Monte Carlo Simulations.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Concepts\n",
    "1. A-A variation, need of A/B\n",
    "2. Double-blind Randomized Controlled Trials (RCT)\n",
    "3. Selection Bias\n",
    "4. Statistic, Sample, Estimator, Sampling Distribution, Standard Error, Confidence Interval\n",
    "5. Simpson's paradox\n",
    "6. Descriptive vs Inferential Statistics\n",
    "7. Iterators / Generators\n",
    "\n",
    "#### Notes\n",
    " * A histogram represents frequencies by areas\n",
    " * CLT: sum of two die outcomes\n",
    " \n",
    "#### Problems to try \n",
    "1. Simulate CLT\n",
    "2. Common Birthday: Given k people, what's the probability that any 2 people share a birthday?\n",
    "3. Given 52 cards with a unique label in 0...n-1, they are shuffled. What's the probability that any j^th card's label is j\n",
    "4. [Newton-Pepys](https://en.wikipedia.org/wiki/Newton%E2%80%93Pepys_problem): Problem posed by a gambler to Newton\n",
    "5. [Monty Hall](https://en.wikipedia.org/wiki/Monty_Hall_problem)\n",
    "6. Inter-arrival time: Given that a bus company's buses follow a Poisson process, if a person visits a stop at some random time, what was that inter-arrival time?\n",
    "\n",
    "Problems discussed at [StackExchange](https://codereview.stackexchange.com/questions/204384/newton-pepys-common-birthdays-and-other-probability-simulations-in-python-3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [],
   "source": [
    "from random import choices, sample, shuffle\n",
    "from statistics import mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def common_birthday(k):\n",
    "    birthdays = choices(range(1, 366), k=k)\n",
    "    return len(set(birthdays)) != k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9701"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "NUM_EXPERIMENTS = 10000\n",
    "sum([common_birthday(50) for _ in range(NUM_EXPERIMENTS)]) / NUM_EXPERIMENTS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 4, 3]"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cards = list(range(1, 5))\n",
    "shuffle(cards)\n",
    "cards"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<enumerate at 0x12429e828>"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "enumerate(range(5, 10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "any([True, True, False])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all([False, True])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [],
   "source": [
    "def matching():\n",
    "    shuffled = sample(range(52), k=52)\n",
    "    return any(idx == label for idx, label in enumerate(shuffled))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6348"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "NUM_TRIALS = 10000\n",
    "sum(matching() for _ in range(NUM_TRIALS)) / NUM_TRIALS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6321205588285577"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 - 1/e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### CLT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# takes `func` which is a random number generator & can give me sample of given size\n",
    "def sampling_dist(func):\n",
    "    for i in range(1000):\n",
    "        sample = func(2, 1, size=100)\n",
    "        statistic = sample.mean()\n",
    "        sampling_distribution.append(statistic)\n",
    "    return sampling_distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# aspirational coding\n",
    "from functools import partial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "normal_mean_1 = partial(np.random.normal, 10, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "''"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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8NTAB/A+wp6reNK4Z+zHHcVwPPB/4frfZfVX1vrEM2Kc5juMK4JXAM8z8vXpf977bqZ9rucVdkpaD5XpaRpKaZtwlqUHGXZIaZNwlqUHGXZIaZNwlqUHGXZIaZNwlqUH/B6s8oeMbmtb9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(normal_mean_1(size=1000), bins=10)\n",
    "''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for dist in [np.random.normal, np.random.gamma, np.random.poisson]:\n",
    "    sampling_distribution = []\n",
    "    for i in range(10000):\n",
    "        sample = dist(1, size=100)\n",
    "        statistic = sample.mean()\n",
    "        sampling_distribution.append(statistic)\n",
    "    plt.hist(sampling_distribution, bins=100)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[4, 4, 3, 2, 2, 1, 4, 6, 3, 1]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from random import randint\n",
    "[randint(1, 6) for i in range(10)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 4, 5, 6]"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(range(1, 7))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.hist?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "outcomes = []\n",
    "for _ in range(10000):\n",
    "    two_die_outcomes = choices(range(1, 7), k=2)\n",
    "    sum_of_two_die = sum(two_die_outcomes)\n",
    "    outcomes.append(sum_of_two_die)\n",
    "plt.hist(outcomes, bins=11)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.920286436967152\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1.9198594584164226"
      ]
     },
     "execution_count": 154,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ls = [3, 7, 5, 8]\n",
    "print(np.std(ls))\n",
    "np.std([choice(ls) for _ in range(1000000)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.707825127659933\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[1.7054823481936128,\n",
       " 5.370941048829339,\n",
       " 17.137334714301403,\n",
       " 54.4102548928968,\n",
       " 169.8482569389218]"
      ]
     },
     "execution_count": 160,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ls = range(1, 7)\n",
    "print(np.std(ls))\n",
    "[np.std([sum(choices(ls, k=num)) for _ in range(10000)]) for num in [1, 10, 100, 1000, 10000]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n",
      "1.7\n",
      "2.4885939805440342\n",
      "2.463301849144761\n"
     ]
    }
   ],
   "source": [
    "for num_trials in [1, 10, 100, 1000]:\n",
    "    print(np.std([sum(choices(range(1, 7), k=2)) for _ in range(num_trials)]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX0AAAD4CAYAAAAAczaOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAARoUlEQVR4nO3df6zddX3H8edrRZ0/B447gi3uoikuSLToDbI5jRv+KGAs7g9XsgkqsRph6jQxRf/QuLB089c0upqqHZBhGRMJjaBS2SJZIsotklJ+SYEityv0OjZxalDwvT/ut/NYbtvbe849B+7n+UhO7ve8v7/e31Be99vP93NOU1VIktrwW6NuQJI0PIa+JDXE0Jekhhj6ktQQQ1+SGnLYqBs4mCOPPLLGx8dH3YYkPWFs3br1R1U1Ntu6x33oj4+PMzk5Oeo2JOkJI8m9+1vn8I4kNeSgoZ9kY5I9Sbb31P4lyU3da2eSm7r6eJKf96z7fM8+L01yc5IdST6TJAtzSZKk/ZnL8M6FwGeBi/cWqurP9y4n+QTw457t76qqFbMcZz3wduC7wNXASuDrh96yJGm+DnqnX1XXAQ/Otq67W38TsOlAx0hyNPCsqrq+Zr734WLgjENvV5LUj37H9F8BPFBVd/bUjk3y/STfTvKKrrYUmOrZZqqrzSrJmiSTSSanp6f7bFGStFe/oX8mv3mXvxt4blWdCLwP+HKSZx3qQatqQ1VNVNXE2Niss44kSfMw7ymbSQ4D/gx46d5aVT0MPNwtb01yF3AcsAtY1rP7sq4mSRqifu70Xw3cXlX/P2yTZCzJkm75ecBy4O6q2g08lOTk7jnAWcCVfZxbkjQPc5myuQn4DvCCJFNJzulWreaxD3BfCWzrpnB+BXhnVe19CPwu4IvADuAunLkjSUOXx/s/ojIxMVF+IlcLaXztVUM93851pw/1fGpPkq1VNTHbOj+RK0kNMfQlqSGGviQ1xNCXpIYY+pLUEENfkhpi6EtSQwx9SWqIoS9JDTH0Jakhhr4kNcTQl6SGGPqS1BBDX5IaYuhLUkMMfUlqiKEvSQ0x9CWpIYa+JDXE0Jekhhj6ktQQQ1+SGnLQ0E+yMcmeJNt7ah9JsivJTd3rtJ515yfZkeSOJK/rqa/sajuSrB38pUiSDmYud/oXAitnqX+qqlZ0r6sBkhwPrAZe2O3zj0mWJFkCfA44FTgeOLPbVpI0RIcdbIOqui7J+ByPtwq4tKoeBu5JsgM4qVu3o6ruBkhyabftrYfcsSRp3voZ0z8vybZu+OeIrrYUuK9nm6mutr/6rJKsSTKZZHJ6erqPFiVJveYb+uuB5wMrgN3AJwbWEVBVG6pqoqomxsbGBnloSWraQYd3ZlNVD+xdTvIF4Gvd213AMT2bLutqHKAuSRqSed3pJzm65+0bgb0zezYDq5M8JcmxwHLge8ANwPIkxyZ5MjMPezfPv21J0nwc9E4/ySbgVcCRSaaADwOvSrICKGAn8A6AqrolyWXMPKB9BDi3qh7tjnMe8E1gCbCxqm4Z+NVIkg5oLrN3zpyl/KUDbH8BcMEs9auBqw+pO0nSQPmJXElqiKEvSQ0x9CWpIfOasilp/sbXXjW0c+1cd/rQzqUnBu/0Jakhhr4kNcTQl6SGGPqS1BBDX5Ia4uwdPe4Mc3aL1Brv9CWpIYa+JDXE0Jekhhj6ktQQQ1+SGmLoS1JDDH1JaoihL0kNMfQlqSGGviQ1xNCXpIYcNPSTbEyyJ8n2ntrHktyeZFuSK5Ic3tXHk/w8yU3d6/M9+7w0yc1JdiT5TJIszCVJkvZnLnf6FwIr96ltAU6oqhcBPwDO71l3V1Wt6F7v7KmvB94OLO9e+x5TkrTADhr6VXUd8OA+tWuq6pHu7fXAsgMdI8nRwLOq6vqqKuBi4Iz5tSxJmq9BjOm/Dfh6z/tjk3w/ybeTvKKrLQWmeraZ6mqzSrImyWSSyenp6QG0KEmCPkM/yYeAR4BLutJu4LlVdSLwPuDLSZ51qMetqg1VNVFVE2NjY/20KEnqMe9/RCXJW4DXA6d0QzZU1cPAw93y1iR3AccBu/jNIaBlXU2SNETzutNPshL4APCGqvpZT30syZJu+XnMPLC9u6p2Aw8lObmbtXMWcGXf3UuSDslB7/STbAJeBRyZZAr4MDOzdZ4CbOlmXl7fzdR5JfDRJL8EfgW8s6r2PgR+FzMzgZ7KzDOA3ucAkqQhOGjoV9WZs5S/tJ9tLwcu38+6SeCEQ+pOkjRQfiJXkhpi6EtSQwx9SWqIoS9JDTH0Jakhhr4kNcTQl6SGzPtrGCQ9/o2vvWqo59u57vShnk+Hzjt9SWqIoS9JDTH0Jakhhr4kNcTQl6SGGPqS1BCnbGpOhj31T9LC8E5fkhpi6EtSQwx9SWqIoS9JDTH0Jakhhr4kNWROoZ9kY5I9Sbb31J6dZEuSO7ufR3T1JPlMkh1JtiV5Sc8+Z3fb35nk7MFfjiTpQOZ6p38hsHKf2lrg2qpaDlzbvQc4FVjevdYA62HmlwTwYeBlwEnAh/f+opAkDcecQr+qrgMe3Ke8CrioW74IOKOnfnHNuB44PMnRwOuALVX1YFX9N7CFx/4ikSQtoH7G9I+qqt3d8v3AUd3yUuC+nu2mutr+6o+RZE2SySST09PTfbQoSeo1kAe5VVVADeJY3fE2VNVEVU2MjY0N6rCS1Lx+Qv+BbtiG7ueerr4LOKZnu2VdbX91SdKQ9BP6m4G9M3DOBq7sqZ/VzeI5GfhxNwz0TeC1SY7oHuC+tqtJkoZkTt+ymWQT8CrgyCRTzMzCWQdcluQc4F7gTd3mVwOnATuAnwFvBaiqB5P8DXBDt91Hq2rfh8OSpAU0p9CvqjP3s+qUWbYt4Nz9HGcjsHHO3UmSBspP5EpSQwx9SWqIoS9JDTH0Jakhhr4kNcTQl6SGGPqS1BBDX5IaYuhLUkMMfUlqiKEvSQ0x9CWpIYa+JDXE0Jekhszpq5UlaS7G11411PPtXHf6UM+3GHinL0kNMfQlqSGGviQ1xNCXpIb4IPcJatgPzCQtDt7pS1JD5h36SV6Q5Kae10NJ3pvkI0l29dRP69nn/CQ7ktyR5HWDuQRJ0lzNe3inqu4AVgAkWQLsAq4A3gp8qqo+3rt9kuOB1cALgecA30pyXFU9Ot8eJEmHZlDDO6cAd1XVvQfYZhVwaVU9XFX3ADuAkwZ0fknSHAwq9FcDm3ren5dkW5KNSY7oakuB+3q2mepqj5FkTZLJJJPT09MDalGS1HfoJ3ky8AbgX7vSeuD5zAz97AY+cajHrKoNVTVRVRNjY2P9tihJ6gziTv9U4MaqegCgqh6oqker6lfAF/j1EM4u4Jie/ZZ1NUnSkAwi9M+kZ2gnydE9694IbO+WNwOrkzwlybHAcuB7Azi/JGmO+vpwVpKnA68B3tFT/vskK4ACdu5dV1W3JLkMuBV4BDjXmTuSNFx9hX5V/RT43X1qbz7A9hcAF/RzTknS/PmJXElqiKEvSQ0x9CWpIYa+JDXE0Jekhhj6ktQQQ1+SGmLoS1JDDH1JaoihL0kNMfQlqSGGviQ1xNCXpIYY+pLUEENfkhpi6EtSQwx9SWqIoS9JDenrn0vUr42vvWrULUjSQXmnL0kN8U5f0hPWMP+GvXPd6UM710Lq+04/yc4kNye5KclkV3t2ki1J7ux+HtHVk+QzSXYk2ZbkJf2eX5I0d4Ma3vmTqlpRVRPd+7XAtVW1HLi2ew9wKrC8e60B1g/o/JKkOVioMf1VwEXd8kXAGT31i2vG9cDhSY5eoB4kSfsYROgXcE2SrUnWdLWjqmp3t3w/cFS3vBS4r2ffqa72G5KsSTKZZHJ6enoALUqSYDAPcv+4qnYl+T1gS5Lbe1dWVSWpQzlgVW0ANgBMTEwc0r6SpP3r+06/qnZ1P/cAVwAnAQ/sHbbpfu7pNt8FHNOz+7KuJkkagr5CP8nTkzxz7zLwWmA7sBk4u9vsbODKbnkzcFY3i+dk4Mc9w0CSpAXW7/DOUcAVSfYe68tV9Y0kNwCXJTkHuBd4U7f91cBpwA7gZ8Bb+zy/JOkQ9BX6VXU38OJZ6v8FnDJLvYBz+zmnJGn+/BoGSWqIoS9JDTH0Jakhhr4kNcTQl6SGGPqS1BBDX5IaYuhLUkMMfUlqiKEvSQ0x9CWpIYa+JDXE0Jekhhj6ktQQQ1+SGmLoS1JDDH1JaoihL0kNMfQlqSGGviQ1xNCXpIYcNt8dkxwDXAwcBRSwoao+neQjwNuB6W7TD1bV1d0+5wPnAI8C766qb/bRuyQNzfjaq4Z6vp3rTl+Q48479IFHgPdX1Y1JnglsTbKlW/epqvp478ZJjgdWAy8EngN8K8lxVfVoHz0c0LD/I0nS4928h3eqandV3dgt/wS4DVh6gF1WAZdW1cNVdQ+wAzhpvueXJB26gYzpJxkHTgS+25XOS7ItycYkR3S1pcB9PbtNceBfEpKkAes79JM8A7gceG9VPQSsB54PrAB2A5+YxzHXJJlMMjk9PX3wHSRJc9JX6Cd5EjOBf0lVfRWgqh6oqker6lfAF/j1EM4u4Jie3Zd1tceoqg1VNVFVE2NjY/20KEnqMe/QTxLgS8BtVfXJnvrRPZu9EdjeLW8GVid5SpJjgeXA9+Z7fknSoetn9s7LgTcDNye5qat9EDgzyQpmpnHuBN4BUFW3JLkMuJWZmT/nLuTMHUnSY8079KvqP4DMsurqA+xzAXDBfM8pSeqPn8iVpIYY+pLUEENfkhpi6EtSQwx9SWqIoS9JDTH0Jakhhr4kNcTQl6SGGPqS1BBDX5IaYuhLUkMMfUlqiKEvSQ0x9CWpIYa+JDXE0Jekhhj6ktQQQ1+SGmLoS1JDDH1JaoihL0kNGXroJ1mZ5I4kO5KsHfb5JallQw39JEuAzwGnAscDZyY5fpg9SFLLhn2nfxKwo6rurqpfAJcCq4bcgyQ167Ahn28pcF/P+yngZftulGQNsKZ7+79J7pjn+Y4EfjTPfZ+ovObFr7XrhQavOX/X1zX//v5WDDv056SqNgAb+j1OksmqmhhAS08YXvPi19r1gtc8SMMe3tkFHNPzfllXkyQNwbBD/wZgeZJjkzwZWA1sHnIPktSsoQ7vVNUjSc4DvgksATZW1S0LeMq+h4iegLzmxa+16wWveWBSVQtxXEnS45CfyJWkhhj6ktSQRRf6SY5J8u9Jbk1yS5L3jLqnYUmyJMn3k3xt1L0MQ5LDk3wlye1Jbkvyh6PuaaEl+evuz/X2JJuS/Paoexq0JBuT7Emyvaf27CRbktzZ/TxilD0O2n6u+WPdn+1tSa5IcvggzrXoQh94BHh/VR0PnAyc29BXPbwHuG3UTQzRp4FvVNUfAC9mkV97kqXAu4GJqjqBmckQq0fb1YK4EFi5T20tcG1VLQeu7d4vJhfy2GveApxQVS8CfgCcP4gTLbrQr6rdVXVjt/wTZoJg6Wi7WnhJlgGnA18cdS/DkOR3gFcCXwKoql9U1f+MtquhOAx4apLDgKcB/znifgauqq4DHtynvAq4qFu+CDhjqE0tsNmuuaquqapHurfXM/O5pr4tutDvlWQcOBH47mg7GYp/AD4A/GrUjQzJscA08E/dkNYXkzx91E0tpKraBXwc+CGwG/hxVV0z2q6G5qiq2t0t3w8cNcpmRuBtwNcHcaBFG/pJngFcDry3qh4adT8LKcnrgT1VtXXUvQzRYcBLgPVVdSLwUxbfX/l/QzeOvYqZX3jPAZ6e5C9H29Xw1cw882bmmif5EDPD1pcM4niLMvSTPImZwL+kqr466n6G4OXAG5LsZOabS/80yT+PtqUFNwVMVdXev8V9hZlfAovZq4F7qmq6qn4JfBX4oxH3NCwPJDkaoPu5Z8T9DEWStwCvB/6iBvShqkUX+knCzDjvbVX1yVH3MwxVdX5VLauqcWYe7P1bVS3qO8Cquh+4L8kLutIpwK0jbGkYfgicnORp3Z/zU1jkD697bAbO7pbPBq4cYS9DkWQlM0O2b6iqnw3quIsu9Jm5630zM3e7N3Wv00bdlBbEXwGXJNkGrAD+dsT9LKjubzVfAW4Ebmbm/99F9/UESTYB3wFekGQqyTnAOuA1Se5k5m8860bZ46Dt55o/CzwT2NLl2OcHci6/hkGS2rEY7/QlSfth6EtSQwx9SWqIoS9JDTH0Jakhhr4kNcTQl6SG/B8PUbKFPnsIkQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist([sum(choices(range(1, 7), k=2)) for _ in range(10000)], bins=11)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from tqdm.notebook import tqdm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy.random import normal\n",
    "from scipy.stats import ttest_ind, binom_test\n",
    "from random import choice, choices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import Counter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### CLT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 4, 5, 6]"
      ]
     },
     "execution_count": 160,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(range(1, 7))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [],
   "source": [
    "sum_of_two_die = sum([choice(range(1, 7)), choice(range(1, 7))])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [],
   "source": [
    "all_sums = []\n",
    "for i in range(10000):\n",
    "    sum_of_two_die = sum([choice(range(1, 7)), choice(range(1, 7))])\n",
    "    all_sums.append(sum_of_two_die)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "''"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(all_sums, bins=11)\n",
    "''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[5, 2, 6]"
      ]
     },
     "execution_count": 192,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "choices([5, 2, 6, 7], k=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_ is just a varaible you dont need\n",
      "_ is just a varaible you dont need\n",
      "_ is just a varaible you dont need\n"
     ]
    }
   ],
   "source": [
    "for _ in range(3):\n",
    "    print('_ is just a varaible you dont need')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "''"
      ]
     },
     "execution_count": 223,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist([sum(choices(range(1, 20), k=2)) for _ in range(100000)], bins=11)\n",
    "''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "''"
      ]
     },
     "execution_count": 231,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(np.random.normal(1, 1, size=10000), bins=100)\n",
    "''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sampling_distribution = []\n",
    "for _ in range(10000):\n",
    "    sample = np.random.normal(1, 1, size=100)\n",
    "    statistic = sample.mean()\n",
    "    sampling_distribution.append(statistic)\n",
    "plt.hist(sampling_distribution, bins=30)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 242,
   "metadata": {},
   "outputs": [],
   "source": [
    "# aspirational coding\n",
    "from functools import partial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "metadata": {},
   "outputs": [],
   "source": [
    "normal_mean_1 = partial(np.random.normal, 1, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 246,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.23665998,  2.97619129,  0.41017402, -0.49979791,  2.76344178,\n",
       "        3.82886414, -1.5485218 , -0.73051907,  1.35197759,  0.17524048])"
      ]
     },
     "execution_count": 246,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "normal_mean_1(size=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "metadata": {},
   "outputs": [],
   "source": [
    "distributions = [partial(np.random.normal, 1, 1), \n",
    "                 partial(np.random.normal, 2, 1), \n",
    "                 partial(np.random.poisson, 1)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for dist in distributions:\n",
    "    sampling_distribution = []\n",
    "    for _ in range(10000):\n",
    "        sample = dist(size=100)\n",
    "        statistic = sample.mean()\n",
    "        sampling_distribution.append(statistic)\n",
    "    plt.hist(sampling_distribution, bins=50)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**`statistic`**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy.random import normal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "''"
      ]
     },
     "execution_count": 173,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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KUoMMd0lqkOHeSfK+JPcm2ZXkC0meO+6a5pPk/Um+0dX72STHjbumuSR5fZIHkvwyyUQuNUtyTpJvJtmT5PJx1zOfJNcmOZjk/nHXspAk65PcluTB7v/9W8dd03ySrEpyZ5Kvd7W+d9w19ZPkmCRfS3Jzv3MN9197f1W9sKo2ATcDfzvughawA3hBVb0Q+G/gijHXM5/7gT8Fbh93IXPpuU3GK4FTgAuSnDLequb1CeCccRcxgMeAt1fVKcAZwKUT/D19FDirql4EbALOSXLGmGvq563A7kFONNw7VfWTnt1nABN7pbmqvlBVj3W7X2X2fQQTp6p2V9U433ncz69uk1FV/wccvk3GxKmq24EfjLuOfqrqQFXd023/lNkgWjvequZWs37W7R7bfUzsz32SdcCrgI8Pcr7h3iPJlUkeBv6MyZ6593oz8J/jLmJKrQUe7tnfx4QG0TRKsgE4DbhjvJXMr2tz7AIOAjuqamJrBf4ReAfwy0FOXlHhnuSLSe6f42MzQFW9q6rWA9cDly381cZba3fOu5j9Nfj6Sa5TK0+SZwKfBt52xG/FE6WqHu9aseuA05O8YNw1zSXJq4GDVXX3oI9ZUX+so6r+eMBTrwduAd49wnIW1K/WJH8BvBo4u8b4ZoVFfE8nkbfJGIEkxzIb7NdX1WfGXc8gqupHSW5j9rrGJF60PhN4TZJzgVXAbyb5t6r68/kesKJm7gtJsrFndzPwjXHV0k/3h1DeAbymqn4+7nqmmLfJGLIkAa4BdlfVB8ddz0KSrD680izJ05n9+xMT+XNfVVdU1bqq2sDsv9MvLRTsYLj3uqprJ9wLvILZq9KT6iPAs4Ad3dLNfxl3QXNJ8tok+4CXAp9L8vlx19Sruyh9+DYZu4EbJ/U2GUk+BXwFeF6SfUkuGXdN8zgTuAg4q/u3uaubbU6iE4Hbup/5u5jtufddYjgtvP2AJDXImbskNchwl6QGGe6S1CDDXZIaZLhLUoMMd0lqkOEuSQ36fzfM2s30uzZNAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "SAMPLE_LEN = 10000\n",
    "NUM_BINS = 100\n",
    "plt.hist(normal(size=SAMPLE_LEN), bins=NUM_BINS)\n",
    "plt.hist([normal(size=100).mean() for _ in range(SAMPLE_LEN)], bins=NUM_BINS)\n",
    "plt.hist([np.mean([normal(size=100).mean() for _ in range(100)]) for _ in range(SAMPLE_LEN)], bins=NUM_BINS)\n",
    "''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## CLT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "from functools import partial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "poisson = partial(np.random.poisson, lam=10)\n",
    "beta = partial(np.random.beta, a=1, b=2)\n",
    "gamma = partial(np.random.gamma, 4, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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zPkne2/273JHkrL52XFUT/8XiBd2vA78APAX4CnDGQX1+H/hAt7wZuGbcda/i2F8I/FS3/KajaexdvxOAm4FbgLlx172KP/cNwJeBk7vHPzvuuldx7NuBN3XLZwC7x133kMb+AuAs4M7DrL8A+GcgwDnArf3sd1rO6M8GdlXVfVX1v8DVwKaD+mwCdnTLnwDOS5JVrHFUeo69qm6qqke6h7ew+L6FFvTzcwf4c+BdwA9Ws7gR62fsvwe8r6oeBqiq/atc46j0M/YCfqZbPhH471Wsb2Sq6mbgoSN02QR8uBbdApyU5NRe+52WoF8HPLDk8Z6u7ZB9quox4ADw9FWpbrT6GftSF7N4xG9Bz7F3L13XV1VrH3rUz8/9WcCzkvxHklu6T4xtQT9j3wa8Jske4HrgD1antLFbbh4Afh59U5K8BpgDfmPctayGJD8BvAd4/ZhLGZc1LE7fnMviq7ibk/xqVX13rFWtjlcBH6qqd3cfoviRJM+pqh+Ou7BJNC1n9P18pMKP+iRZw+LLue+sSnWj1dfHSST5TeBPgJdX1aOrVNuo9Rr7CcBzgH9PspvFOcudjVyQ7efnvgfYWVX/V1XfAP6LxeCfdv2M/WLgWoCq+k/geBY/9Kt1K/p4mWkJ+n4+UmEnsKVbfiXwuequXky5nmNPcibwdyyGfCvztNBj7FV1oKrWVtVsVc2yeH3i5VW1ss+8niz9/M7/I4tn8yRZy+JUzn2rWeSI9DP2bwLnAST5FRaDfmFVqxyPncDrurtvzgEOVNW+XhtNxdRNHeYjFZL8GTBfVTuBK1l8+baLxYsZm8dX8fD0Ofa/Ap4K/EN3/fmbVfXysRU9JH2OvUl9jv2zwEuS3A08DvxxVU39q9g+x/5W4INJ/pDFC7Ovb+HELsnHWTx4r+2uP7wDOBagqj7A4vWIC4BdwCPAG/rabwP/NpKkI5iWqRtJ0goZ9JLUOINekhpn0EtS4wx6SWqcQS9JjTPoJalx/w/6WeGie6tPBAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "distributions = [poisson, beta, gamma]\n",
    "for dist in distributions:\n",
    "    plt.hist(dist(size=1000), bins=100)\n",
    "    sampling_dist = []\n",
    "    for _ in range(10000):\n",
    "        sample = dist(size=100)\n",
    "        statistic = sample.mean()\n",
    "        sampling_dist.append(statistic)\n",
    "    plt.hist(sampling_dist, bins=100)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Common Birthday problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [],
   "source": [
    "from random import randint, choices\n",
    "from statistics import mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [],
   "source": [
    "def common_birthday(k):\n",
    "    '''Returns True if any birthday is repeated'''\n",
    "    return len(set(choices(range(1, 366), k=k))) != k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mean_of_experiments(n, f, *args, **kwargs):\n",
    "    return mean(f(*args, **kwargs) for _ in range(n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [],
   "source": [
    "moe = mean_of_experiments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dice(n, c):\n",
    "    '''Simulates an experiment to roll 'n' dice and and check if count of 6's is at least c'''\n",
    "    return choices(range(1, 7), k=n).count(6) >= c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.655, 0.621, 0.611)"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_of_experiments(1000, dice, 6, 1), mean_of_experiments(1000, dice, 12, 2), moe(1000, dice, 18, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5047"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_of_experiments(10000, common_birthday, 23)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "common_birthday(100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2 Die"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "''"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist([sum(choices(range(1, 7), k=2)) for _ in range(10000)], bins=11)\n",
    "''"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}