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  {
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   "source": [
    "### Central Limit Demo\n",
    "John Horel\n",
    "ATMOS 5340\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "sides = input('enter the number of sides on the die (6 or 10 or...): ')\n",
    "dice = input('enter the sample size (number of dice to roll at the same time): ')\n",
    "rolls = input('enter the number of rolls: ')\n",
    "sides = int(sides)\n",
    "dice = int(dice)\n",
    "rolls = int(rolls)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "rd = np.random.random_sample((rolls,dice))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "rdd = np.ceil(sides*rd)\n",
    "#print(rdd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#define the population as all the possible rolls\n",
    "pop = rdd.flatten();\n",
    "print(len(rd))\n",
    "#compute std of population\n",
    "pstd = np.std(pop,ddof=1);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#compute the sum and mean of the samples\n",
    "if dice>1:\n",
    "    ss = np.sum(rdd,axis=1)\n",
    "    sm = np.mean(rdd,axis=1)\n",
    "else:\n",
    "    ss = rdd\n",
    "    sm = rdd \n",
    "    \n",
    "mean_sum = np.mean(ss)\n",
    "mean_mean = np.mean(sm)\n",
    "print(mean_sum, mean_mean)\n",
    "\n",
    "#compute the std of the sample means \n",
    "sstd = np.std(sm,ddof=0);\n",
    "#does the central limit theorem work? is the following close to sstd?\n",
    "check = pstd/np.sqrt(dice);\n",
    "print(\"population standrd deviation= %.1f\" % pstd)\n",
    "print(\"standard deviation of sample means= %.1f\" % sstd)\n",
    "print(\"check for central limit theorem= %.1f\" % check)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig,(ax1,ax2,ax3) = plt.subplots(3,1,figsize=(10,10))\n",
    "x = np.arange(0,rolls*dice)\n",
    "ax1.bar(x,pop)\n",
    "ax1.set(xlabel=\"\",ylabel='Roll Value')\n",
    "ax1.set(title='Population- each die is rolled independently ')\n",
    "x2 = np.arange(1,sides*dice+2,1)\n",
    "\n",
    "hist_val,bins = np.histogram(ss,bins=x2)\n",
    "#print(hist_val)\n",
    "#print(bins)\n",
    "width = 0.9 * (bins[1] - bins[0])\n",
    "center = (bins[:-1] + bins[1:]) / 2\n",
    "ax2.bar(center,hist_val,align='center',width=width)\n",
    "ax2.set(xlim=(dice,sides*dice+1))\n",
    "ax2.set(xlabel=\"\",ylabel='# of Occurrences')\n",
    "ax2.set(title='Sample Sums')\n",
    "\n",
    "hist_val,bins = np.histogram(sm,bins=x2)\n",
    "#print(bins)\n",
    "width = 0.9 * (bins[1] - bins[0])\n",
    "center = (bins[:-1] + bins[1:]) / 2\n",
    "ax3.bar(center,hist_val,align='center',width=width)\n",
    "ax3.set(xlim=(1,sides+1))\n",
    "ax3.set(xlabel=\"\",ylabel='# of Occurrences')\n",
    "ax3.set(title='Sample Means')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# "
   ]
  }
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