Stat_654_Homework_1.ipynb

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    "# Jabbireddy, Srujan - Homework 1\n",
    "\n",
    "### Submission\n",
    "Replace Last Name, First Name above with your name. When you complete this homework, please click \"File\" -> \"Download as\" and save as a PDF (double check that all your code / markdown is there and that your plots are visible). Submit your homework on eCampus by **11:55pm on Monday 3rd February**. \n",
    "\n",
    "### R versus Python\n",
    "You may complete this homework in either R or Python. The current notebook is written in R. If you are completing your homework in R, you can simply modify this notebook with your answers. If you are completing your homework in Python, initiate a Jupyter Python notebook and write your answers there.\n",
    "\n",
    "### Background Reading for Problems\n",
    "- Section 22.1 - 22.5 in \"Numerical Analysis\" by Lange."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 1: Inverse Method for exponentials\n",
    "\n",
    "1. Use the inverse method and the language $Unif[0,1]$ generator (runif in R, numpy.random.uniform in python), to generate random deviates from an Exponential distribution with mean $\\mu$. $\\mu$ and the number of random deviates should be arguments to your function. Be aware that there are two standard methods for parameterizing the Exponential.\n",
    "2. For some particular $\\mu$ of your choosing, make a histogram of the random deviates and plot the appropriate Exponential density curve on top of the histogram to confirm that the generator is working. Verify that the mean and standard deviation are what they should be.\n",
    "3. Compare the speed of your Exponential generator to the language generator (rexp in R, numpy.random.exponential in Python). Try to make your generator computationally competitive with the built in generator, by avoiding for loops and other slow code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/latex"
   },
   "source": [
    "# Question 1.1 \n",
    "# Generating random from deviates by creating a function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Question1.1\n",
    "def exp_dist(n,mu):\n",
    "    U = np.random.uniform(size=n)\n",
    "    Iexp = -mu*np.log(1-U)\n",
    "    return Iexp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
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       "       9.03823529e+00, 1.93558470e+01, 5.11979438e-01, 2.06585420e+01,\n",
       "       5.14696830e+01, 1.69532415e+01, 7.15881659e+01, 2.25256740e+01,\n",
       "       1.26915174e+01, 1.29357515e+01, 3.05866765e+01, 2.91473655e+01,\n",
       "       2.40956757e+01, 7.65811302e+00, 5.32299762e+00, 1.23165872e+01,\n",
       "       7.84264295e+01, 4.21597732e+01, 3.83982614e-01, 2.97098154e+00,\n",
       "       3.79130753e+01, 3.15654043e+00, 8.77694840e+00, 2.42559345e+01,\n",
       "       8.00156971e+01, 2.58881583e+00, 5.03657104e-01, 4.97486356e+01,\n",
       "       4.86583094e+00, 3.19000199e-01, 5.26100765e+01, 1.87102844e+00,\n",
       "       2.43849378e+00, 4.87975792e+00, 1.95449187e+00, 1.39666765e+01,\n",
       "       3.52433304e+01, 5.96531943e+00, 7.61986324e+01, 2.12624355e+01,\n",
       "       2.46242501e+01, 9.27434467e+00, 6.36475388e+00, 1.86396471e+01,\n",
       "       1.53854910e+01, 6.39843033e+00, 9.43726495e+00, 4.20041689e+01,\n",
       "       2.35400000e+01, 1.26237264e+01, 2.18102456e+02, 4.01786147e+01,\n",
       "       9.65857832e+00, 7.71882683e+00, 5.82753258e+00, 1.59577805e+01,\n",
       "       3.13882277e+01, 4.81522750e+00, 2.08592554e+01, 1.16571054e+01,\n",
       "       4.60126271e+00, 1.48893867e+01, 8.10797786e+00, 2.27178542e+01,\n",
       "       1.42511558e+01, 9.83564631e+00, 1.86440142e+00, 3.02557203e+01,\n",
       "       5.38670213e+01, 6.42655277e+00, 2.37226520e+01, 4.43206025e-01,\n",
       "       1.56240248e+01, 2.22876410e+01, 1.80141926e+01, 9.64667646e+01,\n",
       "       1.20973217e+00, 5.51667151e+01, 2.70202420e+01, 1.28871559e+01,\n",
       "       2.81387234e+00, 8.52894888e+00, 1.30578059e+01, 1.08564490e+00,\n",
       "       5.69553881e+01, 3.18586198e+00, 3.50702056e+00, 1.04273922e+01,\n",
       "       3.87586945e+00, 9.97257204e+01, 2.06708667e+01, 6.34983782e+01,\n",
       "       7.82554135e+00, 6.52786940e+00, 1.19591922e+01, 5.36749328e+01,\n",
       "       3.54639551e+00, 2.52178473e+01, 2.64140053e+00, 9.29401806e+00,\n",
       "       1.14292569e+01, 2.81843155e+00, 3.72557771e+01, 1.65795895e+01,\n",
       "       2.45029846e+01, 3.35982062e+00, 8.06160336e+00, 3.74880049e+01,\n",
       "       7.13191836e+00, 2.49284623e-01, 3.37331579e+01, 1.59713716e+00,\n",
       "       7.31205024e+00, 7.77129503e+01, 2.04474648e+01, 7.96832632e+00,\n",
       "       3.61523348e+01, 3.92105448e+01, 4.18358331e+01, 3.91971417e+00,\n",
       "       4.40264099e+01, 1.06016566e+01, 3.95976273e+00, 7.74962750e+00,\n",
       "       1.23499840e+01, 4.14348752e+01, 6.34564348e+00, 1.39630647e+01,\n",
       "       6.23727292e-01, 4.73976188e+00, 5.19110894e+01, 1.53467519e+02,\n",
       "       1.54713496e+01, 1.34614471e+01, 8.08745605e+00, 3.36078778e+00,\n",
       "       3.74186710e+01, 4.02375501e+01, 5.50621652e+01, 8.39394058e+00,\n",
       "       4.03980477e-01, 7.37619691e+01, 4.87517265e+00, 1.82918240e+00,\n",
       "       2.61043550e+00, 2.40521385e+01, 7.64654694e+00, 7.09644981e+01,\n",
       "       2.35786789e+00, 1.26872922e+01, 2.23079988e+00, 2.28443856e+01,\n",
       "       4.39013179e+01, 1.01942979e+01, 2.22078235e+01, 3.62643055e+01,\n",
       "       8.65231914e+01, 1.17382021e+01, 9.15939447e+00, 4.79391855e+00,\n",
       "       8.47602202e-01, 1.42299143e+01, 2.08774230e+01, 2.06902841e+00,\n",
       "       1.97523078e+01, 3.49690780e+01, 2.31322932e+01, 2.04209035e+01,\n",
       "       5.30755931e+01, 2.71816503e+01, 1.69930492e+01, 1.67839635e+01,\n",
       "       3.42454241e+01, 4.93257604e+00, 4.30152882e+00, 2.01662248e+01,\n",
       "       3.84442891e+01, 1.56475824e+00, 3.95892936e+00, 6.00302859e+01,\n",
       "       5.57198232e+00, 4.84206726e+01, 1.72393019e+01, 8.46503257e+01,\n",
       "       2.51185287e+01, 2.86644723e+00, 3.82284752e+00, 2.27785308e+01,\n",
       "       3.85188666e+01, 1.06050689e+01, 8.86987658e+00, 3.94026247e+00,\n",
       "       2.32253148e+01, 3.50384468e+00, 2.15107698e+01, 1.96739568e+01,\n",
       "       1.81346143e+01, 3.41407425e+01, 1.48099551e+01, 2.00224215e+01,\n",
       "       3.61548456e+00, 7.59161958e+00, 6.08850105e+01, 4.96867933e+00,\n",
       "       1.65209350e+01, 5.13545193e+01, 3.16447180e+01, 1.66908172e+01,\n",
       "       1.32111159e+02, 8.43766708e+00, 1.62102345e+01, 1.58098463e+01,\n",
       "       1.69826890e+01, 3.91361003e+00, 5.49337868e+00, 6.10579339e+00,\n",
       "       1.85583906e+01, 1.15239971e+00, 6.47996037e+00, 1.36023465e+00,\n",
       "       3.37638255e+01, 2.98047252e+01, 2.22198353e+01, 2.21228024e+01,\n",
       "       2.21624615e+01, 1.11032686e+01, 5.41720976e-01, 2.04345265e+01,\n",
       "       1.40099330e+01, 4.17799377e+01, 3.89724394e+01, 4.20856583e+01,\n",
       "       2.82381794e+00, 6.53786985e-01, 4.77024251e+00, 1.85012570e+01,\n",
       "       6.11095622e+00, 8.15747835e+01, 2.21306115e+01, 8.78654200e+00,\n",
       "       2.09625761e+01, 2.96157674e+01, 1.49505111e+01, 8.99913216e+00,\n",
       "       3.57690387e+01, 3.89195915e+00, 1.03231726e+01, 1.15080916e+01,\n",
       "       6.62519232e+00, 2.82506296e+01, 2.60070231e+01, 5.76500797e+00,\n",
       "       1.57745935e+01, 9.21428396e+00, 5.18918327e+01, 9.49457875e-01,\n",
       "       4.00708229e+01, 5.75100937e+01, 1.96010793e+01, 1.31232657e+01,\n",
       "       5.22795281e+00, 1.37975347e+01, 9.05760634e+01, 2.69537790e+01,\n",
       "       1.96001018e+00, 2.11625628e+01, 7.37529002e+01, 9.61211890e+00,\n",
       "       3.35299735e+01, 8.10043467e+01, 4.65746672e+01, 1.99210102e+01,\n",
       "       3.24261333e+01, 9.78201082e+00, 5.62241482e+01, 2.00060302e+01,\n",
       "       2.10893660e+01, 7.00433740e+01, 2.73176885e+01, 2.89817982e+01,\n",
       "       3.40674206e+01, 5.43183431e+00, 1.12341119e+01, 1.59630194e+01,\n",
       "       7.71094295e+01, 3.01216252e+01, 4.37448070e+01, 1.82724776e+00,\n",
       "       4.37856110e+01, 3.92810669e+01, 1.71441322e+01, 6.33026417e+00,\n",
       "       1.86918959e+01, 1.16805809e+01, 9.92620083e+00, 1.49500298e+00,\n",
       "       8.63610381e+00, 1.99411019e+01, 2.68354377e+01, 1.17823463e+01,\n",
       "       9.66191497e+01, 5.44202692e+01, 2.31423232e+01, 3.72802804e+01,\n",
       "       6.21621708e+00, 7.68392850e+01, 1.76667338e+01, 1.17879273e+01,\n",
       "       1.18003875e+00, 1.08864539e+01, 4.10811461e+01, 6.98966058e+01,\n",
       "       6.30055062e+00, 9.26999335e+01, 1.63783893e+01, 2.96318395e+00,\n",
       "       7.22906726e-01, 1.37452339e+01, 1.93006476e+01, 2.48591754e+01,\n",
       "       1.85530683e+01, 1.07192416e+01, 1.45925865e+00, 1.07591100e+01,\n",
       "       2.32366634e+01, 6.32392171e+01, 2.26317339e+01, 1.30208344e-01,\n",
       "       5.32106546e+00, 6.61729177e+00, 2.63574277e+00, 2.67089953e+00,\n",
       "       8.01019396e+00, 9.51836950e+00, 1.97306107e+01, 7.35890260e+01,\n",
       "       2.24463137e+01, 1.68968432e+01, 1.70558936e+01, 1.67833773e+01,\n",
       "       4.69475807e+01, 1.97385971e+01, 9.12314848e+00, 5.19201800e+00,\n",
       "       6.84714064e+01, 9.34595604e-02, 4.95187598e+01, 5.13098002e+00,\n",
       "       7.43574798e+00, 4.25505962e+00, 1.90543291e+01, 7.56148677e+00,\n",
       "       4.76116509e+01, 2.18931452e+01, 9.47712408e+00, 5.83890512e+00,\n",
       "       5.52115338e+01, 3.16849527e+01, 5.54973497e+00, 1.38095342e+01])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import time\n",
    "start_time1 = time.time()\n",
    "#number of deviates - n\n",
    "#n = 1000\n",
    "#mu = 25\n",
    "iept = exp_dist(1000,25)\n",
    "elapsed_time_1 = (time.time() - start_time1)\n",
    "elapsed_time_1\n",
    "iept"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Question-2:\n",
    "#For some particular  𝜇  of your choosing, make a histogram of the random deviates and \n",
    "#plot the appropriate Exponential density curve on top of the histogram to confirm that the generator is working. \n",
    "#Verify that the mean and standard deviation are what they should be."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " \n",
      " mean: 23.655805519970812 \n",
      " \n",
      "std: 23.787276210328827\n"
     ]
    }
   ],
   "source": [
    "# Plot histogram\n",
    "plt.hist(iept, bins= 75, density=True, histtype='stepfilled', alpha=0.8, label='hist')\n",
    "\n",
    "# Plot pdf\n",
    "lambd = 0.04\n",
    "x = np.arange(0,175,0.05)\n",
    "y = lambd * np.exp(-lambd*x)\n",
    "plt.plot(x,y,'r-',lw=3,alpha=0.6,label='exp pdf')\n",
    "plt.title('Simulation of random variables and Exponential Distribution')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('Frequency')\n",
    "\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "print(\"\\n \\n\",\"mean:\",np.mean(iept),\"\\n \\n\" \"std:\",np.std(iept))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import expon\n",
    "plt.hist(iept, bins= 75, density=True, histtype='stepfilled', alpha=0.8,label='hist')\n",
    "\n",
    "x = np.linspace(0,175, 100)\n",
    "plt.plot(x, expon.pdf(x,scale =25),'o', lw=3, alpha=0.6, label='exponential pdf')\n",
    "plt.ylim(0,0.045)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('Frequency')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy import stats\n",
    "plt.hist(iept, bins= 75, density=True, histtype='stepfilled', alpha=0.8,label='hist')\n",
    "\n",
    "x = np.linspace(0.001,200, 100)\n",
    "y = stats.expon.pdf(x,scale =25)\n",
    "plt.plot(x, y,'o', lw=2, alpha=0.5, label='exponential pdf')\n",
    "plt.ylim(0,0.045)\n",
    "#plt.plot(x,y,'r-',lw=3,alpha=0.6)\n",
    "plt.title('Simulation of random variables and Exponential Distribution')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('Frequency')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Theoretical Statistics:\n",
      "Mean: 25.0 Variance: 625.0 S.D: 25.0\n",
      "Sample Statistics:\n",
      "mean: 23.655805519970812  std: 23.787276210328827\n"
     ]
    }
   ],
   "source": [
    "# Compare theoretical mean and variance with that of samples\n",
    "mean, var = stats.expon.stats(scale = 25,moments='mv')\n",
    "print('Theoretical Statistics:')\n",
    "print('Mean:',mean,'Variance:',var,'S.D:',np.sqrt(var))\n",
    "print('Sample Statistics:')\n",
    "print(\"mean:\",np.mean(iept),\" \" \"std:\",np.std(iept))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#Compare the speed of your Exponential generator to the language generator (rexp in R, numpy.random.exponential in Python). \n",
    "#Try to make your generator computationally competitive with the built in generator, \n",
    "#by avoiding for loops and other slow code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "# obtaining speed of language generator (random generator)\n",
    "start_time_2 = time.time()\n",
    "exp_lang = np.random.exponential(scale=25, size=1000)\n",
    "elapsed_time_2 = (time.time() - start_time_2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "speed of our exponential generator: 0.0\n",
      "speed of our language generator: 0.0\n"
     ]
    }
   ],
   "source": [
    "# obtaining speed of our exponential generator\n",
    "print(\"speed of our exponential generator:\",round(elapsed_time_1,10))\n",
    "# obtaining speed of language generator (random generator)\n",
    "print(\"speed of our language generator:\",elapsed_time_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Built-in generator:\n",
      "58.6 µs ± 7.61 µs per loop (mean ± std. dev. of 10 runs, 10000 loops each)\n",
      "exp_dist generator:\n",
      "58.3 µs ± 308 ns per loop (mean ± std. dev. of 10 runs, 10000 loops each)\n"
     ]
    }
   ],
   "source": [
    "# Timing Comparison\n",
    "print('Built-in generator:')\n",
    "%timeit -r10 np.random.exponential(scale=25, size=1000)\n",
    "\n",
    "print('exp_dist generator:')\n",
    "%timeit -r10 exp_dist(1000,25)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Question 2: Simulation Study of the LLN and CLT\n",
    "\n",
    "1. Create a $n \\times m$ matrix $X$ with $n=100$ and $m=1000$ and each entry $1$ with probability $p=0.5$ and $0$ with probability $1-p=0.5$. For intuition, consider the following situation: suppose 1/2 of all voters support proposition A and that we conduct 100 surveys (number of rows of X) each with 1000 voters (number of columns = sample size of poll). A voter responds 1 if they support A, 0 if they do not support A. Note on confusing notation: the sample size of each poll is $m$. Usually $n$ is sample size, but here it is the number of surveys.\n",
    "2. Compute the running mean of each row of $X$ to produce a new matrix $Y$ which is again $100 \\times 1000$. Specifically the row $i$, column $j$ entry of $Y$ is\n",
    "$$Y_{ij} = \\frac{1}{j} \\sum_{k=1}^j X_{ik}$$\n",
    "for $i=1,\\dots,n$ and $j=1,\\dots,m$. Try to avoid using nested for loops.\n",
    "3. Plot each row of $Y$ (on the y-axis) against the column number (on the x-axis). This will result in 1 plot with 100 lines. Then make three histograms 1) first column of $Y$, 2) 10th column of $Y$, and 3) the last column of $Y$. Your images should roughly look like what is below. (If you want to make the results clearer and prettier, draw all histograms or density estimators on top of each other with different colors, see lecture notes from the first class [here](https://nbviewer.jupyter.org/urls/david-jones-statistics.github.io/statcomp/lectures/topic1-intro/00intro.ipynb)  for how to do this with ggplot in R or [here](https://jakevdp.github.io/PythonDataScienceHandbook/04.05-histograms-and-binnings.html) for code in Python from VanderPlas).\n",
    "4. Take the variance of each column of $Y$ to produce a vector $\\boldsymbol{u}$ of length $m$ giving the running variance of the means across the $n$ surveys. Plot $1/\\boldsymbol{u}_j$ (on the y-axis) against $j$ (on the x-axis), and add a line showing $j/(p(1-p))$, for $j=1,\\dots,m$. \n",
    "5. Explain what the simulation results in parts 3 and 4 are showing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0., ..., 1., 1., 0.],\n",
       "       [1., 0., 0., ..., 1., 0., 1.],\n",
       "       [0., 0., 0., ..., 0., 0., 0.],\n",
       "       ...,\n",
       "       [0., 0., 1., ..., 1., 0., 1.],\n",
       "       [0., 1., 0., ..., 1., 1., 1.],\n",
       "       [0., 0., 0., ..., 0., 0., 1.]])"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Question-2.1\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "n=100\n",
    "m=1000\n",
    "X = np.random.choice(a=[0.0,1.0], size=(n,m), p=[0.5, 0.5])\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.5       , 0.33333333, ..., 0.48897796, 0.48948949,\n",
       "        0.489     ],\n",
       "       [1.        , 0.5       , 0.33333333, ..., 0.51002004, 0.50950951,\n",
       "        0.51      ],\n",
       "       [0.        , 0.        , 0.        , ..., 0.51703407, 0.51651652,\n",
       "        0.516     ],\n",
       "       ...,\n",
       "       [0.        , 0.        , 0.33333333, ..., 0.48396794, 0.48348348,\n",
       "        0.484     ],\n",
       "       [0.        , 0.5       , 0.33333333, ..., 0.50501002, 0.50550551,\n",
       "        0.506     ],\n",
       "       [0.        , 0.        , 0.        , ..., 0.46793587, 0.46746747,\n",
       "        0.468     ]])"
      ]
     },
     "execution_count": 163,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Question-2.2\n",
    "Y = np.zeros((n,m))\n",
    "for i in range(0,n):\n",
    "    for j in range(0,m):\n",
    "        Y[i,j] = np.sum(X[i,0:j+1])/(j+1)\n",
    "Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 1000)"
      ]
     },
     "execution_count": 177,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y.shape"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/latex"
   },
   "source": [
    "# Question-2.3 - Part 3 - Plotting each row of Y against its column number"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "T = range(Y.shape[1])\n",
    "for i in range(Y.shape[0]):\n",
    "    plt.plot(T, Y[i,:])\n",
    "    \n",
    "plt.xlabel(\"Survey Size\")\n",
    "plt.ylabel(\"Proportion Supporting\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(requires internet connection to view)\n",
    "\n",
    "<img src=\"https://david-jones-statistics.github.io/statcomp/hw/lln_plot.png\">"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {
    "raw_mimetype": "text/latex"
   },
   "source": [
    "Plotting histograms of 1st, 10th and 1000th column of Y respectively"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x504 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(nrows=1, ncols=3, figsize=(15, 7))\n",
    "axs[0].hist(Y[:,0]);\n",
    "axs[0].set_title('Sample Size 1')\n",
    "axs[0].set_xlabel('Proportion')\n",
    "axs[0].set_ylabel('Frequency')\n",
    "axs[1].hist(Y[:,9]);\n",
    "axs[1].set_title('Sample Size 10')\n",
    "axs[1].set_xlabel('Proportion')\n",
    "axs[1].set_ylabel('Frequency')\n",
    "axs[2].hist(Y[:,999]);\n",
    "axs[2].set_title('Sample Size 1000')\n",
    "axs[2].set_xlabel('Proportion')\n",
    "axs[2].set_ylabel('Frequency')\n",
    "fig.tight_layout()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "(requires internet connection to view)\n",
    "\n",
    "<img src=\"https://david-jones-statistics.github.io/statcomp/hw/clt_histograms.png\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The sampling distribution of sample mean converges to normal distribution as sample size increases."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'frequency')"
      ]
     },
     "execution_count": 174,
     "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(Y[:,0]);\n",
    "plt.hist(Y[:,9]);\n",
    "plt.hist(Y[:,999]);\n",
    "plt.xlabel('proportion')\n",
    "plt.ylabel('frequency')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "According to the above graphs, Sample size 1 plot displays only two discrete values 0 and 1 because the first column has the averages either 0 or 1.\n",
    "\n",
    "The Sample size plot 10 (i.e, 10th column of Y (orange bars)) closely represents a normal curve.\n",
    "The sample size plot 1000 (the last column of Y, i.e. 1000th column (green bars)) reflects a bell-shaped normal curve, although in this graph it is concentrated at the center because of scale.\n",
    "\n",
    "This is consistent with the law of large numbers and Central Limit Theorem (CLT), which says that the distribution of a large set of random numbers tends to approximate a normal distribution and since the last column has the most randomness, its distribution is closer to a normal distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.        , 0.5       , 0.33333333, ..., 0.50901804, 0.50950951,\n",
       "        0.51      ],\n",
       "       [0.        , 0.5       , 0.66666667, ..., 0.50901804, 0.50850851,\n",
       "        0.509     ],\n",
       "       [0.        , 0.        , 0.        , ..., 0.50801603, 0.50750751,\n",
       "        0.507     ],\n",
       "       ...,\n",
       "       [0.        , 0.        , 0.33333333, ..., 0.49198397, 0.49249249,\n",
       "        0.493     ],\n",
       "       [1.        , 0.5       , 0.66666667, ..., 0.51903808, 0.51851852,\n",
       "        0.519     ],\n",
       "       [1.        , 0.5       , 0.33333333, ..., 0.48196393, 0.48248248,\n",
       "        0.482     ]])"
      ]
     },
     "execution_count": 179,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n,m = 100, 1000\n",
    "\n",
    "shape = (n,m)\n",
    "\n",
    "X1 = (np.random.uniform(size = shape)<0.5).astype(float)\n",
    "\n",
    "# Verify\n",
    "# print(mat[1,1])\n",
    "# print(np.sum(mat==1))\n",
    "\n",
    "np.cumsum(X1, axis=1, out=X1)\n",
    "\n",
    "Y1 = np.arange(1,m+1) \n",
    "\n",
    "Y1 = np.divide(X1,Y1,out=X1)\n",
    "Y1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 1000)"
      ]
     },
     "execution_count": 180,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y1.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "col = range(p)\n",
    "\n",
    "for row in range(n):\n",
    "    plt.plot(col, X1[row,:])\n",
    "\n",
    "plt.xlabel('Survey Size')\n",
    "plt.ylabel('Proportion Supporting')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 5.,  3.,  9., 14., 18., 15., 21.,  6.,  7.,  2.]),\n",
       " array([0.471 , 0.4766, 0.4822, 0.4878, 0.4934, 0.499 , 0.5046, 0.5102,\n",
       "        0.5158, 0.5214, 0.527 ]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 182,
     "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(Y1[:,0])\n",
    "plt.hist(Y1[:,9])\n",
    "plt.hist(Y1[:,999])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x504 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(nrows=1, ncols=3, figsize=(15, 7))\n",
    "axs[0].hist(Y1[:,0]);\n",
    "axs[0].set_title('Sample Size 1')\n",
    "axs[1].hist(Y1[:,9]);\n",
    "axs[1].set_title('Sample Size 10')\n",
    "axs[2].hist(Y1[:,999]);\n",
    "axs[2].set_title('Sample Size 1000')\n",
    "fig.tight_layout()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Raw Cell Format",
  "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": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}