NB0 LA Prob Stat.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "791f56eb-c09a-49d9-a0b8-788ef421702b",
   "metadata": {},
   "source": [
    "# Checking for leap year"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7916a3d6-f7a6-4c34-a3cb-4c868b59394c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def is_leap(year: int) -> bool:\n",
    "    \"\"\"\n",
    "    Checks if a given year is leap year or not.\n",
    "\n",
    "    ARGUMENTS:\n",
    "    year -> check if this year is a leap year\n",
    "\n",
    "    RETURNS:\n",
    "    TRUE if leap year, FALSE otherwise\n",
    "    \"\"\"\n",
    "\n",
    "    if year % 4 != 0:\n",
    "        # year is not divisible by 4 -> common year\n",
    "        return False\n",
    "    elif year % 100 == 0 and year % 400 != 0:\n",
    "        # year is divisible by 4 and 100 but not by 400 -> common year\n",
    "        return False\n",
    "    elif year % 3200 == 0:\n",
    "        # Not widely accepted case\n",
    "        # skip leap year every 3200 years\n",
    "        return False\n",
    "    else:\n",
    "        # year is divisible by 4 -> (100 and 400) -> ~3200 -> leap year\n",
    "        return True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d55d3ffe-756c-4f07-b232-b619b97f5432",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2024 is a leap year.\n",
      "2023 is a common year.\n",
      "2022 is a common year.\n",
      "2021 is a common year.\n",
      "2020 is a leap year.\n",
      "2000 is a leap year.\n",
      "1996 is a leap year.\n",
      "1900 is a common year.\n",
      "1600 is a leap year.\n",
      "0300 is a common year.\n",
      "3200 is a common year.\n",
      "6400 is a common year.\n"
     ]
    }
   ],
   "source": [
    "years = [2024, 2023, 2022, 2021, 2020, 2000, 1996, 1900, 1600, 300, 3200, 6400]\n",
    "\n",
    "for year in years:\n",
    "    if is_leap(year):\n",
    "        print(f\"{year:04} is a leap year.\")\n",
    "    else:\n",
    "        print(f\"{year:04} is a common year.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d960ce76-a354-4755-a522-f569fc52dead",
   "metadata": {},
   "source": [
    "# Zeller's Congruence\n",
    "### This function calculates day of any given date"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d3d8903b-c723-4bba-b01a-286a6cd4a876",
   "metadata": {},
   "outputs": [],
   "source": [
    "def day_on(day_of_month: int, month: int, year: int) -> int:\n",
    "    \"\"\"\n",
    "    Calculates ISO day of the week for a given date using Zeller's Congruence.\n",
    "\n",
    "    ARGUMENTS:\n",
    "    day_of_month -> date for which the day of week is to be calculated.\n",
    "    month -> given month\n",
    "    year -> given year\n",
    "\n",
    "    RETURNS:\n",
    "    an integer [1, 7] inclusive of 1 and 7, where every number relates to Mon - Sun in that order.\n",
    "    \"\"\"\n",
    "    \n",
    "    if month == 1 or month == 2:\n",
    "        # if JAN or FEB, decrease year by 1 and add 12 to month value\n",
    "        month += 12\n",
    "        year -= 1\n",
    "    year_of_century = year % 100\n",
    "    zero_based_century = year // 100\n",
    "    \n",
    "    # Congruence equation\n",
    "    day_of_week = (day_of_month\n",
    "                   + (13 * (month + 1)) // 5\n",
    "                   + year_of_century\n",
    "                   + year_of_century // 4\n",
    "                   + zero_based_century // 4\n",
    "                   - 2 * zero_based_century\n",
    "                  ) % 7\n",
    "    return ((day_of_week + 5) % 7) + 1 # convert to ISO format and return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f1f8e706-9feb-4582-8789-433b2baf7958",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Tuesday'"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "day_map = {1: \"Monday\",\n",
    "           2: \"Tuesday\",\n",
    "           3: \"Wednesday\",\n",
    "           4: \"Thursday\",\n",
    "           5: \"Friday\",\n",
    "           6: \"Saturday\",\n",
    "           7: \"Sunday\"\n",
    "          }\n",
    "# assertion case\n",
    "day_map[day_on(5, 2, 2019)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2580bf8b-bd22-4740-aa33-df3d5f942cf3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Day of the week on 29/02/2016: Monday\n",
      "Day of the week on 09/02/2024: Friday\n",
      "Day of the week on 13/07/2020: Monday\n",
      "Day of the week on 01/08/1996: Thursday\n"
     ]
    }
   ],
   "source": [
    "# date format: [day, month, year]\n",
    "dates = [[29, 2, 2016], [9, 2, 2024], [13, 7, 2020], [1, 8, 1996]]\n",
    "for date in dates:\n",
    "    day = day_on(date[0], \n",
    "                 date[1], \n",
    "                 date[2]\n",
    "                )\n",
    "    print(f\"Day of the week on {date[0]:02}/{date[1]:02}/{date[2]:04}: {day_map[day]}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f47618a-7b68-425b-87e2-1c0ccdc37e96",
   "metadata": {},
   "source": [
    "# Print calendar of the year"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0f75e8a2-ec95-433d-9d91-938118cc3d46",
   "metadata": {},
   "outputs": [],
   "source": [
    "month_map = {1: [\"Jan\", 31], 2: [\"Feb\", 28], 3: [\"Mar\", 31], 4: [\"Apr\", 30],\n",
    "             5: [\"May\", 31], 6: [\"Jun\", 30], 7: [\"Jul\", 31], 8: [\"Aug\", 31],\n",
    "             9: [\"Sep\", 30], 10: [\"Oct\", 31], 11: [\"Nov\", 30], 12: [\"Dec\", 31]\n",
    "            }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "34547c30-e5b6-47c0-8a1e-6bb9a755359d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def calendar_of_year(year: int, month_map:dict = month_map) -> None:\n",
    "    \"\"\"\n",
    "    This function repeatedly calls print_calendar function to print calendar for each month.\n",
    "    \n",
    "    ARGUMENTS:\n",
    "    year -> print calendar of this year\n",
    "    month_map -> gives numeric value to months and with total number of days in that specific month\n",
    "\n",
    "    RETURNS:\n",
    "    NONE\n",
    "    \"\"\"\n",
    "\n",
    "    if is_leap(year):\n",
    "        # if leap year, change number of days in February\n",
    "        month_map[2][1] = 29\n",
    "    \n",
    "    for n, month in month_map.items():\n",
    "        # get the day of the week on which the month starts\n",
    "        start_of_month = day_on(1, n, year)\n",
    "        # call print_calendar function for the month\n",
    "        print_calendar(start_of_month, month[0], month[1], year)\n",
    "\n",
    "\n",
    "def print_calendar(start_of_month: int, month_name: str, end_date: int, year: int) -> None:\n",
    "    \"\"\"\n",
    "    This function prints calendar of a given month and year.\n",
    "\n",
    "    ARGUMENTS:\n",
    "    start_of_month -> the day of the week on which the month begin.\n",
    "    month_name -> name of the month.\n",
    "    end_date -> number of days in that month.\n",
    "    year -> year for which the calendar is being prints.\n",
    "\n",
    "    RETURNS:\n",
    "    NONE\n",
    "    \"\"\"\n",
    "    # date starts from 1\n",
    "    curr = 1 \n",
    "    # print heading and subheading\n",
    "    print(f\"{month_name:>12} {year}\\n\")\n",
    "    print(f\"Mon Tue Wed Thu Fri Sat Sun\\n\")\n",
    "\n",
    "    # loop through days per week of a month\n",
    "    for i in range(6):\n",
    "        # printing weeks\n",
    "        \n",
    "        print(\" \", end=\"\")\n",
    "        for j in range(1, 8):\n",
    "            # printing dates of a week\n",
    "            \n",
    "            if curr > end_date:\n",
    "                # if current date is greater than end date of month, stop printing\n",
    "                break\n",
    "            if i == 0 and j >= start_of_month:\n",
    "                # for first week, find where to start printing dates\n",
    "                print(f\"{curr:02}  \", end = \"\")\n",
    "                curr += 1\n",
    "            elif i == 0 and j < start_of_month:\n",
    "                # insert bland spaces before start date of first week\n",
    "                print(f\"{' ':4}\", end = \"\")\n",
    "            elif i != 0:\n",
    "                # print dates for every other week\n",
    "                print(f\"{curr:02}  \", end = \"\")\n",
    "                curr += 1\n",
    "        print(f\"\\n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "476cd637-f1f5-41cf-b9a0-553febf25e63",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         Feb 2024\n",
      "\n",
      "Mon Tue Wed Thu Fri Sat Sun\n",
      "\n",
      "             01  02  03  04  \n",
      "\n",
      " 05  06  07  08  09  10  11  \n",
      "\n",
      " 12  13  14  15  16  17  18  \n",
      "\n",
      " 19  20  21  22  23  24  25  \n",
      "\n",
      " 26  27  28  29  \n",
      "\n",
      " \n",
      "\n"
     ]
    }
   ],
   "source": [
    "# sanity check\n",
    "print_calendar(4, \"Feb\", 29, 2024)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "4ed84728-1e14-42b4-a47c-df17f621010f",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         Jan 2024\n",
      "\n",
      "Mon Tue Wed Thu Fri Sat Sun\n",
      "\n",
      " 01  02  03  04  05  06  07  \n",
      "\n",
      " 08  09  10  11  12  13  14  \n",
      "\n",
      " 15  16  17  18  19  20  21  \n",
      "\n",
      " 22  23  24  25  26  27  28  \n",
      "\n",
      " 29  30  31  \n",
      "\n",
      " \n",
      "\n",
      "         Feb 2024\n",
      "\n",
      "Mon Tue Wed Thu Fri Sat Sun\n",
      "\n",
      "             01  02  03  04  \n",
      "\n",
      " 05  06  07  08  09  10  11  \n",
      "\n",
      " 12  13  14  15  16  17  18  \n",
      "\n",
      " 19  20  21  22  23  24  25  \n",
      "\n",
      " 26  27  28  29  \n",
      "\n",
      " \n",
      "\n",
      "         Mar 2024\n",
      "\n",
      "Mon Tue Wed Thu Fri Sat Sun\n",
      "\n",
      "                 01  02  03  \n",
      "\n",
      " 04  05  06  07  08  09  10  \n",
      "\n",
      " 11  12  13  14  15  16  17  \n",
      "\n",
      " 18  19  20  21  22  23  24  \n",
      "\n",
      " 25  26  27  28  29  30  31  \n",
      "\n",
      " \n",
      "\n",
      "         Apr 2024\n",
      "\n",
      "Mon Tue Wed Thu Fri Sat Sun\n",
      "\n",
      " 01  02  03  04  05  06  07  \n",
      "\n",
      " 08  09  10  11  12  13  14  \n",
      "\n",
      " 15  16  17  18  19  20  21  \n",
      "\n",
      " 22  23  24  25  26  27  28  \n",
      "\n",
      " 29  30  \n",
      "\n",
      " \n",
      "\n",
      "         May 2024\n",
      "\n",
      "Mon Tue Wed Thu Fri Sat Sun\n",
      "\n",
      "         01  02  03  04  05  \n",
      "\n",
      " 06  07  08  09  10  11  12  \n",
      "\n",
      " 13  14  15  16  17  18  19  \n",
      "\n",
      " 20  21  22  23  24  25  26  \n",
      "\n",
      " 27  28  29  30  31  \n",
      "\n",
      " \n",
      "\n",
      "         Jun 2024\n",
      "\n",
      "Mon Tue Wed Thu Fri Sat Sun\n",
      "\n",
      "                     01  02  \n",
      "\n",
      " 03  04  05  06  07  08  09  \n",
      "\n",
      " 10  11  12  13  14  15  16  \n",
      "\n",
      " 17  18  19  20  21  22  23  \n",
      "\n",
      " 24  25  26  27  28  29  30  \n",
      "\n",
      " \n",
      "\n",
      "         Jul 2024\n",
      "\n",
      "Mon Tue Wed Thu Fri Sat Sun\n",
      "\n",
      " 01  02  03  04  05  06  07  \n",
      "\n",
      " 08  09  10  11  12  13  14  \n",
      "\n",
      " 15  16  17  18  19  20  21  \n",
      "\n",
      " 22  23  24  25  26  27  28  \n",
      "\n",
      " 29  30  31  \n",
      "\n",
      " \n",
      "\n",
      "         Aug 2024\n",
      "\n",
      "Mon Tue Wed Thu Fri Sat Sun\n",
      "\n",
      "             01  02  03  04  \n",
      "\n",
      " 05  06  07  08  09  10  11  \n",
      "\n",
      " 12  13  14  15  16  17  18  \n",
      "\n",
      " 19  20  21  22  23  24  25  \n",
      "\n",
      " 26  27  28  29  30  31  \n",
      "\n",
      " \n",
      "\n",
      "         Sep 2024\n",
      "\n",
      "Mon Tue Wed Thu Fri Sat Sun\n",
      "\n",
      "                         01  \n",
      "\n",
      " 02  03  04  05  06  07  08  \n",
      "\n",
      " 09  10  11  12  13  14  15  \n",
      "\n",
      " 16  17  18  19  20  21  22  \n",
      "\n",
      " 23  24  25  26  27  28  29  \n",
      "\n",
      " 30  \n",
      "\n",
      "         Oct 2024\n",
      "\n",
      "Mon Tue Wed Thu Fri Sat Sun\n",
      "\n",
      "     01  02  03  04  05  06  \n",
      "\n",
      " 07  08  09  10  11  12  13  \n",
      "\n",
      " 14  15  16  17  18  19  20  \n",
      "\n",
      " 21  22  23  24  25  26  27  \n",
      "\n",
      " 28  29  30  31  \n",
      "\n",
      " \n",
      "\n",
      "         Nov 2024\n",
      "\n",
      "Mon Tue Wed Thu Fri Sat Sun\n",
      "\n",
      "                 01  02  03  \n",
      "\n",
      " 04  05  06  07  08  09  10  \n",
      "\n",
      " 11  12  13  14  15  16  17  \n",
      "\n",
      " 18  19  20  21  22  23  24  \n",
      "\n",
      " 25  26  27  28  29  30  \n",
      "\n",
      " \n",
      "\n",
      "         Dec 2024\n",
      "\n",
      "Mon Tue Wed Thu Fri Sat Sun\n",
      "\n",
      "                         01  \n",
      "\n",
      " 02  03  04  05  06  07  08  \n",
      "\n",
      " 09  10  11  12  13  14  15  \n",
      "\n",
      " 16  17  18  19  20  21  22  \n",
      "\n",
      " 23  24  25  26  27  28  29  \n",
      "\n",
      " 30  31  \n",
      "\n"
     ]
    }
   ],
   "source": [
    "calendar_of_year(2024)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7cb24860-8fb7-4cd7-b407-bd078deea82f",
   "metadata": {},
   "source": [
    "# Linear Algebra"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "33269191-07b1-47b6-967e-567800b15935",
   "metadata": {},
   "outputs": [],
   "source": [
    "# import dependencies\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "107ce303-b673-421c-b4fa-54bba961e506",
   "metadata": {},
   "outputs": [],
   "source": [
    "# matrices\n",
    "A = np.array([[2, -1],\n",
    "              [-1, 2]]\n",
    "            )\n",
    "B = np.array([0, 3]).T"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c32c29e8-291d-493b-aaca-70a494d2cd24",
   "metadata": {},
   "source": [
    "Method 1: Solving for X using NumPy solver"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "514db710-2828-43c0-9991-bf2bdbfe4ad5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 2.])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = np.linalg.solve(A, B)\n",
    "X"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48a651e8-759e-449d-aab3-025c506a67b5",
   "metadata": {},
   "source": [
    "Method 2: Solving for X using inverse of A: X = A_inv @ B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "004319e6-6a55-4093-afa7-90d1ac3e37cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 2.])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = np.linalg.inv(A) @ B\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "8c65ba33-f72d-480b-aaf6-ad90bac97929",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Sanity check\n",
    "A @ X == B"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d5c6e891-e126-45a0-831b-5631ab79f02d",
   "metadata": {},
   "source": [
    "Given X, solve for B using linear combination of column vectors of matrix A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "e3d18977-b08f-49d2-b7e2-c08ccf01d8f6",
   "metadata": {},
   "outputs": [],
   "source": [
    "def linear_combo(A: np.array([]), X: np.array([])) -> None:\n",
    "    \"\"\"\n",
    "    Calculates linear combination of A scaled by X\n",
    "    \n",
    "    PARAMETERS:\n",
    "    A -> 2x2 matrix\n",
    "    X -> 1x2 vector\n",
    "    \n",
    "    RETURNS:\n",
    "    NONE\n",
    "    \"\"\"\n",
    "    return np.array([X[0] * A[:,0] + X[1] * A[:, 1]]).squeeze()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "af7b3e61-3a13-4f70-8e55-413fcc7a6bfe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True,  True])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Sanity check\n",
    "linear_combo(A, X) == B "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "3fee3bef-773f-48fd-9d7d-f466423d95ab",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_combo(A: np.array([]), X: np.array([])) -> None:\n",
    "    \"\"\"\n",
    "    Plots linear combination of A scaled by X\n",
    "    \n",
    "    PARAMETERS:\n",
    "    A -> 2x2 matrix\n",
    "    X -> 1x2 vector\n",
    "    \n",
    "    RETURNS:\n",
    "    NONE\n",
    "    \"\"\"\n",
    "    \n",
    "    plt.figure(figsize=(7, 5))\n",
    "    linear_comb = linear_combo(A, X)\n",
    "    \n",
    "    scaled_ax0 = np.array([X[0] * A[0, 0], X[0] * A[1, 0]])\n",
    "    scaled_ax1 = np.array([X[1] * A[0, 1], X[1] * A[1, 1]])\n",
    "    \n",
    "    plt.plot([0, A[0,0]], \n",
    "             [0, A[1, 0]], \n",
    "             c=\"blue\", \n",
    "             label=\"AV1 vector\"\n",
    "            )\n",
    "    plt.plot([0, A[0,1]], \n",
    "             [0, A[1, 1]], \n",
    "             c=\"green\", \n",
    "             label=\"AV2 vector\"\n",
    "            )\n",
    "    plt.plot([0, scaled_ax0[0]], \n",
    "             [0, scaled_ax0[1]], \n",
    "             c=\"black\", \n",
    "             label=\"AV1 vector scaled by X0\"\n",
    "            )\n",
    "    plt.plot(np.array([0, scaled_ax1[0]]) + scaled_ax0[0], \n",
    "             np.array([0, scaled_ax1[1]]) + scaled_ax0[1], \n",
    "             c=\"yellow\", \n",
    "             label=\"AV2 vector scaled by X1\"\n",
    "            )\n",
    "    plt.plot([0, linear_comb[0]], \n",
    "             [0, linear_comb[1]], \n",
    "             c=\"red\", \n",
    "             label=\"Linear Combination\"\n",
    "            )\n",
    "    \n",
    "    plt.legend()\n",
    "    plt.grid()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "2518cb77-ba85-4b5b-a0f9-3a3423355e04",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_combo(A, X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "2d31de66-0652-4bd5-8696-8ec1c333a5c7",
   "metadata": {},
   "outputs": [],
   "source": [
    "def custom_solver(A: np.array([]), B: np.array([])) -> None:\n",
    "    \"\"\"\n",
    "    Solves AX = B for X and plots linear combination graph\n",
    "    \n",
    "    PARAMETERS:\n",
    "    A -> 2x2 matrix\n",
    "    B -> 1x2 solution vector\n",
    "    \n",
    "    RETURNS:\n",
    "    NONE\n",
    "    \"\"\"\n",
    "    X = np.linalg.solve(A, B)\n",
    "    plot_combo(A, X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "5b1a1b70-ee58-4904-9db4-e6ffd49a515c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# example in the Lab sheet\n",
    "new_B = [-1, 3]\n",
    "custom_solver(A, new_B)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9e73dc0-55c5-45cb-a263-7d5b30c6ec26",
   "metadata": {},
   "source": [
    "# Probability and Statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "63854e6c-ae83-488e-931b-4166af53f14a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# import dependencies\n",
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "5336ff87-e4be-4dc2-8978-958e00749291",
   "metadata": {},
   "outputs": [],
   "source": [
    "def Binomial(n: int, p: float) -> int:\n",
    "    \"\"\"\n",
    "    Conducts n number of trials with p probability of success\n",
    "    where success is the measures of drawning a ball of desired \n",
    "    color from the bag.\n",
    "\n",
    "    ARGUMENTS:\n",
    "    n -> Number of times the ball needs to be drawn with replacement\n",
    "    p -> Probability of drawning the right ball.\n",
    "\n",
    "    RETURNS:\n",
    "    number of success or number of times the right ball was drawn from the bag\n",
    "    \"\"\"\n",
    "    success = 0\n",
    "    c = random.randint(1, 101)\n",
    "    for i in range(n):\n",
    "        draw_prob = random.randint(1, 101)\n",
    "        if draw_prob < p * 100:\n",
    "            success += 1\n",
    "    return success    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "d04e8271",
   "metadata": {},
   "outputs": [],
   "source": [
    "def histogram(n: int, p: float, trials: int) -> None:\n",
    "    \"\"\"\n",
    "    Plots histogram of the number of success in each trial.\n",
    "\n",
    "    ARGUMENTS:\n",
    "    n -> Number of times the ball needs to be drawn with replacement\n",
    "    p -> Probability of drawning the right ball.\n",
    "    trials -> Number of trials to be conducted.\n",
    "\n",
    "    RETURNS:\n",
    "    NONE\n",
    "    \"\"\"\n",
    "    results = [Binomial(n, p) for _ in range(trials)]\n",
    "    plt.hist(results, bins=range(n+2), align=\"left\")\n",
    "    plt.xlabel(\"Number of Success\")\n",
    "    plt.ylabel(\"Frequency\")\n",
    "    plt.title(f\"Binomial Distribution of {trials} trials, n={n}, p={p}\")\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "58624958",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0CC4uLjA0NKxTv/v37y+FKgCwtraGlZWVxu8jJycnHD58uFrbe/h326BBgzR+Hvr27QsfHx84Ojrio48+wk8//aSxbnX/HWvCxMRE6+fQz88Pq1evxp49e6SzEj///LPGv0VlHn59j+rbo/pta2uLVatWabS99tprcHFxQVhYGAICArRmWBuChtcjemw6d+4MZ2dn6fmgQYNw8eJFzJw5E2+//TaaNWtW5foWFhYaz5VKJYAHf9EB//9X1cPT/2XUarVWMKrory99fX2tdn19fQDAvXv3Ku1baWkpvLy8kJmZidmzZ8PR0RHGxsYoLS2Fq6ur1Ec5FRQU4Pr161rT3A97/vnn8dtvvyE6OhqTJ09GQUEB2rZti6CgIK2p9qpUNKaVKX8q6eG2uvxlWx3Xr1+v9N+/ov0/6piqSNmMTU32IzcLC4sK91F2GqvsGC57fZXVPnysW1hYIDU1VauuoKAARUVFUq2ZmRkUCkWN9182o1TV/quzzdqq7jEcExODkJAQTJo0CR9//DEsLS2ho6OD2bNn4/Tp01Wuu2jRIrRo0QLfffcdoqKiYGBgAG9vbyxYsADt27evVb/LH6PAg+P04WO0adOm6N69e7W296gg0KZNG/Tu3RsHDhzQ6kN1jqOaKn9cABX/vrC3t3/kH5KA5nWKFhYWuHfvHu7cuaM1U37jxg2NP6yrS09PD6+//jrCwsJw9uxZ6Q/vhoTXWD3jyq7J+Ouvv+q8rbIf/qysLK1lmZmZsLS0rPM+KpOWloZjx45hwYIFmDp1Ktzd3fHiiy9W+EtRLtu2bUNJSUmVpyYAoE+fPvj555+Rl5eHAwcOwM3NDcHBwTW6D0tN/iKt6P43ZW1l42FgYAAAWn+B1vVCfwsLi0r//QHIcgyYmZmhSZMmj30/VXF0dMSJEye02svaHBwcNP5bWW3Z8rJtXr16Vevfr/w2DQ0N0a5du0q3aWhoKM2KloX+8rX379/HmTNntPZ/+vRpreuAyu+/tqp7DG/YsAHu7u5Yvnw5fHx84OLiAmdnZ9y6deuR6xobG2Pu3Lk4c+YMsrOzsXz5chw4cACDBw+uU98fZffu3dDT06vWozr33hNCaASUmhxHNXXlyhWttvK/L4AHfyRW5/XNmzdPWqey4y87OxvXrl2rdb/LAl51P2zypDXMXtETU/YXctkn0+piwIABAKBxzQwAHD58GKdPn4aHh0ed91GZsl/aZTMeZR7+xJ6cLl26hNDQUKhUKkycOLFa6+jo6MDFxUX69FTZzRyrM0tTEydPnsSxY8c02jZu3AgTExP06NEDAKRrPI4fP65RV9FFoeX/Oq+Kh4cHkpKStK47++abb2BkZCTLdU7GxsZwcXHBli1bNPpVWlqKDRs2oEWLFujQoUOd91OV4cOH48yZMxqflLt//z42bNgAFxcXaebsueeew0svvYQNGzZoXJB/4MABpKenY8SIEVLb0KFDoVAotD5BuXbtWhgaGmqcMho+fDiSkpKQkZEhtd26dQtbtmzBkCFDpFkRFxcX2NraYu3atRrb/OGHH3D79m2N/Q8fPhy3b9/G5s2bNWrXrVsHtVoNFxeXKsdEruNYoVBo/RwfP368yg9NVMTa2hoBAQF48803kZ6ejjt37tSpX1UpOxVYnUf5U2XlnT9/Hvv27dP4WanJcVRTt27d0vq537hxI5o0aYK+fftKbT///HO1Xt+ECROkdQYNGgQDAwOt46/sU8nDhg2rcX+Li4vx3XffwdLSEu3atavx+k8CTwU+Q9LS0qS/Rq9fv44tW7YgMTERw4cPh52dXZ2337FjR0yYMAGLFy9GkyZN8PLLL+PChQuYPXs2WrZsqXFBqdw6deqE559/HmFhYdKFvT///DMSExPrvO2ycbt//z5ycnLwxx9/YM2aNdDR0UFcXFyVoXTFihVISkqCj48PWrVqhXv37uHrr78GAAwcOBDAg2scWrdujZ9++gkeHh4wNzeHpaXlI28NUBm1Wo0hQ4Zgzpw5sLW1xYYNG5CYmIioqChpOv7FF19Ex44dERoaivv378PMzAxxcXHYu3ev1vYcHR2xZcsWLF++HE5OTmjSpInGKeWHhYeH45dffkH//v3x0UcfwdzcHN9++y22bduG6OhojQvX62L+/Pnw9PRE//79ERoaCn19fSxbtgxpaWnYtGlTra85OXLkiDSjkJ+fDyEEfvjhBwAPxqzs9gZjxozB0qVL8dprryEyMhJWVlZYtmwZ0tPT8dtvv2lsMyoqCp6ennjttdcQGBiInJwchIWFwcHBQeNj6F26dMHYsWMRHh4OHR0dvPjii0hISMCqVavwySefaJzuCQ0Nxfr16+Hj44N58+ZBqVQiMjIS9+7d07h1gY6ODqKjo+Hv74+JEyfizTffxNmzZzFz5kx4enpqhLWXX34Znp6eePfdd5Gfn4927dph06ZNiI+Px4YNG6Cjo1Pl2JXNTkRFReHll1+Gjo4OunbtKp3Kry5fX198/PHHCA8PR79+/ZCeno558+bBzs6u0k/VlXFxcYGvry+6du0KMzMznD59GuvXr5fuVg48+KSunZ0dRo8erfWGX1smJiaV/kxUZeDAgejbty+6du0qXbweHR0NhUKBjz/+WKO2uscR8P9/OFVndszCwgLvvvsuLl26hA4dOmD79u1YvXo13n33XenCdUD7k33VYW5ujn//+9+YPXs2zM3N4eXlhcOHD2POnDkYN24c7O3tpdpvvvkGY8aMwddff41Ro0YBePApz+LiYumTyRkZGVi8eDFSU1Ol38ENUv3cPouepLKb0D38UKlUonv37iImJkbrrr0od9O9ym5it3PnTgFA7Ny5U2orKSkRUVFRokOHDkJPT09YWlqKt99+W+vOyv369RNdunTR6mtlN7gEICZPnqzVp4dv8nnq1Cnh6ekpTExMhJmZmXjttdfEpUuXKn091b1BaNlDX19fWFlZiX79+omIiAiRk5OjtU54eLjGTRKTk5PF8OHDRevWrYVSqRQWFhaiX79+Wne7/+2338QLL7wglEqlACBGjx6tsb2rV68+cl9C/P/4/fDDD6JLly5CX19ftGnTRsTExGit/9dffwkvLy9hamoqmjdvLqZOnSrdJPLhf9MbN26If/3rX6JZs2ZCoVBo7LP82AohxIkTJ8TgwYOFSqUS+vr6olu3bmLNmjUaNWXHzvfff6/RXnZDwPL1Ffnjjz/EgAEDhLGxsTA0NBSurq7i559/rnB71b3B4OjRo7V+Vsoe5fuUnZ0tRo0aJczNzYWBgYFwdXXVuhN/mYSEBOHq6ioMDAyEubm5GDVqlLhy5YpWXVFRkQgPDxetWrUS+vr6okOHDmLRokUVbvN///ufGDZsmDA1NRVGRkbCw8NDpKSkVFi7ceNG0bVrV6Gvry9sbGxEUFCQuHXrllbdrVu3RFBQkLCxsRH6+vqia9euYtOmTY8YtQcKCwvFuHHjRPPmzaXjpOxnrPzP78PKH0OFhYUiNDRUPPfcc8LAwED06NFD/Pjjj2L06NFaN6otv25YWJhwdnYWZmZmQqlUirZt24r33ntP4y7dJ06cEABEWFjYI19TZf1u3bq19DNaF8HBwcLe3l6YmJgIXV1doVarxdtvvy3S09MrrK/ucWRpaSlcXV0fuf+y38O7du0Szs7OQqlUCltbW/HBBx9o3Ii0rr788kvRoUMHoa+vL1q1aiXCw8O17iz/8F3oy3z11VfipZdeEubm5kJXV1eYmZkJb29v8euvv8rWt8dBIUQ1rkYjIiJ6CixbtgwzZ87EuXPnKrxwu7E7deoUunTpgl9++eWRt5pwd3fHtWvX6nQfLNLGa6yIiOiZsXPnTgQFBT2VoQp48Prc3NzqfP8uqj3OWBERET2DOGP1eDBYEREREcmEpwKJiIiIZMJgRURERCQTBisiIiIimfAGoU9YaWkpMjMzYWJiUucvNSUiIqInQwiBW7duQa1WV/l1OgxWT1hmZiZatmxZ390gIiKiWsjIyECLFi0qXc5g9YSZmJgAePAPY2pqWs+9ISIiourIz89Hy5YtpffxyjBYPWFlp/9MTU0ZrIiIiBqZR13Gw4vXiYiIiGTCYEVEREQkEwYrIiIiIpkwWBERERHJhMGKiIiISCYMVkREREQyYbAiIiIikgmDFREREZFMGKyIiIiIZMJgRURERCQTBisiIiIimTBYEREREcmEwYqIiIhIJgxWRERERDJhsCIiIiKSiW59d4CIqCFqE7btkTUXIn2eQE+IqDHhjBURERGRTBisiIiIiGTCYEVEREQkEwYrIiIiIpkwWBERERHJhMGKiIiISCYMVkREREQy4X2siIhqife6IqLyOGNFREREJBMGKyIiIiKZMFgRERERyYTBioiIiEgmDFZEREREMmGwIiIiIpIJgxURERGRTBisiIiIiGTCYEVEREQkEwYrIiIiIpkwWBERERHJhN8VSETPnOp8xx8RUW1wxoqIiIhIJgxWRERERDJhsCIiIiKSCYMVERERkUwYrIiIiIhkwmBFREREJBMGKyIiIiKZMFgRERERyYTBioiIiEgmDFZEREREMmGwIiIiIpIJgxURERGRTBisiIiIiGRSr8Fqz549GDx4MNRqNRQKBX788UeN5UIIzJkzB2q1GoaGhnB3d8fJkyc1agoLCzF16lRYWlrC2NgYQ4YMweXLlzVqcnNz4e/vD5VKBZVKBX9/f9y8eVOj5tKlSxg8eDCMjY1haWmJoKAgFBUVadScOHEC/fr1g6GhIZ577jnMmzcPQgjZxoOIiIgat3oNVgUFBejWrRuWLFlS4fLo6GjExMRgyZIlOHz4MGxsbODp6Ylbt25JNcHBwYiLi0NsbCz27t2L27dvw9fXFyUlJVKNn58fUlNTER8fj/j4eKSmpsLf319aXlJSAh8fHxQUFGDv3r2IjY3F5s2bERISItXk5+fD09MTarUahw8fxuLFi7Fw4ULExMQ8hpEhIiKixkghGsiUi0KhQFxcHIYNGwbgwWyVWq1GcHAw3n//fQAPZqesra0RFRWFiRMnIi8vD82bN8f69evx+uuvAwAyMzPRsmVLbN++Hd7e3jh9+jTs7e1x4MABuLi4AAAOHDgANzc3nDlzBh07dsSOHTvg6+uLjIwMqNVqAEBsbCwCAgKQk5MDU1NTLF++HLNmzcKVK1egVCoBAJGRkVi8eDEuX74MhUJRrdeZn58PlUqFvLw8mJqayjmERFRNbcK2PbF9XYj0eWL7IqLHp7rv3w32Gqvz588jOzsbXl5eUptSqUS/fv2wf/9+AEBKSgqKi4s1atRqNRwcHKSa5ORkqFQqKVQBgKurK1QqlUaNg4ODFKoAwNvbG4WFhUhJSZFq+vXrJ4WqsprMzExcuHBB/gEgIiKiRqfBBqvs7GwAgLW1tUa7tbW1tCw7Oxv6+vowMzOrssbKykpr+1ZWVho15fdjZmYGfX39KmvKnpfVVKSwsBD5+fkaDyIiIno6NdhgVab8KTYhxCNPu5Wvqahejpqys6hV9Wf+/PnSRfMqlQotW7assu9ERETUeDXYYGVjYwNAezYoJydHmimysbFBUVERcnNzq6y5cuWK1vavXr2qUVN+P7m5uSguLq6yJicnB4D2rNrDZs2ahby8POmRkZFR9QsnIiKiRqvBBis7OzvY2NggMTFRaisqKsLu3bvRs2dPAICTkxP09PQ0arKyspCWlibVuLm5IS8vD4cOHZJqDh48iLy8PI2atLQ0ZGVlSTUJCQlQKpVwcnKSavbs2aNxC4aEhASo1Wq0adOm0tehVCphamqq8SAiIqKnk2597vz27dv43//+Jz0/f/48UlNTYW5ujlatWiE4OBgRERFo37492rdvj4iICBgZGcHPzw8AoFKpMHbsWISEhMDCwgLm5uYIDQ2Fo6MjBg4cCADo3LkzBg0ahPHjx2PlypUAgAkTJsDX1xcdO3YEAHh5ecHe3h7+/v5YsGABbty4gdDQUIwfP14KQn5+fpg7dy4CAgLwwQcf4OzZs4iIiMBHH31U7U8EEtGzpzqfQOQnB4meHvUarI4cOYL+/ftLz6dPnw4AGD16NNauXYuZM2fi7t27CAwMRG5uLlxcXJCQkAATExNpnc8//xy6uroYOXIk7t69Cw8PD6xduxY6OjpSzbfffougoCDp04NDhgzRuHeWjo4Otm3bhsDAQPTq1QuGhobw8/PDwoULpRqVSoXExERMnjwZzs7OMDMzw/Tp06U+ExERETWY+1g9K3gfK6L69yTvY1UdnLEiavga/X2siIiIiBobBisiIiIimTBYEREREcmEwYqIiIhIJgxWRERERDJhsCIiIiKSCYMVERERkUwYrIiIiIhkwmBFREREJBMGKyIiIiKZMFgRERERyYTBioiIiEgmDFZEREREMmGwIiIiIpIJgxURERGRTBisiIiIiGTCYEVEREQkE9367gARkdzahG2r7y4Q0TOKM1ZEREREMmGwIiIiIpIJgxURERGRTBisiIiIiGTCYEVEREQkEwYrIiIiIpkwWBERERHJhMGKiIiISCYMVkREREQyYbAiIiIikgmDFREREZFMGKyIiIiIZMJgRURERCQTBisiIiIimTBYEREREcmEwYqIiIhIJgxWRERERDJhsCIiIiKSCYMVERERkUwYrIiIiIhkwmBFREREJBMGKyIiIiKZMFgRERERyYTBioiIiEgmDFZEREREMmGwIiIiIpIJgxURERGRTBisiIiIiGSiW98dICJ61rUJ2/bImguRPk+gJ0RUV5yxIiIiIpIJgxURERGRTBisiIiIiGTCYEVEREQkEwYrIiIiIpk06GB1//59/Pvf/4adnR0MDQ3Rtm1bzJs3D6WlpVKNEAJz5syBWq2GoaEh3N3dcfLkSY3tFBYWYurUqbC0tISxsTGGDBmCy5cva9Tk5ubC398fKpUKKpUK/v7+uHnzpkbNpUuXMHjwYBgbG8PS0hJBQUEoKip6bK+fiIiIGpcGHayioqKwYsUKLFmyBKdPn0Z0dDQWLFiAxYsXSzXR0dGIiYnBkiVLcPjwYdjY2MDT0xO3bt2SaoKDgxEXF4fY2Fjs3bsXt2/fhq+vL0pKSqQaPz8/pKamIj4+HvHx8UhNTYW/v7+0vKSkBD4+PigoKMDevXsRGxuLzZs3IyQk5MkMBhERETV4CiGEqO9OVMbX1xfW1tb46quvpLZXX30VRkZGWL9+PYQQUKvVCA4Oxvvvvw/gweyUtbU1oqKiMHHiROTl5aF58+ZYv349Xn/9dQBAZmYmWrZsie3bt8Pb2xunT5+Gvb09Dhw4ABcXFwDAgQMH4ObmhjNnzqBjx47YsWMHfH19kZGRAbVaDQCIjY1FQEAAcnJyYGpqWq3XlJ+fD5VKhby8vGqvQ0Q1U537QjU2vI8VUf2q7vt3g56x6t27N37//Xf89ddfAIBjx45h7969eOWVVwAA58+fR3Z2Nry8vKR1lEol+vXrh/379wMAUlJSUFxcrFGjVqvh4OAg1SQnJ0OlUkmhCgBcXV2hUqk0ahwcHKRQBQDe3t4oLCxESkpKpa+hsLAQ+fn5Gg8iIiJ6OjXoO6+///77yMvLQ6dOnaCjo4OSkhJ8+umnePPNNwEA2dnZAABra2uN9aytrXHx4kWpRl9fH2ZmZlo1ZetnZ2fDyspKa/9WVlYaNeX3Y2ZmBn19fammIvPnz8fcuXNr8rKJiIiokWrQM1bfffcdNmzYgI0bN+LPP//EunXrsHDhQqxbt06jTqFQaDwXQmi1lVe+pqL62tSUN2vWLOTl5UmPjIyMKvtFREREjVeDnrGaMWMGwsLC8MYbbwAAHB0dcfHiRcyfPx+jR4+GjY0NgAezSba2ttJ6OTk50uySjY0NioqKkJubqzFrlZOTg549e0o1V65c0dr/1atXNbZz8OBBjeW5ubkoLi7Wmsl6mFKphFKprM3LJyIiokamQc9Y3blzB02aaHZRR0dHut2CnZ0dbGxskJiYKC0vKirC7t27pdDk5OQEPT09jZqsrCykpaVJNW5ubsjLy8OhQ4ekmoMHDyIvL0+jJi0tDVlZWVJNQkIClEolnJycZH7lRERE1Bg16BmrwYMH49NPP0WrVq3QpUsXHD16FDExMRgzZgyAB6fmgoODERERgfbt26N9+/aIiIiAkZER/Pz8AAAqlQpjx45FSEgILCwsYG5ujtDQUDg6OmLgwIEAgM6dO2PQoEEYP348Vq5cCQCYMGECfH190bFjRwCAl5cX7O3t4e/vjwULFuDGjRsIDQ3F+PHj+ek+IiIiAtDAg9XixYsxe/ZsBAYGIicnB2q1GhMnTsRHH30k1cycORN3795FYGAgcnNz4eLigoSEBJiYmEg1n3/+OXR1dTFy5EjcvXsXHh4eWLt2LXR0dKSab7/9FkFBQdKnB4cMGYIlS5ZIy3V0dLBt2zYEBgaiV69eMDQ0hJ+fHxYuXPgERoKIiIgagwZ9H6unEe9jRfT48T5WRCS3p+I+VkRERESNCYMVERERkUwYrIiIiIhkwmBFREREJBMGKyIiIiKZMFgRERERyYTBioiIiEgmDFZEREREMmGwIiIiIpIJgxURERGRTBisiIiIiGTCYEVEREQkE9367gARUU08jV+wTERPD85YEREREcmEwYqIiIhIJgxWRERERDJhsCIiIiKSCYMVERERkUwYrIiIiIhkwmBFREREJBMGKyIiIiKZMFgRERERyYTBioiIiEgmDFZEREREMmGwIiIiIpIJgxURERGRTGoVrM6fPy93P4iIiIgavVoFq3bt2qF///7YsGED7t27J3efiIiIiBqlWgWrY8eO4YUXXkBISAhsbGwwceJEHDp0SO6+ERERETUqtQpWDg4OiImJwT///IM1a9YgOzsbvXv3RpcuXRATE4OrV6/K3U8iIiKiBq9OF6/r6upi+PDh+O9//4uoqCicO3cOoaGhaNGiBUaNGoWsrCy5+klERETU4NUpWB05cgSBgYGwtbVFTEwMQkNDce7cOSQlJeGff/7B0KFD5eonERERUYOnW5uVYmJisGbNGqSnp+OVV17BN998g1deeQVNmjzIaXZ2dli5ciU6deoka2eJiIiIGrJaBavly5djzJgxeOedd2BjY1NhTatWrfDVV1/VqXNEREREjUmtgtXZs2cfWaOvr4/Ro0fXZvNEREREjVKtrrFas2YNvv/+e63277//HuvWratzp4iIiIgao1oFq8jISFhaWmq1W1lZISIios6dIiIiImqMahWsLl68CDs7O6321q1b49KlS3XuFBEREVFjVKtgZWVlhePHj2u1Hzt2DBYWFnXuFBEREVFjVKtg9cYbbyAoKAg7d+5ESUkJSkpKkJSUhGnTpuGNN96Qu49EREREjUKtPhX4ySef4OLFi/Dw8ICu7oNNlJaWYtSoUbzGioiIiJ5ZtQpW+vr6+O677/Dxxx/j2LFjMDQ0hKOjI1q3bi13/4iIiIgajVoFqzIdOnRAhw4d5OoLERERUaNWq2BVUlKCtWvX4vfff0dOTg5KS0s1liclJcnSOSIieqBN2LYql1+I9HlCPSGiqtQqWE2bNg1r166Fj48PHBwcoFAo5O4XERERUaNTq2AVGxuL//73v3jllVfk7g8RERFRo1Wr2y3o6+ujXbt2cveFiIiIqFGrVbAKCQnBl19+CSGE3P0hIiIiarRqdSpw79692LlzJ3bs2IEuXbpAT09PY/mWLVtk6RwRERFRY1KrYNWsWTMMHz5c7r4QERERNWq1ClZr1qyRux9EREREjV6trrECgPv37+O3337DypUrcevWLQBAZmYmbt++LVvniIiIiBqTWgWrixcvwtHREUOHDsXkyZNx9epVAEB0dDRCQ0Nl7eA///yDt99+GxYWFjAyMkL37t2RkpIiLRdCYM6cOVCr1TA0NIS7uztOnjypsY3CwkJMnToVlpaWMDY2xpAhQ3D58mWNmtzcXPj7+0OlUkGlUsHf3x83b97UqLl06RIGDx4MY2NjWFpaIigoCEVFRbK+XiIiImq8ahWspk2bBmdnZ+Tm5sLQ0FBqHz58OH7//XfZOpebm4tevXpBT08PO3bswKlTp/DZZ5+hWbNmUk10dDRiYmKwZMkSHD58GDY2NvD09JRm0QAgODgYcXFxiI2Nxd69e3H79m34+vqipKREqvHz80Nqairi4+MRHx+P1NRU+Pv7S8tLSkrg4+ODgoIC7N27F7Gxsdi8eTNCQkJke71ERETUuClELe6ZYGlpiX379qFjx44wMTHBsWPH0LZtW1y4cAH29va4c+eOLJ0LCwvDvn378Mcff1S4XAgBtVqN4OBgvP/++wAezE5ZW1sjKioKEydORF5eHpo3b47169fj9ddfB/DglGXLli2xfft2eHt74/Tp07C3t8eBAwfg4uICADhw4ADc3Nxw5swZdOzYETt27ICvry8yMjKgVqsBPLhRakBAAHJycmBqalqt15Sfnw+VSoW8vLxqr0NE/+9RX+3yrOJX2hA9XtV9/67VjFVpaanGbE+Zy5cvw8TEpDabrNDWrVvh7OyM1157DVZWVnjhhRewevVqafn58+eRnZ0NLy8vqU2pVKJfv37Yv38/ACAlJQXFxcUaNWq1Gg4ODlJNcnIyVCqVFKoAwNXVFSqVSqPGwcFBClUA4O3tjcLCQo1Tk+UVFhYiPz9f40FERERPp1oFK09PT3zxxRfSc4VCgdu3byM8PFzWr7n5+++/sXz5crRv3x6//vorJk2ahKCgIHzzzTcAgOzsbACAtbW1xnrW1tbSsuzsbOjr68PMzKzKGisrK639W1lZadSU34+ZmRn09fWlmorMnz9fum5LpVKhZcuWNRkCIiIiakRqdbuFzz//HP3794e9vT3u3bsHPz8/nD17FpaWlti0aZNsnSstLYWzszMiIiIAAC+88AJOnjyJ5cuXY9SoUVJd+S+BFkI88ouhy9dUVF+bmvJmzZqF6dOnS8/z8/MZroiIiJ5StQpWarUaqamp2LRpE/7880+UlpZi7NixeOuttzQuZq8rW1tb2Nvba7R17twZmzdvBgDY2NgAeDCbZGtrK9Xk5ORIs0s2NjYoKipCbm6uxqxVTk4OevbsKdVcuXJFa/9Xr17V2M7Bgwc1lufm5qK4uFhrJuthSqUSSqWy2q+ZiIiIGq9a38fK0NAQY8aMwZIlS7Bs2TKMGzdO1lAFAL169UJ6erpG219//YXWrVsDAOzs7GBjY4PExERpeVFREXbv3i2FJicnJ+jp6WnUZGVlIS0tTapxc3NDXl4eDh06JNUcPHgQeXl5GjVpaWnIysqSahISEqBUKuHk5CTr6yYiIqLGqVYzVmXXOFXm4dN0dfHee++hZ8+eiIiIwMiRI3Ho0CGsWrUKq1atAvDg1FxwcDAiIiLQvn17tG/fHhERETAyMoKfnx8AQKVSYezYsQgJCYGFhQXMzc0RGhoKR0dHDBw4EMCDWbBBgwZh/PjxWLlyJQBgwoQJ8PX1RceOHQEAXl5esLe3h7+/PxYsWIAbN24gNDQU48eP56f7iIiICEAtb7dQ/kLw4uJi3LlzB/r6+jAyMsKNGzdk6+Avv/yCWbNm4ezZs7Czs8P06dMxfvx4abkQAnPnzsXKlSuRm5sLFxcXLF26FA4ODlLNvXv3MGPGDGzcuBF3796Fh4cHli1bpnGt040bNxAUFIStW7cCAIYMGYIlS5Zo3DPr0qVLCAwMRFJSEgwNDeHn54eFCxfW6FQfb7dAVDe83ULFeLsFoseruu/ftQpWFTl79izeffddzJgxA97e3nJs8qnEYEVUNwxWFWOwInq8Hut9rCrSvn17REZGYtq0aXJtkoiIiKhRkS1YAYCOjg4yMzPl3CQRERFRo1Gri9fLrkMqI4RAVlYWlixZgl69esnSMSIiIqLGplbBatiwYRrPFQoFmjdvjgEDBuCzzz6To19EREREjU6tglVpaanc/SAiIiJq9GS9xoqIiIjoWVarGauHv/vuUWJiYmqzCyIiIqJGp1bB6ujRo/jzzz9x//596c7kf/31F3R0dNCjRw+p7lFfhExERET0NKlVsBo8eDBMTEywbt066S7subm5eOedd9CnTx+EhITI2kkiejbw5p9E1NjV6hqrzz77DPPnz9f4ahszMzN88skn/FQgERERPbNqFazy8/Nx5coVrfacnBzcunWrzp0iIiIiaoxqFayGDx+Od955Bz/88AMuX76My5cv44cffsDYsWMxYsQIuftIRERE1CjU6hqrFStWIDQ0FG+//TaKi4sfbEhXF2PHjsWCBQtk7SARERFRY1GrYGVkZIRly5ZhwYIFOHfuHIQQaNeuHYyNjeXuHxEREVGjUacbhGZlZSErKwsdOnSAsbExhBBy9YuIiIio0alVsLp+/To8PDzQoUMHvPLKK8jKygIAjBs3jrdaICIiomdWrYLVe++9Bz09PVy6dAlGRkZS++uvv474+HjZOkdERETUmNTqGquEhAT8+uuvaNGihUZ7+/btcfHiRVk6RkRERNTY1GrGqqCgQGOmqsy1a9egVCrr3CkiIiKixqhWwapv37745ptvpOcKhQKlpaVYsGAB+vfvL1vniIiIiBqTWp0KXLBgAdzd3XHkyBEUFRVh5syZOHnyJG7cuIF9+/bJ3UciIiKiRqFWM1b29vY4fvw4XnrpJXh6eqKgoAAjRozA0aNH8fzzz8vdRyIiIqJGocYzVsXFxfDy8sLKlSsxd+7cx9EnIiIiokapxjNWenp6SEtLg0KheBz9ISIiImq0anUqcNSoUfjqq6/k7gsRERFRo1ari9eLiorwn//8B4mJiXB2dtb6jsCYmBhZOkdERETUmNQoWP39999o06YN0tLS0KNHDwDAX3/9pVHDU4RERET0rKpRsGrfvj2ysrKwc+dOAA++wmbRokWwtrZ+LJ0jIiIiakxqdI2VEELj+Y4dO1BQUCBrh4iIiIgaq1pdvF6mfNAiIiIiepbVKFgpFAqta6h4TRURERHRAzW6xkoIgYCAAOmLlu/du4dJkyZpfSpwy5Yt8vWQiIiIqJGoUbAaPXq0xvO3335b1s4QERERNWY1ClZr1qx5XP0gIiIiavTqdPE6EREREf0/BisiIiIimTBYEREREcmkVt8VSEREDUubsG2PrLkQ6fMEekL0bOOMFREREZFMGKyIiIiIZMJgRURERCQTBisiIiIimTBYEREREcmEwYqIiIhIJgxWRERERDJhsCIiIiKSCYMVERERkUwYrIiIiIhkwmBFREREJBMGKyIiIiKZMFgRERERyaRRBav58+dDoVAgODhYahNCYM6cOVCr1TA0NIS7uztOnjypsV5hYSGmTp0KS0tLGBsbY8iQIbh8+bJGTW5uLvz9/aFSqaBSqeDv74+bN29q1Fy6dAmDBw+GsbExLC0tERQUhKKiosf1comIiKiRaTTB6vDhw1i1ahW6du2q0R4dHY2YmBgsWbIEhw8fho2NDTw9PXHr1i2pJjg4GHFxcYiNjcXevXtx+/Zt+Pr6oqSkRKrx8/NDamoq4uPjER8fj9TUVPj7+0vLS0pK4OPjg4KCAuzduxexsbHYvHkzQkJCHv+LJyIiokahUQSr27dv46233sLq1athZmYmtQsh8MUXX+DDDz/EiBEj4ODggHXr1uHOnTvYuHEjACAvLw9fffUVPvvsMwwcOBAvvPACNmzYgBMnTuC3334DAJw+fRrx8fH4z3/+Azc3N7i5uWH16tX45ZdfkJ6eDgBISEjAqVOnsGHDBrzwwgsYOHAgPvvsM6xevRr5+flPflCIiIiowWkUwWry5Mnw8fHBwIEDNdrPnz+P7OxseHl5SW1KpRL9+vXD/v37AQApKSkoLi7WqFGr1XBwcJBqkpOToVKp4OLiItW4urpCpVJp1Dg4OECtVks13t7eKCwsREpKSqV9LywsRH5+vsaDiIiInk669d2BR4mNjUVKSgqOHDmitSw7OxsAYG1trdFubW2NixcvSjX6+voaM11lNWXrZ2dnw8rKSmv7VlZWGjXl92NmZgZ9fX2ppiLz58/H3LlzH/UyiYiI6CnQoGesMjIyMG3aNHz77bcwMDCotE6hUGg8F0JotZVXvqai+trUlDdr1izk5eVJj4yMjCr7RURERI1Xgw5WKSkpyMnJgZOTE3R1daGrq4vdu3dj0aJF0NXVlWaQys8Y5eTkSMtsbGxQVFSE3NzcKmuuXLmitf+rV69q1JTfT25uLoqLi7Vmsh6mVCphamqq8SAiIqKnU4MOVh4eHjhx4gRSU1Olh7OzM9566y2kpqaibdu2sLGxQWJiorROUVERdu/ejZ49ewIAnJycoKenp1GTlZWFtLQ0qcbNzQ15eXk4dOiQVHPw4EHk5eVp1KSlpSErK0uqSUhIgFKphJOT02MdByIiImocGvQ1ViYmJnBwcNBoMzY2hoWFhdQeHByMiIgItG/fHu3bt0dERASMjIzg5+cHAFCpVBg7dixCQkJgYWEBc3NzhIaGwtHRUboYvnPnzhg0aBDGjx+PlStXAgAmTJgAX19fdOzYEQDg5eUFe3t7+Pv7Y8GCBbhx4wZCQ0Mxfvx4zkIRERERgAYerKpj5syZuHv3LgIDA5GbmwsXFxckJCTAxMREqvn888+hq6uLkSNH4u7du/Dw8MDatWuho6Mj1Xz77bcICgqSPj04ZMgQLFmyRFquo6ODbdu2ITAwEL169YKhoSH8/PywcOHCJ/diiYiIqEFTCCFEfXfiWZKfnw+VSoW8vDzOdBGV0yZsW3134al2IdKnvrtA1GhV9/27QV9jRURERNSYNPpTgUTUOHA2ioieBZyxIiIiIpIJgxURERGRTBisiIiIiGTCYEVEREQkEwYrIiIiIpkwWBERERHJhMGKiIiISCYMVkREREQyYbAiIiIikgmDFREREZFMGKyIiIiIZMJgRURERCQTBisiIiIimTBYEREREcmEwYqIiIhIJgxWRERERDJhsCIiIiKSCYMVERERkUwYrIiIiIhkwmBFREREJBMGKyIiIiKZMFgRERERyUS3vjtARERPRpuwbY+suRDp8wR6QvT04owVERERkUwYrIiIiIhkwmBFREREJBMGKyIiIiKZMFgRERERyYTBioiIiEgmDFZEREREMmGwIiIiIpIJgxURERGRTBisiIiIiGTCYEVEREQkEwYrIiIiIpkwWBERERHJhMGKiIiISCYMVkREREQyYbAiIiIikgmDFREREZFMGKyIiIiIZMJgRURERCQT3fruABE1fm3CttV3F4iIGgTOWBERERHJhMGKiIiISCYMVkREREQyYbAiIiIikgmDFREREZFMGKyIiIiIZMJgRURERCSTBh2s5s+fjxdffBEmJiawsrLCsGHDkJ6erlEjhMCcOXOgVqthaGgId3d3nDx5UqOmsLAQU6dOhaWlJYyNjTFkyBBcvnxZoyY3Nxf+/v5QqVRQqVTw9/fHzZs3NWouXbqEwYMHw9jYGJaWlggKCkJRUdFjee1ERETU+DToYLV7925MnjwZBw4cQGJiIu7fvw8vLy8UFBRINdHR0YiJicGSJUtw+PBh2NjYwNPTE7du3ZJqgoODERcXh9jYWOzduxe3b9+Gr68vSkpKpBo/Pz+kpqYiPj4e8fHxSE1Nhb+/v7S8pKQEPj4+KCgowN69exEbG4vNmzcjJCTkyQwGERERNXgKIYSo705U19WrV2FlZYXdu3ejb9++EEJArVYjODgY77//PoAHs1PW1taIiorCxIkTkZeXh+bNm2P9+vV4/fXXAQCZmZlo2bIltm/fDm9vb5w+fRr29vY4cOAAXFxcAAAHDhyAm5sbzpw5g44dO2LHjh3w9fVFRkYG1Go1ACA2NhYBAQHIycmBqalptV5Dfn4+VCoV8vLyqr0OUUPHO68/PS5E+tR3F4gapOq+fzfoGavy8vLyAADm5uYAgPPnzyM7OxteXl5SjVKpRL9+/bB//34AQEpKCoqLizVq1Go1HBwcpJrk5GSoVCopVAGAq6srVCqVRo2Dg4MUqgDA29sbhYWFSElJqbTPhYWFyM/P13gQERHR06nRBCshBKZPn47evXvDwcEBAJCdnQ0AsLa21qi1traWlmVnZ0NfXx9mZmZV1lhZWWnt08rKSqOm/H7MzMygr68v1VRk/vz50nVbKpUKLVu2rMnLJiIiokak0QSrKVOm4Pjx49i0aZPWMoVCofFcCKHVVl75morqa1NT3qxZs5CXlyc9MjIyquwXERERNV6NIlhNnToVW7duxc6dO9GiRQup3cbGBgC0ZoxycnKk2SUbGxsUFRUhNze3yporV65o7ffq1asaNeX3k5ubi+LiYq2ZrIcplUqYmppqPIiIiOjp1KCDlRACU6ZMwZYtW5CUlAQ7OzuN5XZ2drCxsUFiYqLUVlRUhN27d6Nnz54AACcnJ+jp6WnUZGVlIS0tTapxc3NDXl4eDh06JNUcPHgQeXl5GjVpaWnIysqSahISEqBUKuHk5CT/iyciIqJGR7e+O1CVyZMnY+PGjfjpp59gYmIizRipVCoYGhpCoVAgODgYERERaN++Pdq3b4+IiAgYGRnBz89Pqh07dixCQkJgYWEBc3NzhIaGwtHREQMHDgQAdO7cGYMGDcL48eOxcuVKAMCECRPg6+uLjh07AgC8vLxgb28Pf39/LFiwADdu3EBoaCjGjx/PWSgiIiIC0MBvt1DZtUtr1qxBQEAAgAezWnPnzsXKlSuRm5sLFxcXLF26VLrAHQDu3buHGTNmYOPGjbh79y48PDywbNkyjQvJb9y4gaCgIGzduhUAMGTIECxZsgTNmjWTai5duoTAwEAkJSXB0NAQfn5+WLhwIZRKZbVfE2+3QE8j3m7h2cJbMtCzqLrv3w06WD2NGKzoacRg9WxhsKJn0VN5HysiIiKihozBioiIiEgmDFZEREREMmGwIiIiIpIJgxURERGRTBisiIiIiGTCYEVEREQkEwYrIiIiIpkwWBERERHJhMGKiIiISCYMVkREREQyYbAiIiIikolufXeAiBo2fsEyEVH1ccaKiIiISCYMVkREREQyYbAiIiIikgmDFREREZFMGKyIiIiIZMJgRURERCQTBisiIiIimTBYEREREcmEwYqIiIhIJgxWRERERDLhV9oQEVGNVOdrji5E+jyBnhA1PJyxIiIiIpIJgxURERGRTBisiIiIiGTCYEVEREQkEwYrIiIiIpkwWBERERHJhMGKiIiISCYMVkREREQyYbAiIiIikgnvvE70jKvOXbSJiKh6OGNFREREJBMGKyIiIiKZMFgRERERyYTBioiIiEgmDFZEREREMuGnAomISHbV+bTphUifJ9AToieLM1ZEREREMmGwIiIiIpIJgxURERGRTBisiIiIiGTCi9eJnmL8uhoioieLM1ZEREREMmGwIiIiIpIJgxURERGRTHiNFRER1QveRJSeRpyxIiIiIpIJgxURERGRTHgqsBaWLVuGBQsWICsrC126dMEXX3yBPn361He36BnDWykQETU8DFY19N133yE4OBjLli1Dr169sHLlSrz88ss4deoUWrVqVd/dIyJ6qjzqDwheg0UNDU8F1lBMTAzGjh2LcePGoXPnzvjiiy/QsmVLLF++vL67RkRERPWMM1Y1UFRUhJSUFISFhWm0e3l5Yf/+/fXUK3oa8TQfUfXwk4XU0DBY1cC1a9dQUlICa2trjXZra2tkZ2dXuE5hYSEKCwul53l5eQCA/Pz8x9dRatAcwn+t7y4QPVNavff9I2vS5no/gZ5QY1b2vi2EqLKOwaoWFAqFxnMhhFZbmfnz52Pu3Lla7S1btnwsfSMioppTfVHfPaDG4tatW1CpVJUuZ7CqAUtLS+jo6GjNTuXk5GjNYpWZNWsWpk+fLj0vLS3FjRs3YGFhUWkYk0N+fj5atmyJjIwMmJqaPrb9PMs4xo8Xx/fx4xg/Xhzfx+9JjrEQArdu3YJara6yjsGqBvT19eHk5ITExEQMHz5cak9MTMTQoUMrXEepVEKpVGq0NWvW7HF2U4OpqSl/oB8zjvHjxfF9/DjGjxfH9/F7UmNc1UxVGQarGpo+fTr8/f3h7OwMNzc3rFq1CpcuXcKkSZPqu2tERERUzxisauj111/H9evXMW/ePGRlZcHBwQHbt29H69at67trREREVM8YrGohMDAQgYGB9d2NKimVSoSHh2udhiT5cIwfL47v48cxfrw4vo9fQxxjhXjU5waJiIiIqFp453UiIiIimTBYEREREcmEwYqIiIhIJgxWRERERDJhsHpKLVu2DHZ2djAwMICTkxP++OOP+u5So7Vnzx4MHjwYarUaCoUCP/74o8ZyIQTmzJkDtVoNQ0NDuLu74+TJk/XT2UZm/vz5ePHFF2FiYgIrKysMGzYM6enpGjUc37pZvnw5unbtKt1A0c3NDTt27JCWc3zlNX/+fCgUCgQHB0ttHOO6mTNnDhQKhcbDxsZGWt7QxpfB6in03XffITg4GB9++CGOHj2KPn364OWXX8alS5fqu2uNUkFBAbp164YlS5ZUuDw6OhoxMTFYsmQJDh8+DBsbG3h6euLWrVtPuKeNz+7duzF58mQcOHAAiYmJuH//Pry8vFBQUCDVcHzrpkWLFoiMjMSRI0dw5MgRDBgwAEOHDpXeeDi+8jl8+DBWrVqFrl27arRzjOuuS5cuyMrKkh4nTpyQljW48RX01HnppZfEpEmTNNo6deokwsLC6qlHTw8AIi4uTnpeWloqbGxsRGRkpNR27949oVKpxIoVK+qhh41bTk6OACB2794thOD4Pi5mZmbiP//5D8dXRrdu3RLt27cXiYmJol+/fmLatGlCCB7DcggPDxfdunWrcFlDHF/OWD1lioqKkJKSAi8vL412Ly8v7N+/v5569fQ6f/48srOzNcZbqVSiX79+HO9ayMvLAwCYm5sD4PjKraSkBLGxsSgoKICbmxvHV0aTJ0+Gj48PBg4cqNHOMZbH2bNnoVarYWdnhzfeeAN///03gIY5vrzz+lPm2rVrKCkpgbW1tUa7tbU1srOz66lXT6+yMa1ovC9evFgfXWq0hBCYPn06evfuDQcHBwAcX7mcOHECbm5uuHfvHpo2bYq4uDjY29tLbzwc37qJjY1FSkoKjhw5orWMx3Ddubi44JtvvkGHDh1w5coVfPLJJ+jZsydOnjzZIMeXweoppVAoNJ4LIbTaSD4c77qbMmUKjh8/jr1792ot4/jWTceOHZGamoqbN29i8+bNGD16NHbv3i0t5/jWXkZGBqZNm4aEhAQYGBhUWscxrr2XX35Z+n9HR0e4ubnh+eefx7p16+Dq6gqgYY0vTwU+ZSwtLaGjo6M1O5WTk6OV6Knuyj6ZwvGum6lTp2Lr1q3YuXMnWrRoIbVzfOWhr6+Pdu3awdnZGfPnz0e3bt3w5ZdfcnxlkJKSgpycHDg5OUFXVxe6urrYvXs3Fi1aBF1dXWkcOcbyMTY2hqOjI86ePdsgj2EGq6eMvr4+nJyckJiYqNGemJiInj171lOvnl52dnawsbHRGO+ioiLs3r2b410NQghMmTIFW7ZsQVJSEuzs7DSWc3wfDyEECgsLOb4y8PDwwIkTJ5Camio9nJ2d8dZbbyE1NRVt27blGMussLAQp0+fhq2tbcM8huvlknl6rGJjY4Wenp746quvxKlTp0RwcLAwNjYWFy5cqO+uNUq3bt0SR48eFUePHhUARExMjDh69Ki4ePGiEEKIyMhIoVKpxJYtW8SJEyfEm2++KWxtbUV+fn4997zhe/fdd4VKpRK7du0SWVlZ0uPOnTtSDce3bmbNmiX27Nkjzp8/L44fPy4++OAD0aRJE5GQkCCE4Pg+Dg9/KlAIjnFdhYSEiF27dom///5bHDhwQPj6+goTExPpPa2hjS+D1VNq6dKlonXr1kJfX1/06NFD+vg61dzOnTsFAK3H6NGjhRAPPu4bHh4ubGxshFKpFH379hUnTpyo3043EhWNKwCxZs0aqYbjWzdjxoyRfhc0b95ceHh4SKFKCI7v41A+WHGM6+b1118Xtra2Qk9PT6jVajFixAhx8uRJaXlDG1+FEELUz1wZERER0dOF11gRERERyYTBioiIiEgmDFZEREREMmGwIiIiIpIJgxURERGRTBisiIiIiGTCYEVEREQkEwYrInoqXLhwAQqFAqmpqfXdFcmZM2fg6uoKAwMDdO/evb67Q0RPAIMVEckiICAACoUCkZGRGu0//vhjvX3LfH0LDw+HsbEx0tPT8fvvv1dYk5OTg4kTJ6JVq1ZQKpWwsbGBt7c3kpOTn3BviUgODFZEJBsDAwNERUUhNze3vrsim6Kiolqve+7cOfTu3RutW7eGhYVFhTWvvvoqjh07hnXr1uGvv/7C1q1b4e7ujhs3btR6v0RUfxisiEg2AwcOhI2NDebPn19pzZw5c7ROi33xxRdo06aN9DwgIADDhg1DREQErK2t0axZM8ydOxf379/HjBkzYG5ujhYtWuDrr7/W2v6ZM2fQs2dPGBgYoEuXLti1a5fG8lOnTuGVV15B06ZNYW1tDX9/f1y7dk1a7u7ujilTpmD69OmwtLSEp6dnha+jtLQU8+bNQ4sWLaBUKtG9e3fEx8dLyxUKBVJSUjBv3jwoFArMmTNHaxs3b97E3r17ERUVhf79+6N169Z46aWXMGvWLPj4+ACo+BTnzZs3oVAoNF7byZMn4ePjA1NTU5iYmKBPnz44d+6ctPzrr79Gly5doFQqYWtriylTpkjL8vLyMGHCBFhZWcHU1BQDBgzAsWPHpOXHjh1D//79YWJiAlNTUzg5OeHIkSMAgIsXL2Lw4MEwMzODsbExunTpgu3bt1c4ZkTPAgYrIpKNjo4OIiIisHjxYly+fLlO20pKSkJmZib27NmDmJgYzJkzB76+vjAzM8PBgwcxadIkTJo0CRkZGRrrzZgxAyEhITh69Ch69uyJIUOG4Pr16wCArKws9OvXD927d8eRI0cQHx+PK1euYOTIkRrbWLduHXR1dbFv3z6sXLmywv59+eWX+Oyzz7Bw4UIcP34c3t7eGDJkCM6ePSvtq0uXLggJCUFWVhZCQ0O1ttG0aVM0bdoUP/74IwoLC2s9Vv/88w/69u0LAwMDJCUlISUlBWPGjMH9+/cBAMuXL8fkyZMxYcIEnDhxAlu3bkW7du0AAEII+Pj4IDs7G9u3b0dKSgp69OgBDw8PadbsrbfeQosWLXD48GGkpKQgLCwMenp6AIDJkyejsLAQe/bswYkTJxAVFYWmTZvW+rUQNXr19vXPRPRUGT16tBg6dKgQQghXV1cxZswYIYQQcXFx4uFfNeHh4aJbt24a637++eeidevWGttq3bq1KCkpkdo6duwo+vTpIz2/f/++MDY2Fps2bRJCCHH+/HkBQERGRko1xcXFokWLFiIqKkoIIcTs2bOFl5eXxr4zMjIEAJGeni6EEKJfv36ie/fuj3y9arVafPrppxptL774oggMDJSed+vWTYSHh1e5nR9++EGYmZkJAwMD0bNnTzFr1ixx7NgxaXnZ6zp69KjUlpubKwCInTt3CiGEmDVrlrCzsxNFRUWV9vXDDz+scNnvv/8uTE1Nxb179zTan3/+ebFy5UohhBAmJiZi7dq1Fa7v6Ogo5syZU+VrJHqWcMaKiGQXFRWFdevW4dSpU7XeRpcuXdCkyf//irK2toajo6P0XEdHBxYWFsjJydFYz83NTfp/XV1dODs74/Tp0wCAlJQU7Ny5U5opatq0KTp16gQAGqfNnJ2dq+xbfn4+MjMz0atXL432Xr16SfuqrldffRWZmZnYunUrvL29sWvXLvTo0QNr166t9jZSU1PRp08faRbpYTk5OcjMzISHh0eF66akpOD27duwsLDQGJfz589LYzJ9+nSMGzcOAwcORGRkpMZYBQUF4ZNPPkGvXr0QHh6O48eP1+j1Ez1tGKyISHZ9+/aFt7c3PvjgA61lTZo0gRBCo624uFirrnxIUCgUFbaVlpY+sj9ln0osLS3F4MGDkZqaqvE4e/Ys+vbtK9UbGxs/cpsPb7eMEKJWn4A0MDCAp6cnPvroI+zfvx8BAQEIDw8HAClcPjxm5cfL0NCw0m1XtQx4MCa2trZaY5Keno4ZM2YAeHBdXNk1XElJSbC3t0dcXBwAYNy4cfj777/h7++PEydOwNnZGYsXL67xGBA9LRisiOixmD9/Pn7++Wfs379fo7158+bIzs7WCApy3nvqwIED0v/fv38fKSkp0qxUjx49cPLkSbRp0wbt2rXTeFQ3TAGAqakp1Go19u7dq9G+f/9+dO7cuc6vwd7eHgUFBQAejBfw4JqtMuXHq2vXrvjjjz8qDKgmJiZo06ZNpbd76NGjB7Kzs6Grq6s1JpaWllJdhw4d8N577yEhIQEjRozAmjVrpGUtW7bEpEmTsGXLFoSEhGD16tW1fu1EjR2DFRE9Fl27dsVbb72lNXvh7u6Oq1evIjo6GufOncPSpUuxY8cO2fa7dOlSxMXF4cyZM5g8eTJyc3MxZswYAA8utL5x4wbefPNNHDp0CH///TcSEhIwZswYlJSU1Gg/M2bMQFRUFL777jukp6cjLCwMqampmDZtWrW3cf36dQwYMAAbNmzA8ePHcf78eXz//feIjo7G0KFDATyYcXJ1dUVkZCROnTqFPXv24N///rfGdqZMmYL8/Hy88cYbOHLkCM6ePYv169cjPT0dwIMZp88++wyLFi3C2bNn8eeff0r/LgMHDoSbmxuGDRuGX3/9FRcuXMD+/fvx73//G0eOHMHdu3cxZcoU7Nq1CxcvXsS+fftw+PBhKUAGBwfj119/xfnz5/Hnn38iKSlJlnBJ1FgxWBHRY/Pxxx9rnfbr3Lkzli1bhqVLl6Jbt244dOhQhZ+Yq63IyEhERUWhW7du+OOPP/DTTz9JMy9qtRr79u1DSUkJvL294eDggGnTpkGlUmlcz1UdQUFBCAkJQUhICBwdHREfH4+tW7eiffv21d5G06ZN4eLigs8//xx9+/aFg4MDZs+ejfHjx2PJkiVS3ddff43i4mI4Oztj2rRp+OSTTzS2Y2FhgaSkJNy+fRv9+vWDk5MTVq9eLZ06HT16NL744gssW7YMXbp0ga+vr/TpRYVCge3bt6Nv374YM2YMOnTogDfeeAMXLlyAtbU1dHR0cP36dYwaNQodOnTAyJEj8fLLL2Pu3LkAgJKSEkyePBmdO3fGoEGD0LFjRyxbtqxGY0n0NFGI8r/1iIiIiKhWOGNFREREJBMGKyIiIiKZMFgRERERyYTBioiIiEgmDFZEREREMmGwIiIiIpIJgxURERGRTBisiIiIiGTCYEVEREQkEwYrIiIiIpkwWBERERHJhMGKiIiISCb/B+MK8VOlb3ZBAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# sanity check\n",
    "histogram(50, 0.5, 1000000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "66e34fc7",
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 10\n",
    "p = 0.7\n",
    "NUM_TRIALS = 10000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "2b127604",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# call histogram function to plot the distribution\n",
    "histogram(n, p, NUM_TRIALS)"
   ]
  }
 ],
 "metadata": {
  "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": "3.11.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}