ahickm18.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IPython version:      %6.6s 8.3.0\n"
     ]
    }
   ],
   "source": [
    "import IPython\n",
    "import json\n",
    "# Numpy is a library for working with Arrays\n",
    "import numpy as np\n",
    "# SciPy implements many different numerical algorithms\n",
    "import scipy as sp\n",
    "# Pandas is good with data tables\n",
    "import pandas as pd\n",
    "# Module for plotting\n",
    "import matplotlib\n",
    "#BeautifulSoup parses HTML documents (once you get them via requests)\n",
    "import bs4\n",
    "# Nltk helps with some natural language tasks, like stemming\n",
    "import nltk\n",
    "# Bson is a binary format of json to be stored in databases\n",
    "import bson\n",
    "# Mongo is one of common nosql databases \n",
    "# it stores/searches json documents natively\n",
    "import pymongo\n",
    "print (\"IPython version:      %6.6s\", IPython.__version__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Make a 2 row x 3 column array of random numbers\n",
      "[[0.51126122 0.90299541 0.92818506]\n",
      " [0.88545375 0.73158935 0.287759  ]]\n",
      "Add 5 to every element\n",
      "[[5.51126122 5.90299541 5.92818506]\n",
      " [5.88545375 5.73158935 5.287759  ]]\n",
      "Get the first row\n",
      "[5.51126122 5.90299541 5.92818506]\n"
     ]
    }
   ],
   "source": [
    "#Here is what numpy can do\\n\",\n",
    "print (\"Make a 2 row x 3 column array of random numbers\")\n",
    "x = np.random.random((2, 3))\n",
    "print (x)\n",
    "\n",
    "#array operation (as in R)\n",
    "print (\"Add 5 to every element\")\n",
    "x = x + 5\n",
    "print (x)\n",
    "\n",
    "# get a slice (first row) (as in R)\n",
    "print (\"Get the first row\")\n",
    "print (x[0, :])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function ndarray.any>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# IPython is quite modern: just press <TAB> at the end of the unfinished statement to see the documentation\n",
    "#       on possible completions.\n",
    "#       In the code cell below, type x.<TAB>, to find built-in operations for x\n",
    "x.any"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Hz4afDfx3X8Zx+Fl5IXBTt9r1wJ/05RvKMdznyr1fkkng5cCWWYtOoffbHeZ+K4X5SmKoZmdM8qEkDwFvAt4/6oz9+ZKsA3ZW1W2zVhurYwi8s/sv+YVJDhx1xln5Xgi8KsmWJF9O8tujzjdHxse9Cni0qu7v5scp43uAD3c/Kx8Bzh51xln57uKJ99v6U5646XNo+fbZck/yTOCzwHv6z4iTnAPsAi4ZVba+LE/KWFXnVNVaevneOS756B2z9/HEL5yxMMcxPB94PvAy4GF6lxVGZo58K4CD6F0y+Evgiu4MeWR297MCnMwTZ+0jNUfGtwNndD8rZwAXjFm+U4B3JNlK73LNT4e9z32y3JM8ld6BvqSqruobfwvweuBN1V0AY0RvpbC7jH0u4Yn/yu31jHPkez69a4S3JdneZbglya+PIt9uMlJVj1bVz6rq58CneeK/vONwDKF3pnZVd9ngq8DP6b351dgcw258BfDHwOV9q49TxvXA49P/wph9n6vq3qp6bVW9gt4vyG8OPd9yPpkwjh/0nki5GPjYrPFjgLuBiVnjL+YXn+B4gOV/kmh3GQ/rm34XcGU3fTy/+CTRV0eRb9Y623niCdW9mm+BY3hI3/QZ9K5v7vXv8zz53gb8dTf9Qnr/Rc84PQ67ZccAX541NjYZ6V3bfnU3fTSwdRSPxXnyPf5E+VO65acM+xgu2z9qXD+A36P3ZMvtwK3dx3H0nrh4qG/sU33bnEPvN+t9dM/AjyjjZ4E7u/HP03uS9fEH0Ce7jHcAU6PIN2ud7TxR7ns13wLH8J+6DLfTe7+j/rLfa9/nefLtD/xz932+BXjNuD0Ou2UXAW+bY5uxyNiNb6VXlFuAV4zisThPvtPpvXLmG8BGuncLGOYx9O0HJKlB++Q1d0lqneUuSQ2y3CWpQZa7JDXIcpekBlnuktQgy12SGvT/85qvZdhe5lwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline \n",
    "import matplotlib.pyplot as plt\n",
    "heads = np.random.binomial(500, .5, size=500)\n",
    "histogram = plt.hist(heads, bins=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Task 1\n",
    "## write a program to produce Fibonacci numbers up to 1000000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "1\n",
      "2\n",
      "3\n",
      "5\n",
      "8\n",
      "13\n",
      "21\n",
      "34\n",
      "55\n",
      "89\n",
      "144\n",
      "233\n",
      "377\n",
      "610\n",
      "987\n",
      "1597\n",
      "2584\n",
      "4181\n",
      "6765\n",
      "10946\n",
      "17711\n",
      "28657\n",
      "46368\n",
      "75025\n",
      "121393\n",
      "196418\n",
      "317811\n",
      "514229\n",
      "832040\n",
      "1346269\n",
      "2178309\n",
      "3524578\n",
      "5702887\n",
      "9227465\n",
      "14930352\n",
      "24157817\n",
      "39088169\n",
      "63245986\n",
      "102334155\n",
      "165580141\n",
      "267914296\n",
      "433494437\n",
      "701408733\n",
      "1134903170\n",
      "1836311903\n",
      "2971215073\n",
      "4807526976\n",
      "7778742049\n",
      "12586269025\n",
      "20365011074\n",
      "32951280099\n",
      "53316291173\n",
      "86267571272\n",
      "139583862445\n",
      "225851433717\n",
      "365435296162\n",
      "591286729879\n",
      "956722026041\n",
      "1548008755920\n",
      "2504730781961\n",
      "4052739537881\n",
      "6557470319842\n",
      "10610209857723\n",
      "17167680177565\n",
      "27777890035288\n",
      "44945570212853\n",
      "72723460248141\n",
      "117669030460994\n",
      "190392490709135\n",
      "308061521170129\n",
      "498454011879264\n",
      "806515533049393\n",
      "1304969544928657\n",
      "2111485077978050\n",
      "3416454622906707\n",
      "5527939700884757\n",
      "8944394323791464\n",
      "14472334024676221\n",
      "23416728348467685\n",
      "37889062373143906\n",
      "61305790721611591\n",
      "99194853094755497\n",
      "160500643816367088\n",
      "259695496911122585\n",
      "420196140727489673\n",
      "679891637638612258\n",
      "1100087778366101931\n",
      "1779979416004714189\n",
      "2880067194370816120\n",
      "4660046610375530309\n",
      "7540113804746346429\n",
      "12200160415121876738\n",
      "19740274219868223167\n",
      "31940434634990099905\n",
      "51680708854858323072\n",
      "83621143489848422977\n",
      "135301852344706746049\n",
      "218922995834555169026\n",
      "354224848179261915075\n",
      "None\n"
     ]
    }
   ],
   "source": [
    "def fib(max):\n",
    "    a=0\n",
    "    b=1\n",
    "    for i in range(max):\n",
    "        print(b)\n",
    "        a,b= b,a+b\n",
    "\n",
    "obj = fib(100)\n",
    "print(obj)\n",
    "        \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Task 2\n",
    "## write a program to simulate 1000 tosses of a fair coin (use np.random.binomial)\n",
    "## Calculate the mean and standard deviation of that sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean =  0.519\n",
      "standard deviation =  0.49963886958482323\n",
      "Sample tosses\n",
      " [0 1 1 0 1 1 0 1 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 1 0 1\n",
      " 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1\n",
      " 1 1 0 1 0 0 0 0 1 1 1 0 0 0 1 0 1 0 1 0 1 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 1\n",
      " 0 0 1 0 0 0 0 1 1 1 1 1 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 1 1 1 0 0\n",
      " 0 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 0 0 0 0 1 1 0\n",
      " 0 0 1 0 1 0 1 0 1 0 0 1 0 0 1 1 0 0 1 1 0 0 1 0 1 1 1 0 0 1 1 0 0 0 1 0 0\n",
      " 1 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 1 1 0 1 1\n",
      " 0 1 0 1 1 0 0 1 0 0 0 1 1 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 0 1 1 1 1\n",
      " 0 1 1 0 1 1 0 1 0 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 0 1 0 0 0 1\n",
      " 1 0 1 1 1 0 1 1 0 1 0 1 0 0 1 1 0 0 0 0 0 1 1 1 1 0 1 1 0 0 1 1 1 1 1 0 1\n",
      " 0 1 1 0 1 0 1 1 1 1 1 0 0 0 1 0 1 1 0 1 0 1 1 1 1 1 1 0 1 1 0 0 1 1 1 1 0\n",
      " 1 0 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 0 0 0 0 1 0 0 1 0 1 1 1 1\n",
      " 1 0 1 1 0 0 0 0 1 1 0 0 0 0 0 1 1 1 0 1 0 0 1 1 1 0 1 1 1 1 0 1 1 1 0 0 1\n",
      " 1 0 0 1 1 1 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 0 1 1 0 1 1 1 0 0 0 0 0 1 0 1 1\n",
      " 0 1 1 1 1 1 0 1 0 0 1 0 1 1 0 0 0 0 0 0 1 1 1 0 1 1 0 1 1 0 1 1 1 1 0 1 1\n",
      " 0 0 0 1 1 1 1 0 0 1 1 0 0 1 0 0 1 0 0 1 0 1 1 0 1 1 1 0 1 0 0 1 0 1 1 0 1\n",
      " 1 0 0 0 1 1 1 0 1 1 1 1 0 0 1 1 0 1 1 0 0 0 0 0 0 1 1 0 0 0 1 1 0 1 1 0 0\n",
      " 1 0 0 0 0 0 1 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 1\n",
      " 1 1 1 0 0 1 1 1 1 0 1 0 1 0 1 1 0 0 1 1 0 0 1 0 1 1 1 1 0 1 0 0 1 1 0 0 0\n",
      " 1 1 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 1 1 0 1 0 0 0 1 1 1 0 1 0 1 1 0 1 0 0\n",
      " 1 1 0 0 1 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1 0 1 1 1 1 0 0 1 0 1 1 0 1 0 0 1 1\n",
      " 1 0 0 0 0 0 1 0 0 0 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1 0 1 0 0 1 1 0 1 0 0 1 1\n",
      " 0 1 1 1 0 1 1 1 1 0 1 0 1 0 1 1 1 0 0 0 1 1 0 0 1 0 0 0 0 1 1 0 1 1 0 0 1\n",
      " 0 1 0 0 1 1 0 1 0 0 0 1 1 1 1 0 1 1 0 0 0 1 0 0 0 0 0 1 1 1 0 1 0 1 0 1 1\n",
      " 0 1 1 1 0 1 0 1 1 0 0 1 1 1 0 1 1 1 1 1 1 0 0 1 0 0 1 0 0 1 1 0 0 1 1 0 0\n",
      " 1 0 1 0 1 1 0 1 1 0 0 1 0 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 1 1 1 1 0 1 1 0 1\n",
      " 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 1 0 1 1 1 0 1 0 0 0 1 1 0 0 0 0 1 1 1 0 0 0\n",
      " 0]\n"
     ]
    }
   ],
   "source": [
    "ct = np.random.binomial(1, .5, 1000)\n",
    "print(\"mean = \", np.mean(ct))\n",
    "print(\"standard deviation = \", np.std(ct))\n",
    "print(\"Sample tosses\\n\", ct)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Task 3\n",
    "## Produce a scatterplot of y = 0.5*x+e where x has gaussian (0, 5) and e has gaussian (0, 1) distributions \n",
    "### use numpy.random.normal to generate gaussian distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.random.normal(0, 5, 100)\n",
    "e = np.random.normal(0, 1, 100)\n",
    "y = 0.5*x+e\n",
    "\n",
    "plt.title(\"scatterplot\")\n",
    "plt.scatter(x, y)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}