}$\n",
    "\n",
    "* This equation is the probability function for a random variable `X` distributed according to a binomial distribution\n",
    "\n",
    "  * Think of it as a convenient function to assign probabilities to any value in the sample space\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### The Binomial Distribution -- Cont'd\n",
    "\n",
    "- We can easily model (reason about) a problem that fits the binomial since we have access to the distribution\n",
    "\n",
    "  * E.g., assume after downloading your app, the probability of subscribing to a monthly plan in your app is  $p=0.05$. \n",
    "  * If, on average, 10k users download your app each month, how many (on average) subscribed users will you have after 1 year?\n",
    "  * What is the probability of having at least 3,000 users\n",
    "  * You can use this simple model to derive various valuable insights about your app\n",
    "  * E.g., total revenue after one year, the number of servers you will need to support your user base, the number of customer service employees to support your clientele, etc.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1171875\n"
     ]
    }
   ],
   "source": [
    "from scipy.special import comb\n",
    "\n",
    "def binomial_probability(n, m, p):\n",
    "    \"\"\"\n",
    "    Calculate the binomial probability.\n",
    "\n",
    "    :param n: Number of trials\n",
    "    :param m: Number of successful outcomes\n",
    "    :param p: Probability of success in each trial\n",
    "    :return: Binomial probability\n",
    "    \"\"\"\n",
    "    probability = comb(n, m) * (p ** m) * ((1 - p) ** (n - m))\n",
    "    return probability\n",
    "\n",
    "n = 10  # Total number of trials\n",
    "m = 3   # Number of successes\n",
    "p = 0.5 # Probability of success in each trial\n",
    "\n",
    "print(binomial_probability(n, m, p))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# comb(10_000, 150)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Binomial Distribution -- Cont'd\n",
    "\n",
    "* Once we know the parameter of the distribution (e.g., here p=0.05), it's easy to answer the questions above\n",
    "  * This may be trivial in some cases and challenging in others\n",
    "  * How did we get the $p=0.05$? How sure are we of that value? How likely is it to be $p=0.06$ instead?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Probability Distributions for Discrete Random Variables\n",
    "\n",
    "- A probability distribution for a discrete random variable is called probability mass function (__pmf__) \n",
    "\n",
    "  - `pmf`s take a discrete random variable $X$ and assign a probability to each value of its sample space\n",
    "\n",
    "- A probability distribution can be derived from first principles for many other canonical distributions\n",
    "\n",
    "- These functions allow us to compute probabilities for events seamlessly\n",
    "\n",
    "  - A byproduct is that we can also derive expected values, probabilities for subspace, use them to sample from that distribution, etc."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Probability Distributions for Discrete Random Variables\n",
    "\n",
    "- A probability distribution for a discrete random variable is called probability mass function (__pmf__) \n",
    "\n",
    "  - `pmf`s take a discrete random variable $X$ and assign a probability to each value of its sample space\n",
    "\n",
    "- These functions allow us to compute probabilities for events seamlessly\n",
    "\n",
    "  - A byproduct is that we can also derive expected values, probabilities for subspace, use them to sample from that distribution, etc."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### `pmf` in Python\n",
    "\n",
    "- Programming languages and data analysis software commonly support popular PMFs\n",
    "\n",
    "- The common graphical representation for a `pmf` is a histogram\n",
    "\n",
    "- The x-axis contains observed values \n",
    "\n",
    "- The y-axis shows the probability for the corresponding x values\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.02834999999999999"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import binom\n",
    "\n",
    "n = 5 \n",
    "p = 0.7\n",
    "binom.pmf(1, n, p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### NumPy and SciPy\n",
    "* Popular Python libraries for scientific computing. \n",
    "  * Both libraries provide a variety of functions for working with arrays, but they have different strengths and weaknesses.\n",
    "  * NumPy is a library for scientific computing with Python. \n",
    "    * It provides a high-performance multidimensional array object, and tools for working with large arrays and matrices. \n",
    "  * SciPy is a library that builds on NumPy and provides a variety of scientific functions, including clustering, image processing, integration, differentiation, gradient optimization, etc. \n",
    "  * SciPy is often used for more advanced scientific computing tasks, such as machine learning, natural language processing, and bioinformatics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3659328202500547"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import binom\n",
    "\n",
    "n = 9000 \n",
    "p = 0.0001\n",
    "binom.pmf(1, n, p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 5 \n",
    "p = 0.7\n",
    "\n",
    "x = range( n + 1 )\n",
    "p_x = [binom.pmf(val, n, p) for val in x]\n",
    "print(sum(p_x))\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.bar(x, p_x)\n",
    "plt.xlabel(\"Number of Successes\")\n",
    "plt.ylabel(\"Probility\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Example\n",
    "- Given a biased coin that comes up heads with a probability ($p=0.4$) \n",
    "- If you flip the coin 100 times, what is the probability of observing 42 heads?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.07420719403438258\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import binom\n",
    "\n",
    "n = 100 \n",
    "p = 0.4\n",
    "print(binom.pmf(42, n, p))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 100 \n",
    "p = 0.4\n",
    "\n",
    "x = range(n + 1)  # our x-axis\n",
    "p_x = [binom.pmf(val, n, p) for val in x]  # our y-axis\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.bar(x, p_x, color=\"#3498db\", alpha=0.5)\n",
    "\n",
    "# Add the horizontal and vertical bars\n",
    "x_val = 42\n",
    "y_val = binom.pmf(42, n, p)\n",
    "\n",
    "plt.axvline(x_val, color='r', alpha=0.5)\n",
    "plt.axhline(y_val, color='r', alpha=0.5)\n",
    "plt.xlabel('Number of heads in five coin flips')\n",
    "_ = plt.ylabel('Probability')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<BarContainer object of 11 artists>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n= 10\n",
    "p = 0.33\n",
    "\n",
    "x = list(range(n + 1))\n",
    "p_x = binom.pmf(x, n , p)\n",
    "plt.bar(x, p_x)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.82283780e-02, 8.97815635e-02, 1.98993465e-01, 2.61364552e-01,\n",
       "       2.25280640e-01, 1.33150945e-01, 5.46515074e-02, 1.53816609e-02,\n",
       "       2.84101573e-03, 3.10956945e-04, 1.53157899e-05])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binom.pmf(x, n , p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 6 \n",
    "p = 0.2 # let's change p\n",
    "x = range(n+1)\n",
    "\n",
    "p_x = [binom.pmf(val, n, p) for val in x]\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.bar(x, p_x, color=\"red\", alpha =.3)\n",
    "plt.xlabel('Number of heads in five coin flips')\n",
    "_ = plt.ylabel('Probability')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.9961880718422935,\n",
       " 0.2519235333578185,\n",
       " 0.8746079925006227,\n",
       " 0.48263227110004503,\n",
       " 0.756894977445736,\n",
       " 0.03945269049786393,\n",
       " 0.19636029680580547,\n",
       " 0.7671141621501543,\n",
       " 0.032691047022138764,\n",
       " 0.59351472592614,\n",
       " 0.2831678483848675,\n",
       " 0.2979138200545267,\n",
       " 0.44153451845193015,\n",
       " 0.48883658195006796,\n",
       " 0.702037597422274,\n",
       " 0.5212404392160327,\n",
       " 0.7500239560593932,\n",
       " 0.18492642904658063,\n",
       " 0.4221372405043634,\n",
       " 0.24633377680698598,\n",
       " 0.41112568750324163,\n",
       " 0.20483717380579858,\n",
       " 0.4316569375882843,\n",
       " 0.007536268151143943,\n",
       " 0.3320417436217896,\n",
       " 0.5411599937780315,\n",
       " 0.09792599641242028,\n",
       " 0.9718913179362234,\n",
       " 0.7689544044482871,\n",
       " 0.9693298851538051,\n",
       " 0.18468033000066397,\n",
       " 0.664900220399651,\n",
       " 0.799423005115583,\n",
       " 0.18051602152453872,\n",
       " 0.8738099540745723,\n",
       " 0.809916560231316,\n",
       " 0.17327503416615175,\n",
       " 0.5895103156288082,\n",
       " 0.4125170860614976,\n",
       " 0.3394476141493543,\n",
       " 0.6589776055142943,\n",
       " 0.9514420944839003,\n",
       " 0.132482638166332,\n",
       " 0.1026617863309277,\n",
       " 0.967560566704668,\n",
       " 0.45901760034806616,\n",
       " 0.1661259354909238,\n",
       " 0.8559247841073129,\n",
       " 0.21709865686018293,\n",
       " 0.3100351669214201,\n",
       " 0.7866661005972532,\n",
       " 0.45232596529836266,\n",
       " 0.6802814145491031,\n",
       " 0.4149733552816106,\n",
       " 0.36814311975836167,\n",
       " 0.6800637108892279,\n",
       " 0.31507606173536984,\n",
       " 0.2884840898257879,\n",
       " 0.7923557291465178,\n",
       " 0.3133526305253067,\n",
       " 0.9956127218264605,\n",
       " 0.08053523493945947,\n",
       " 0.694741061096293,\n",
       " 0.5605743536358814,\n",
       " 0.26415611395504945,\n",
       " 0.13856495331653407,\n",
       " 0.3119429824168126,\n",
       " 0.8389338496333358,\n",
       " 0.10034971055360054,\n",
       " 0.9222168648243049,\n",
       " 0.14196948962451816,\n",
       " 0.9731671420073259,\n",
       " 0.05435303657899393,\n",
       " 0.425485048398513,\n",
       " 0.6956681974980999,\n",
       " 0.7356563625573617,\n",
       " 0.7966757638254409,\n",
       " 0.3591348149910448,\n",
       " 0.9731021213829666,\n",
       " 0.5595187037148414,\n",
       " 0.07462626878732936,\n",
       " 0.5078768938128206,\n",
       " 0.3814114036374672,\n",
       " 0.27982783866279026,\n",
       " 0.6679122935221266,\n",
       " 0.18680877541494945,\n",
       " 0.6001142415255992,\n",
       " 0.40789313482115996,\n",
       " 0.0929905161181599,\n",
       " 0.08375294134274591,\n",
       " 0.05239622617745299,\n",
       " 0.44399459111067374,\n",
       " 0.6724136640846711,\n",
       " 0.9419592966452531,\n",
       " 0.5613557088411538,\n",
       " 0.14319266906067485,\n",
       " 0.08422451049800828,\n",
       " 0.7741571757380488,\n",
       " 0.04095221537007543,\n",
       " 0.589435783931756]"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import random\n",
    "[random.random() for i in range(100)] "
   ]
  },
  {
   "attachments": {
    "cffb0f4f-dc2c-44dd-a93c-6883a4c97be5.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Comparing Distributions\n",
    "\n",
    "* From the two previous examples, it can be seen that the two distributions differ\n",
    "<center>\n",
    "<img src=\"attachment:cffb0f4f-dc2c-44dd-a93c-6883a4c97be5.png\" width=400>\n",
    "</center>\n",
    "* Binomial distributions parameterized with different values of $n$ and/or $p$ will produce different `pmf`s\n",
    " * Therefore, it is important to describe a PMF's parameters when describing it.\n",
    "  * Modifying these parameters results in a different probability distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Probability')"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 100 \n",
    "p = 0.4\n",
    "x = range(n + 1) # our x-axis\n",
    "p_x = [binom.pmf(val, n, p) for val in x]  # our y-axis\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.bar(x, p_x, color=\"#3498db\", alpha=0.6, label=\"$p=0.4$\")\n",
    "\n",
    "p = 0.7\n",
    "p_x =  [binom.pmf(val, n, p) for val in x]  # our y-axis\n",
    "plt.bar(x, p_x, color=\"#e6b8af\", alpha=0.6, label=\"$p=0.7$\")\n",
    "plt.legend()\n",
    "plt.xlabel(\"Nb successes in 100 trials\")\n",
    "plt.ylabel(\"Probability\")\n",
    "# plt.savefig('two-distributions.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Binomial Distribution Summary: `X`, `n`, `p` and the `pmf` \n",
    "\n",
    "- The number of observed successes is said to be a random variable $X$,  distributed as a binomial distribution\n",
    "\n",
    "- We write the above statement as: \n",
    "$$ \n",
    "X \\sim Binomial(n,p)\n",
    "$$\n",
    "\n",
    "- This simply means that: \n",
    "\n",
    "  - The random variable $X$ takes on values in the sample space describes as a binomial distribution\n",
    "    - The sample space here is countably finite and range from $0$ to $n$\n",
    "  - The parameters of the binomial probability distributions are $n$ and $p$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 100 \n",
    "p = 0.4\n",
    "x = range(n + 1) # our x-axis\n",
    "p_x = [binom.pmf(val, n, p) for val in x]  # our y-axis\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.bar(x, p_x, color=\"#3498db\", alpha=0.6, label=\"$p=0.4$\")\n",
    "\n",
    "p = 0.7\n",
    "p_x =  [binom.pmf(val, n, p) for val in x]  # our y-axis\n",
    "plt.bar(x, p_x, color=\"#e6b8af\", alpha=0.6, label=\"$p=0.7$\")\n",
    "plt.legend()\n",
    "plt.xlabel(\"Nb successes in 100 trials\")\n",
    "plt.ylabel(\"Probability\")\n",
    "# plt.savefig('two-distributions.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Probability')"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 500 \n",
    "p = 0.4\n",
    "x = range(n + 1) # our x-axis\n",
    "p_x = [binom.pmf(val, n, p) for val in x]  # our y-axis\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.bar(x, p_x, color=\"#3498db\", alpha=0.6, label=\"$p=0.4$\")\n",
    "\n",
    "p = 0.7\n",
    "p_x =  [binom.pmf(val, n, p) for val in x]  # our y-axis\n",
    "plt.bar(x, p_x, color=\"#e6b8af\", alpha=0.6, label=\"$p=0.7$\")\n",
    "plt.legend()\n",
    "plt.xlabel(\"Nb successes in 100 trials\")\n",
    "plt.ylabel(\"Probability\")\n",
    "# plt.savefig('two-distributions.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Probability')"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 50 \n",
    "p = 0.4\n",
    "x = range(n + 1) # our x-axis\n",
    "p_x = [binom.pmf(val, n, p) for val in x]  # our y-axis\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.bar(x, p_x, color=\"#3498db\", alpha=0.6, label=\"$p=0.4$\")\n",
    "\n",
    "p = 0.7\n",
    "p_x =  [binom.pmf(val, n, p) for val in x]  # our y-axis\n",
    "plt.bar(x, p_x, color=\"#e6b8af\", alpha=0.6, label=\"$p=0.7$\")\n",
    "plt.legend()\n",
    "plt.xlabel(\"Nb successes in 100 trials\")\n",
    "plt.ylabel(\"Probability\")\n",
    "# plt.savefig('two-distributions.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<BarContainer object of 10 artists>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = range(0, 10)\n",
    "p_x = binom.pmf(x, n=10, p=0.5)\n",
    "plt.bar(x, p_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[4,\n",
       " 7,\n",
       " 2,\n",
       " 4,\n",
       " 7,\n",
       " 5,\n",
       " 3,\n",
       " 3,\n",
       " 6,\n",
       " 8,\n",
       " 7,\n",
       " 6,\n",
       " 5,\n",
       " 6,\n",
       " 8,\n",
       " 3,\n",
       " 4,\n",
       " 7,\n",
       " 4,\n",
       " 2,\n",
       " 7,\n",
       " 7,\n",
       " 8,\n",
       " 4,\n",
       " 3,\n",
       " 5,\n",
       " 6,\n",
       " 4,\n",
       " 5,\n",
       " 4,\n",
       " 6,\n",
       " 4,\n",
       " 7,\n",
       " 6,\n",
       " 7,\n",
       " 6,\n",
       " 7,\n",
       " 3,\n",
       " 3,\n",
       " 5,\n",
       " 7,\n",
       " 4,\n",
       " 7,\n",
       " 4,\n",
       " 6,\n",
       " 6,\n",
       " 6,\n",
       " 6,\n",
       " 5,\n",
       " 3,\n",
       " 2,\n",
       " 3,\n",
       " 7,\n",
       " 5,\n",
       " 7,\n",
       " 5,\n",
       " 5,\n",
       " 7,\n",
       " 4,\n",
       " 5,\n",
       " 3,\n",
       " 5,\n",
       " 4,\n",
       " 7,\n",
       " 4,\n",
       " 5,\n",
       " 6,\n",
       " 6,\n",
       " 4,\n",
       " 7,\n",
       " 7,\n",
       " 3,\n",
       " 6,\n",
       " 7,\n",
       " 6,\n",
       " 3,\n",
       " 7,\n",
       " 3,\n",
       " 5,\n",
       " 4,\n",
       " 5,\n",
       " 3,\n",
       " 7,\n",
       " 3,\n",
       " 5,\n",
       " 4,\n",
       " 4,\n",
       " 4,\n",
       " 5,\n",
       " 4,\n",
       " 6,\n",
       " 7,\n",
       " 5,\n",
       " 6,\n",
       " 8,\n",
       " 4,\n",
       " 2,\n",
       " 6,\n",
       " 5,\n",
       " 3,\n",
       " 5,\n",
       " 4,\n",
       " 6,\n",
       " 6,\n",
       " 7,\n",
       " 3,\n",
       " 4,\n",
       " 6,\n",
       " 8,\n",
       " 7,\n",
       " 6,\n",
       " 4,\n",
       " 3,\n",
       " 6,\n",
       " 5,\n",
       " 8,\n",
       " 8,\n",
       " 4,\n",
       " 4,\n",
       " 4,\n",
       " 6,\n",
       " 3,\n",
       " 5,\n",
       " 6,\n",
       " 6,\n",
       " 7,\n",
       " 5,\n",
       " 5,\n",
       " 5,\n",
       " 4,\n",
       " 5,\n",
       " 7,\n",
       " 3,\n",
       " 4,\n",
       " 5,\n",
       " 6,\n",
       " 4,\n",
       " 5,\n",
       " 7,\n",
       " 5,\n",
       " 3,\n",
       " 6,\n",
       " 2,\n",
       " 7,\n",
       " 3,\n",
       " 4,\n",
       " 4,\n",
       " 6,\n",
       " 5,\n",
       " 3,\n",
       " 4,\n",
       " 5,\n",
       " 6,\n",
       " 1,\n",
       " 6,\n",
       " 6,\n",
       " 6,\n",
       " 6,\n",
       " 4,\n",
       " 4,\n",
       " 4,\n",
       " 4,\n",
       " 6,\n",
       " 7,\n",
       " 5,\n",
       " 5,\n",
       " 4,\n",
       " 4,\n",
       " 4,\n",
       " 2,\n",
       " 6,\n",
       " 7,\n",
       " 7,\n",
       " 6,\n",
       " 4,\n",
       " 5,\n",
       " 0,\n",
       " 7,\n",
       " 5,\n",
       " 4,\n",
       " 6,\n",
       " 4,\n",
       " 5,\n",
       " 3,\n",
       " 7,\n",
       " 5,\n",
       " 6,\n",
       " 4,\n",
       " 4,\n",
       " 4,\n",
       " 5,\n",
       " 5,\n",
       " 7,\n",
       " 7,\n",
       " 5,\n",
       " 5,\n",
       " 3,\n",
       " 6,\n",
       " 3,\n",
       " 8,\n",
       " 5,\n",
       " 3,\n",
       " 7,\n",
       " 5,\n",
       " 3,\n",
       " 6,\n",
       " 4,\n",
       " 5,\n",
       " 4,\n",
       " 4,\n",
       " 7,\n",
       " 6,\n",
       " 4,\n",
       " 5,\n",
       " 4,\n",
       " 5,\n",
       " 5,\n",
       " 6,\n",
       " 5,\n",
       " 5,\n",
       " 5,\n",
       " 7,\n",
       " 2,\n",
       " 4,\n",
       " 6,\n",
       " 6,\n",
       " 5,\n",
       " 7,\n",
       " 6,\n",
       " 6,\n",
       " 5,\n",
       " 5,\n",
       " 7,\n",
       " 4,\n",
       " 5,\n",
       " 7,\n",
       " 5,\n",
       " 6,\n",
       " 2,\n",
       " 4,\n",
       " 5,\n",
       " 7,\n",
       " 3,\n",
       " 5,\n",
       " 4,\n",
       " 5,\n",
       " 5,\n",
       " 2,\n",
       " 6,\n",
       " 4,\n",
       " 8,\n",
       " 4,\n",
       " 6,\n",
       " 3,\n",
       " 6,\n",
       " 3,\n",
       " 5,\n",
       " 5,\n",
       " 5,\n",
       " 5,\n",
       " 6,\n",
       " 5,\n",
       " 5,\n",
       " 7,\n",
       " 5,\n",
       " 5,\n",
       " 3,\n",
       " 5,\n",
       " 7,\n",
       " 4,\n",
       " 5,\n",
       " 4,\n",
       " 2,\n",
       " 5,\n",
       " 5,\n",
       " 4,\n",
       " 9,\n",
       " 4,\n",
       " 5,\n",
       " 6,\n",
       " 7,\n",
       " 7,\n",
       " 5,\n",
       " 3,\n",
       " 4,\n",
       " 5,\n",
       " 5,\n",
       " 5,\n",
       " 4,\n",
       " 6,\n",
       " 4,\n",
       " 7,\n",
       " 2,\n",
       " 6,\n",
       " 3,\n",
       " 3,\n",
       " 4,\n",
       " 2,\n",
       " 4,\n",
       " 5,\n",
       " 7,\n",
       " 3,\n",
       " 6,\n",
       " 8,\n",
       " 6,\n",
       " 5,\n",
       " 4,\n",
       " 5,\n",
       " 3,\n",
       " 9,\n",
       " 6,\n",
       " 7,\n",
       " 4,\n",
       " 5,\n",
       " 6,\n",
       " 4,\n",
       " 5,\n",
       " 3,\n",
       " 3,\n",
       " 6,\n",
       " 4,\n",
       " 4,\n",
       " 7,\n",
       " 7,\n",
       " 4,\n",
       " 2,\n",
       " 2,\n",
       " 7,\n",
       " 6,\n",
       " 4,\n",
       " 5,\n",
       " 3,\n",
       " 7,\n",
       " 5,\n",
       " 2,\n",
       " 5,\n",
       " 4,\n",
       " 5,\n",
       " 4,\n",
       " 2,\n",
       " 6,\n",
       " 7,\n",
       " 4,\n",
       " 5,\n",
       " 7,\n",
       " 7,\n",
       " 7,\n",
       " 5,\n",
       " 3,\n",
       " 5,\n",
       " 8,\n",
       " 4,\n",
       " 5,\n",
       " 4,\n",
       " 4,\n",
       " 6,\n",
       " 8,\n",
       " 5,\n",
       " 5,\n",
       " 4,\n",
       " 4,\n",
       " 7,\n",
       " 3,\n",
       " 5,\n",
       " 5,\n",
       " 4,\n",
       " 6,\n",
       " 5,\n",
       " 6,\n",
       " 3,\n",
       " 5,\n",
       " 6,\n",
       " 3,\n",
       " 5,\n",
       " 5,\n",
       " 3,\n",
       " 3,\n",
       " 4,\n",
       " 7,\n",
       " 6,\n",
       " 5,\n",
       " 7,\n",
       " 5,\n",
       " 6,\n",
       " 6,\n",
       " 7,\n",
       " 7,\n",
       " 4,\n",
       " 5,\n",
       " 7,\n",
       " 6,\n",
       " 9,\n",
       " 3,\n",
       " 4,\n",
       " 6,\n",
       " 6,\n",
       " 6,\n",
       " 4,\n",
       " 7,\n",
       " 7,\n",
       " 6,\n",
       " 6,\n",
       " 7,\n",
       " 4,\n",
       " 5,\n",
       " 0,\n",
       " 4,\n",
       " 8,\n",
       " 7,\n",
       " 1,\n",
       " 4,\n",
       " 8,\n",
       " 4,\n",
       " 4,\n",
       " 8,\n",
       " 7,\n",
       " 7,\n",
       " 4,\n",
       " 4,\n",
       " 6,\n",
       " 3,\n",
       " 4,\n",
       " 4,\n",
       " 6,\n",
       " 2,\n",
       " 5,\n",
       " 7,\n",
       " 5,\n",
       " 2,\n",
       " 2,\n",
       " 4,\n",
       " 6,\n",
       " 4,\n",
       " 2,\n",
       " 5,\n",
       " 4,\n",
       " 6,\n",
       " 7,\n",
       " 7,\n",
       " 6,\n",
       " 4,\n",
       " 6,\n",
       " 4,\n",
       " 4,\n",
       " 5,\n",
       " 3,\n",
       " 6,\n",
       " 6,\n",
       " 6,\n",
       " 3,\n",
       " 7,\n",
       " 4,\n",
       " 4,\n",
       " 6,\n",
       " 7,\n",
       " 5,\n",
       " 5,\n",
       " 8,\n",
       " 4,\n",
       " 5,\n",
       " 4,\n",
       " 4,\n",
       " 7,\n",
       " 6,\n",
       " 3,\n",
       " 2,\n",
       " 6,\n",
       " 5,\n",
       " 6,\n",
       " 5,\n",
       " 5,\n",
       " 4,\n",
       " 6,\n",
       " 5,\n",
       " 7,\n",
       " 5,\n",
       " 5,\n",
       " 2,\n",
       " 6,\n",
       " 7,\n",
       " 5,\n",
       " 5,\n",
       " 3,\n",
       " 3,\n",
       " 5,\n",
       " 5,\n",
       " 6,\n",
       " 6,\n",
       " 4,\n",
       " 4,\n",
       " 6,\n",
       " 4,\n",
       " 4,\n",
       " 5,\n",
       " 6,\n",
       " 4,\n",
       " 7,\n",
       " 4,\n",
       " 6,\n",
       " 5,\n",
       " 8,\n",
       " 4,\n",
       " 5,\n",
       " 3,\n",
       " 6,\n",
       " 6,\n",
       " 3,\n",
       " 5,\n",
       " 6,\n",
       " 3,\n",
       " 5,\n",
       " 8,\n",
       " 8,\n",
       " 3,\n",
       " 7,\n",
       " 7,\n",
       " 6,\n",
       " 7,\n",
       " 7,\n",
       " 3,\n",
       " 4,\n",
       " 5,\n",
       " 5,\n",
       " 6,\n",
       " 6,\n",
       " 3,\n",
       " 7,\n",
       " 7,\n",
       " 7,\n",
       " 6,\n",
       " 4,\n",
       " 5,\n",
       " 4,\n",
       " 5,\n",
       " 8,\n",
       " 5,\n",
       " 3,\n",
       " 6,\n",
       " 7,\n",
       " 4,\n",
       " 6,\n",
       " 3,\n",
       " 5,\n",
       " 4,\n",
       " 5,\n",
       " 6,\n",
       " 1,\n",
       " 4,\n",
       " 3,\n",
       " 5,\n",
       " 6,\n",
       " 5,\n",
       " 4,\n",
       " 7,\n",
       " 3,\n",
       " 4,\n",
       " 2,\n",
       " 5,\n",
       " 3,\n",
       " 5,\n",
       " 7,\n",
       " 7,\n",
       " 4,\n",
       " 4,\n",
       " 3,\n",
       " 4,\n",
       " 8,\n",
       " 1,\n",
       " 4,\n",
       " 7,\n",
       " 2,\n",
       " 1,\n",
       " 5,\n",
       " 4,\n",
       " 5,\n",
       " 3,\n",
       " 5,\n",
       " 3,\n",
       " 7,\n",
       " 6,\n",
       " 3,\n",
       " 6,\n",
       " 7,\n",
       " 8,\n",
       " 3,\n",
       " 2,\n",
       " 4,\n",
       " 4,\n",
       " 4,\n",
       " 5,\n",
       " 4,\n",
       " 3,\n",
       " 4,\n",
       " 3,\n",
       " 6,\n",
       " 5,\n",
       " 5,\n",
       " 3,\n",
       " 4,\n",
       " 5,\n",
       " 6,\n",
       " 5,\n",
       " 5,\n",
       " 6,\n",
       " 6,\n",
       " 7,\n",
       " 3,\n",
       " 4,\n",
       " 6,\n",
       " 4,\n",
       " 2,\n",
       " 2,\n",
       " 6,\n",
       " 6,\n",
       " 7,\n",
       " 5,\n",
       " 4,\n",
       " 6,\n",
       " 4,\n",
       " 7,\n",
       " 5,\n",
       " 7,\n",
       " 4,\n",
       " 3,\n",
       " 6,\n",
       " 3,\n",
       " 5,\n",
       " 5,\n",
       " 3,\n",
       " 4,\n",
       " 2,\n",
       " 7,\n",
       " 5,\n",
       " 4,\n",
       " 6,\n",
       " 7,\n",
       " 2,\n",
       " 6,\n",
       " 4,\n",
       " 5,\n",
       " 5,\n",
       " 6,\n",
       " 3,\n",
       " 7,\n",
       " 5,\n",
       " 7,\n",
       " 8,\n",
       " 5,\n",
       " 8,\n",
       " 4,\n",
       " 5,\n",
       " 2,\n",
       " 5,\n",
       " 5,\n",
       " 5,\n",
       " 4,\n",
       " 8,\n",
       " 2,\n",
       " 6,\n",
       " 4,\n",
       " 6,\n",
       " 4,\n",
       " 7,\n",
       " 7,\n",
       " 5,\n",
       " 7,\n",
       " 4,\n",
       " 4,\n",
       " 3,\n",
       " 5,\n",
       " 3,\n",
       " 6,\n",
       " 7,\n",
       " 4,\n",
       " 8,\n",
       " 1,\n",
       " 2,\n",
       " 5,\n",
       " 6,\n",
       " 5,\n",
       " 7,\n",
       " 8,\n",
       " 1,\n",
       " 8,\n",
       " 7,\n",
       " 4,\n",
       " 3,\n",
       " 6,\n",
       " 3,\n",
       " 2,\n",
       " 5,\n",
       " 7,\n",
       " 5,\n",
       " 6,\n",
       " 5,\n",
       " 6,\n",
       " 8,\n",
       " 5,\n",
       " 5,\n",
       " 4,\n",
       " 5,\n",
       " 6,\n",
       " 8,\n",
       " 3,\n",
       " 2,\n",
       " 7,\n",
       " 5,\n",
       " 5,\n",
       " 7,\n",
       " 2,\n",
       " 6,\n",
       " 5,\n",
       " 7,\n",
       " 7,\n",
       " 4,\n",
       " 8,\n",
       " 4,\n",
       " 3,\n",
       " 7,\n",
       " 4,\n",
       " 4,\n",
       " 3,\n",
       " 4,\n",
       " 4,\n",
       " 6,\n",
       " 4,\n",
       " 4,\n",
       " 6,\n",
       " 2,\n",
       " 6,\n",
       " 5,\n",
       " 7,\n",
       " 7,\n",
       " 5,\n",
       " 6,\n",
       " 3,\n",
       " 7,\n",
       " 5,\n",
       " 4,\n",
       " 4,\n",
       " 6,\n",
       " 5,\n",
       " 5,\n",
       " 6,\n",
       " 6,\n",
       " 5,\n",
       " 5,\n",
       " 5,\n",
       " 5,\n",
       " 7,\n",
       " 3,\n",
       " 6,\n",
       " 8,\n",
       " 4,\n",
       " 6,\n",
       " 8,\n",
       " 6,\n",
       " 6,\n",
       " 6,\n",
       " 3,\n",
       " 2,\n",
       " 6,\n",
       " 5,\n",
       " 5,\n",
       " 7,\n",
       " 7,\n",
       " 4,\n",
       " 4,\n",
       " 3,\n",
       " 6,\n",
       " 5,\n",
       " 5,\n",
       " 3,\n",
       " 8,\n",
       " 3,\n",
       " 4,\n",
       " 4,\n",
       " 5,\n",
       " 3,\n",
       " 5,\n",
       " 4,\n",
       " 6,\n",
       " 6,\n",
       " 2,\n",
       " 5,\n",
       " 3,\n",
       " 5,\n",
       " 4,\n",
       " 5,\n",
       " 7,\n",
       " 7,\n",
       " 5,\n",
       " 5,\n",
       " 6,\n",
       " 3,\n",
       " 4,\n",
       " 7,\n",
       " 5,\n",
       " 6,\n",
       " 3,\n",
       " 6,\n",
       " 6,\n",
       " 6,\n",
       " 4,\n",
       " 6,\n",
       " 6,\n",
       " 6,\n",
       " 4,\n",
       " 4,\n",
       " 5,\n",
       " 6,\n",
       " 6,\n",
       " 8,\n",
       " 6,\n",
       " 2,\n",
       " 6,\n",
       " 2,\n",
       " 4,\n",
       " 3,\n",
       " 4,\n",
       " 5,\n",
       " 3,\n",
       " 4,\n",
       " 3,\n",
       " 6,\n",
       " 5,\n",
       " 5,\n",
       " 5,\n",
       " 5,\n",
       " 4,\n",
       " 4,\n",
       " 6,\n",
       " 7,\n",
       " 4,\n",
       " 7,\n",
       " 4,\n",
       " 4,\n",
       " 6,\n",
       " 5,\n",
       " 3,\n",
       " 6,\n",
       " 5,\n",
       " 5,\n",
       " 5,\n",
       " 7,\n",
       " 7,\n",
       " 7,\n",
       " 2,\n",
       " 7,\n",
       " 6,\n",
       " 4,\n",
       " 3,\n",
       " 4,\n",
       " 3,\n",
       " 7,\n",
       " 4,\n",
       " 3,\n",
       " 4,\n",
       " 5,\n",
       " 5,\n",
       " 3,\n",
       " 6,\n",
       " 6,\n",
       " 5,\n",
       " 6,\n",
       " 5,\n",
       " 10,\n",
       " 6,\n",
       " 5,\n",
       " 2,\n",
       " 7,\n",
       " 5,\n",
       " 7,\n",
       " 6,\n",
       " 5,\n",
       " 4,\n",
       " 6,\n",
       " 6,\n",
       " 4,\n",
       " 7,\n",
       " 4,\n",
       " 8,\n",
       " 4,\n",
       " 6,\n",
       " 1,\n",
       " 4,\n",
       " 4,\n",
       " 7,\n",
       " 4,\n",
       " 6,\n",
       " 5,\n",
       " 6,\n",
       " 4,\n",
       " 3,\n",
       " 6,\n",
       " 7,\n",
       " 6,\n",
       " 8,\n",
       " 6,\n",
       " 3,\n",
       " 4,\n",
       " 4,\n",
       " 6,\n",
       " 5,\n",
       " 4,\n",
       " 5,\n",
       " 6,\n",
       " 6,\n",
       " 5,\n",
       " 3,\n",
       " 5,\n",
       " 6,\n",
       " 4,\n",
       " 4,\n",
       " 4,\n",
       " 7,\n",
       " 6,\n",
       " 3,\n",
       " 4,\n",
       " 8,\n",
       " 3,\n",
       " 7,\n",
       " 9,\n",
       " 5,\n",
       " 6,\n",
       " 3,\n",
       " 8,\n",
       " 4,\n",
       " 3,\n",
       " 5,\n",
       " 5,\n",
       " 7,\n",
       " 5,\n",
       " 3,\n",
       " 3,\n",
       " 6,\n",
       " 5,\n",
       " 3,\n",
       " 4,\n",
       " 3,\n",
       " 5,\n",
       " 6,\n",
       " 6,\n",
       " 4,\n",
       " 7,\n",
       " 6,\n",
       " 5,\n",
       " 5,\n",
       " 6,\n",
       " 4,\n",
       " 5,\n",
       " 4,\n",
       " 4,\n",
       " 9,\n",
       " 4,\n",
       " 4,\n",
       " 6,\n",
       " 5,\n",
       " 6,\n",
       " 6,\n",
       " 4,\n",
       " 5,\n",
       " 6,\n",
       " 4,\n",
       " 6,\n",
       " 5,\n",
       " 6,\n",
       " 7,\n",
       " 7,\n",
       " 4,\n",
       " 4,\n",
       " 7,\n",
       " 3,\n",
       " 6,\n",
       " 4,\n",
       " 3,\n",
       " 3,\n",
       " 4,\n",
       " 5,\n",
       " 6,\n",
       " 8,\n",
       " 5,\n",
       " 4,\n",
       " 7,\n",
       " 3,\n",
       " 4,\n",
       " 8,\n",
       " 3,\n",
       " 4,\n",
       " 6,\n",
       " 5,\n",
       " 7,\n",
       " 7,\n",
       " 2,\n",
       " 4,\n",
       " 5,\n",
       " 6,\n",
       " 7,\n",
       " 4,\n",
       " 4]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = [binom.rvs(n=10, p=0.5) for _ in range(1000)]\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import Counter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  1.,   7.,  40.,  94., 215., 243., 212., 127.,  56.,   5.]),\n",
       " array([0. , 0.9, 1.8, 2.7, 3.6, 4.5, 5.4, 6.3, 7.2, 8.1, 9. ]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.16"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}