Lab 11.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lab 11: Radioactive Decay\n",
    "\n",
    "Shreya Parjan\n",
    "12/15/18"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats\n",
    "import scipy.optimize\n",
    "import scipy.misc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "lData = np.loadtxt('part1lifetime.txt')\n",
    "t = lData [:,0]\n",
    "rcount = lData [:,1]\n",
    "\n",
    "radData = np.loadtxt ('radwsample.txt')\n",
    "t2 = radData [:,0]\n",
    "r2 = radData [:,1]\n",
    "\n",
    "noradData = np.loadtxt ('radnosample.txt')\n",
    "t1 = noradData [:,0]\n",
    "r1 = noradData [:,1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "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": [
      "[ 4.29029288  4.0749632   4.06987413  3.86797441  3.79122146  3.58202514\n",
      "  3.47850964  3.41345896  3.22653667  3.13339804  3.01126717  2.83481074\n",
      "  2.73979291  2.59098698  2.36129217  2.31811999  2.170484    2.08140436\n",
      "  1.83628191  1.8598124   1.77068462  1.39444915  1.66343909  1.30406509\n",
      "  1.30406509  1.20469262  1.15888308  0.73766962  0.97029191  0.87120101\n",
      "  0.58351894  0.76120012  0.52636052  0.25809654  0.49650756  0.40119738\n",
      "  0.40119738  0.25809654  0.13549422 -0.43505064 -0.10962824 -0.69741491\n",
      " -0.43505064 -0.2919498  -0.36094267 -0.51509335 -0.16678666 -0.43505064\n",
      " -0.2919498  -0.2919498  -0.43505064 -1.61370564 -1.20824053 -0.51509335\n",
      " -0.16678666 -0.69741491 -0.36094267 -1.05408985 -0.80277542 -0.51509335]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Activity')"
      ]
     },
     "execution_count": 40,
     "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.plot (t, np.log(rcount), 'bo')\n",
    "plt.axhline(y = 3, color = 'r')\n",
    "plt.title ('Activity vs Time')\n",
    "plt.xlabel ('Time (min)')\n",
    "plt.ylabel ('Activity')\n",
    "plt.show()\n",
    "\n",
    "rcount2 = lData [:,1] - 3\n",
    "t2 = lData[:,0]-3\n",
    "print (np.log(rcount) - 3)\n",
    "\n",
    "plt.plot (t, np.log(rcount), 'bo')\n",
    "plt.plot (t2, np.log(rcount2), 'ro')\n",
    "plt.title ('Activity vs Time')\n",
    "plt.xlabel ('Time (min)')\n",
    "plt.ylabel ('Activity')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[7.29029288 7.0749632  7.06987413 6.86797441 6.79122146 6.58202514\n",
      " 6.47850964 6.41345896 6.22653667 6.13339804 6.01126717 5.83481074\n",
      " 5.73979291 5.59098698 5.36129217 5.31811999 5.170484   5.08140436\n",
      " 4.83628191 4.8598124  4.77068462 4.39444915 4.66343909 4.30406509\n",
      " 4.30406509 4.20469262 4.15888308 3.73766962 3.97029191 3.87120101\n",
      " 3.58351894 3.76120012 3.52636052 3.25809654 3.49650756 3.40119738\n",
      " 3.40119738 3.25809654 3.13549422]\n"
     ]
    }
   ],
   "source": [
    "rcountshort = rcount [0:39]\n",
    "tshort = t[0:39] \n",
    "print(np.log(rcountshort))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "best-fit parameters: [ 7.20006443 -0.22274076]\n",
      "covariance matrix:\n",
      "[[ 2.98649889e-03 -2.26822701e-04]\n",
      " [-2.26822701e-04  2.26822702e-05]]\n",
      "uncertainties: [0.05464887 0.00476259]\n"
     ]
    }
   ],
   "source": [
    "def straight_line_model(x,A,B):\n",
    "    return A+B*x\n",
    "\n",
    "popt,pcov = scipy.optimize.curve_fit(straight_line_model, tshort[0:40], np.log(rcountshort[0:40]))\n",
    "print('best-fit parameters:', popt)\n",
    "print('covariance matrix:')\n",
    "print(pcov)\n",
    "\n",
    "popt_uncertainties = np.sqrt(np.diag(pcov))\n",
    "print('uncertainties:', popt_uncertainties)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Activity')"
      ]
     },
     "execution_count": 43,
     "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": [
    "best_fit_line = straight_line_model(tshort[0:40], popt[0], popt[1])\n",
    "plt.plot (tshort, np.log(rcountshort), 'bo')\n",
    "plt.plot (tshort, best_fit_line, 'm')\n",
    "\n",
    "plt.title ('Truncated Activity vs Time')\n",
    "plt.xlabel ('Time (min)')\n",
    "plt.ylabel ('Activity')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "halftime in minutes =  3.1119009899724244\n",
      "halftime uncertainty =  0.0665379382841684\n"
     ]
    }
   ],
   "source": [
    "htime = (np.log(2))/(-popt[1])\n",
    "print(\"halftime in minutes = \", htime)\n",
    "htimeUncert = (htime*popt_uncertainties[1])/-popt[1]\n",
    "print (\"halftime uncertainty = \", htimeUncert)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. From my results, the halflife is 3.11 min +/- .07 min which is slightly higher than the true value of 2.55 min.\n",
    "2. Without subtracting the background radiation, the line is less linear and has a smaller slope. This means that the halflife time is bigger."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Low Activity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.7   0.254 0.042 0.002]\n",
      "0.998\n",
      "[7.08440376e-01 2.44191873e-01 4.20851725e-02 4.83543732e-03\n",
      " 4.16680972e-04]\n",
      "0.9995528588227083\n"
     ]
    }
   ],
   "source": [
    "nu1 = bins\n",
    "mu1 = np.mean(r1)\n",
    "P = mu1**nu1*np.exp(-mu1)/scipy.special.factorial(nu1)\n",
    "stdP = np.sqrt(mu1)\n",
    "hist1 = np.histogram(r1, bins = np.arange(r1.max() + 2))\n",
    "\n",
    "histnorm = hist1 [0] / 500\n",
    "print (histnorm)\n",
    "print(np.sum(histnorm))\n",
    "print(P*1)\n",
    "bins1 = np.arange(4)\n",
    "\n",
    "P = mu1**bins1 /scipy.special.factorial(bins1)*np.exp(-mu1)\n",
    "print(sum(P))\n",
    "Gaussian = np.exp(-(bins1 - mu1)**2/(2*stdP**2)*1/stdP*np.sqrt(2*np.pi))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bins = np.arange(r1.max() +2)\n",
    "plt.hist(r1, bins = np.arange(r1.max() +2))\n",
    "plt.xlabel ('Bins')\n",
    "plt.ylabel ('Counts')\n",
    "plt.show()\n",
    "\n",
    "plt.bar(bins1, histnorm)\n",
    "plt.plot(bins1, P,'r--')\n",
    "plt.plot(bins1, Gaussian, 'g--')\n",
    "plt.xlabel ('Bins')\n",
    "plt.ylabel ('Counts')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## High Activity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5871025283181082\n",
      "0.5675129916564136\n",
      " \n",
      "5.389070807508162\n",
      "5.403204762763165\n"
     ]
    }
   ],
   "source": [
    "hist2, hist2bins = np.histogram(r2, bins = 10)\n",
    "bins2 = hist2bins[:-1]\n",
    "hist2norm = hist2/len(r2)\n",
    "\n",
    "mu2 = np.mean(r2)\n",
    "binWidth = bins2[1] - bins2[0]\n",
    "P2 = mu2**bins2/scipy.special.factorial(bins2)*np.exp(-mu2)*binWidth\n",
    "sigma_p = np.sqrt(mu2)\n",
    "Gaussian2 = np.exp(-(bins2 - mu2)**2/(2*sigma_p**2))/(sigma_p*np.sqrt(2*np.pi))*binWidth\n",
    "#print(sum(Gaussian2))\n",
    "\n",
    "stdG = np.std(r1)\n",
    "print (stdP)\n",
    "print (stdG)\n",
    "print(\" \")\n",
    "sigmaP = np.sqrt(mu2)\n",
    "sigmaG = np.std(r2)\n",
    "\n",
    "print (sigmaP)\n",
    "print (sigmaG)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Counts')"
      ]
     },
     "execution_count": 49,
     "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.bar (bins2, hist2)\n",
    "plt.xlabel ('Bins')\n",
    "plt.ylabel ('Counts')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Counts')"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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3tNu1A2DgyoEcjzjOmDpjcIj+c78vDgeMHg1HjlgdHYHBNQYTGRtJv+X97M2mPE5bQynfsWkTnDkDkyaBvz9/nfmL0WtH06JUC8qHlLc7nW+oUsXqqLdlCxhDkaxF+DjsY/39pgJaLJTvqFzZ6hOQJQsAOdLloF35dnSu2NnmYD5m8mRIk+bmy9ZlW9sYRiUXPS9X3s8Ya6pUY24WCoDMaTIzvNZwcqTPYWM4H3SjUBw4YA04CJy9epZms5ux6vAqG4MpT9JiobzfrFnw1FPwww8AXIu+RsNpDVl3dJ3NwXxYTAxUqwZvvgnGEOQXxOJ9i3UYEB+mxUJ5tytXoEMHa/Ke554D4MPVHzLn7zlcjb5qczgf5ucHPXvC77/DzJmkC0jHgOoDWHN0DbP+mmV3OuUBWiyUd3v/fat1zqefgp8fhy4c4oPfP+DFEi9SPbS63el8W8uWVpHu3BmuX6d5qeaUyF6Cbr92Izo22u50KolpsVDe66+/YMQIaN4cnnwSgE6LOiEIw2sNtzdbauB0Wk1oDx6E0aPxc/gxtOZQ9pzbw/jN4xPcXHkXLRbKe504AcWKwdChAKw8tJKZu2bSo3IP8gXnszlcKvHUU9blv3PnAKhbpC5Daw6lYbGGNgdTSc2jTWdFJAz4CHACXxpjhtzyfhVgNFASaGyM+SHOe7HAdvfLw8aYBp7MqrxQtWqwbZs1FAVQIaQCn9X9jOalmtsaK9X54Qerwx4gInR5sovNgZQneOzMQkScwFigDlACaCIiJW5Z7TDQHJgaz7e4Zowp5X5ooVD/unzZmswoKupmoXAZF/5Of94u8zZBfkE2B0xl3IWC1athxw4Adp3eRZ1v63D88nEbg6mk5MnLUOWAvcaY/caYKGAa8D/npsaYg8aYbYDLgzmUr+nfH8LDYetWAE5EnKDE2BIs2b/E5mCp2LVr0LAhtGkDxhDgDGDJ/iU6DIgP8WSxyAMcifP6qHtZYgWJyEYRWSsiz8a3goi0cq+z8fTp0/eTVXmJoqcPWuMTvfEGlC0LQLdfu7H//H7yBue1N1xqliaNVcSXL4effqJQlkK0LtOaL//4kl2nd9mdTiUBTxaL+KYiu5veOvmMMWWAV4DRIlLoP9/MmHHGmDLGmDLZs2e/15zKWxjDgMWfW/NDf/ABAGuOrGHS1kmEVwinaNaiNgdM5Vq1smYnfO89iIykV5VepA9IT7cl3exOppKAJ4vFUSDuR70Q4FhiNzbGHHN/3Q8sB0onZTjlfRruXM4TR/60CkW2bMS6Ymk7vy25M+SmV5VedsdTfn5WU9p9+2DMGLKny063J7sx5+85/H74d7vTqfvkydZQG4AiIhIK/AM0xjpLSJCIZAauGmMiRSQb8CQwzGNJlVc4kCUP00rWonHLlgDM3zufTcc38W2jb0kfkN7mdAqA2rWhSZOb40e1f6I9Ac4ASufUz3rezmPFwhgTIyJtgIVYTWe/NsbsEJEBwEZjzBwRKQvMAjID9UWkvzHmIeBB4AsRcWGd/Qwxxuz0VFblHbblKsq2XEVp7HQCVpv+pU2XUq1ANXuDqf819d/GjWn909KpYicbw6ik4tFOecaYecaYosaYQsaYQe5lfYwxc9zPNxhjQowx6YwxWd2FAmPMamPMI8aYR91fv/JkTpWyFT91gMELPiHj9X/ner54/SIiQvXQ6ojEd3tM2coY+O67m01pF+1bRNiUMKJio2wOpu6V9uBWKZsxDFz0GbV3r0bco5luO7mNkFEhzN8z3+Zw6rYuXIB337UGeTSGWFcsC/ctZNymcXYnU/dIi4VK0Z7/cyll/9nJkGrNuZgmAwZD2/ltCXQG6uxsKVnmzNY86L/+CnPnElY4jOoFqtN/RX8uRV6yO526B1osVIqVPvIq3Zd/zabcxfnhkZoAXHWuZOWhlQx+ajBZ0mRJ4DsoW7VubY3d1akTEhPDsKeHcebqGYat0rYq3kiLhUqx3tgwi2xXL9L36bcx4sDFNc77f8VjuR6jZemWdsdTCfH3t0YF3r0bPv2UMrnL0OThJoxcM1KHAfFCd90ayt2sNa97mA6lPGbmw09xNm0wf+YsDMB1xxZiucAndT7B6XDanE4lyjPPWL3tQ0MBGFRjEPWK1tOpbr1QooqFiCwHGrjX3wKcFpEVxphwD2ZTqdyRTDmZ/Fi9m6/TuiqQJ/JLKuStYGMqdVdEYPy/c1uEZg4lNHOojYHUvUrsZahgY8wloBEwwRjzOFDTc7FUapY94jyfzxpE6Ll/bi6LksMA+JkH7Iql7se1azB4MOy0ukt9uuFTXp/1us2h1N1IbLHwE5FcwEvALx7MoxTvrJ1OzT3rcLn7T1x1rOd40Dtcc2y0OZm6ZxERMGyYNW4UEBEVwZRtU1h+cLm9uVSiJbZY9Mfqib3XGLNBRAoCezwXS6VWuS+d4pUt85nxSE0OZc6NIYrz/uPxd+UlyFXK7njqXmXPDr17w/z5sGABbcu1JW/GvHRe3BmX0RkKvEFii8VxY0xJY8w7cHNwv5Gei6VSqzarvwdgzJONAbjkN5sYx3EyR7+FeHZiR+VpbdtC4cIQHk4a8Wdg9YFsPLaRGTtm2J1MJUJii8WYRC5T6t7t3ctL2xYztVQdjmV8gBjOcNHve9LGViSNnlV4v4AAGD4cdu2CL77gtZKvUTJHSXos7UGMK8budCoBd/yoJiIVgIpAdhGJ2/IpI9bggEolnezZ+aTiy3xbqg4AUY79CEFkjtY+FT6jQQNrlsPy5XE6nHxW9zOMMfg59KwxpUvoCAUA6d3rZYiz/BLwgqdCqVQqOJjRlV69+TKtqxxprk9ACLAxlEpSIlZHPbeKeSvaGEbdjTsWC2PMCmCFiEw0xhxKpkwqNereHSpXBsBguO7YTJDrMS0UvurMGejRAzp1wlW0CO3mtyNzUGYG1hhodzJ1G4m9ZxEoIuNEZJGILL3x8GgylXps3gxDhsD69YA1/tOpwL5cc6y1OZjymNhYmDYNOnfGIQ4uRl5k+JrhHLl4xO5k6jYSWyxmAH8AvYDOcR5K3b8+faxRSjt2xEUk5/0mEuAqRBpXObuTKU/JkQN69YKff4Zff+X96u/jMi76LO9jdzJ1G4ktFjHGmM+MMeuNMZtuPDyaTKUOa9bA3LnQpQsEB3PJbxaxjtNkjn4D0TYUvq19eyhYEDp2JH/6PLQr145JWyax/eR2u5OpeCS2WPwsIu+ISC4RyXLj4dFkKnXo1QseeADatuXY5WNc8vuBtLEVCXI9Yncy5WmBgVav7j//hK++onvl7gQHBdNzaU+7k6l4JLa9WjP317iXngxQMGnjqFTFGHjlFWso63TpOHRkG06ThUzRLexOppJLo0bw/vtQty5Z0mRhynNTKJG9hN2pVDwSVSyMMTpMpEp6ItDy3z4UFfJWIHfk54hOs5J6iEDPf88k6hate/O5MUbnV09BEvW/UkSaxvfwdDjlw5YsgY8+gqgojDF8s/Ubrsdc10KRWu3bB3XqwN69nL92nme+fYbv/vzO7lQqjsT+zywb51EZ6Ic1v4VSd88Y6NzZKhbAzF0zaTa7Gd//+b3NwZRt0qaF336DLl0IDgrmRMQJeizpQWRMpN3JlFtiL0O1jftaRIKByR5JpHzfjz/CH3/ApElcd7jovLgzJXOU5LWSr9F32gK70ym3At3mJrjOwSF1E1wnUXLlsjrp9eyJY8VKhj09jKcnP83YDWMJr6BzrKUE93rOfxUokpRBVCoRG2v1qyheHF59ldFrR3PwwkFG1R6lU6Wmdh07Qr580LEjNfNXp3ah2ry/8n3OXztvdzJF4u9Z/Cwic9yPucDfwE+ejaZ80nffWbOlDRjAiWunGfTbIBoWa0iN0Bp2J1N2S5PGakq7ZQtMmcLQmkO5cP0CI9fobAgpQWKbzg6P8zwGOGSMOeqBPMrXFSgAzZvD889z8dweSucszYdPf2h3KpVSvPQSnD8Pzz/Po+nT8/0L31OrUC27UykSf89ihYjkwLrBDTpLnrpXlSpZD6BYtmKsbLHS5kAqRRGBt9+2nhvDiw+96H6qzWjtltjLUC8B64EXsebhXiciOkS5SrzISOjXD06fxhjDiNUjOHXllN2pVEq1aROUKgUHDrDz9E5KfVGKLSe22J0qVUvsDe6eQFljTDNjTFOgHNDbc7GUzxk3Dvr3h61bmf3XbN5b/B4zd860O5VKqXLkgD17oGtXcmfIzdFLR+n6a1e7U6VqiS0WDmNM3I+BZ+9iW5XaXbkCgwZBtWpEVq3Ee4vf46HsD/Hm42/anUylVCEh0LUrzJhBpg3b6VW5F4v2LWLRvkV2J0u1EvsHf4GILBSR5iLSHJgLzPNcLOVTxo6Fkydh4EDGbPiE/ef3M6r2KJ1KU91Z585W0ejYkXcef5vQTKF0WNBBO+rZ5I7FQkQKi8iTxpjOwBdASeBRYA0wLhnyKW936RIMHQphYZwqXZSBKwdSr2g9ni70tN3JVEqXNq01KdamTQT+PI+xz4xl15ldTNgywe5kqVJCH+1GAz0AjDE/Aj8CiEgZ93v1PZpOeb+ICKhRA7p1I9YVS90idelbta/dqZS3aNLE6n/RsCF1nE5+afILYYXD7E6VKiVULAoYY7bdutAYs1FECngkkfItuXPDjBkA5AKmPj/V3jzKuzgc1jDmANHRN0elPX/tPJmCMmlz2mSU0D2LoDu8lyYpgygfNG0a7NqFMYZeS3ux49QOuxMpb7VwIYSGwuHD7D67m6KfFGXyNh2eLjklVCw2iMh/mqyISEsgwWlVRSRMRP4Wkb0i0i2e96uIyGYRibm134aINBORPe5Hs1u3VSnciRPWXBWDBvHL7l8Y9Nsglh1cZncq5a0efBDOnoUOHSicuRBFsxYlfGE4Z66esTtZqpFQsegAtBCR5SIywv1YAbwBtL/ThiLiBMYCdYASQBMRuXUKrMNAc2DqLdtmAfoC5bH6dPQVkcyJ2yWVIgwZApGRRPXqTqdFnXgw24O89fhbdqdS3ipfPhgwAGbNwjHlW76o9wUXIy/SeXHnhLdVSeKO9yyMMSeBiiJSHXjYvXiuMWZpIr53OWCvMWY/gIhMAxoCO+N8/4Pu91y3bFsbWGyMOed+fzEQBuhsKB6UZENSHzkCn30GzZsz9vwi9pzbw7xX5uHv9E+ClCrVCg+Hn3+Gtm15eNs2OlfszAe/f0DTkk2pHlrd7nQ+L1H9LIwxy4wxY9yPxBQKgDzAkTivj7qXeXpbZbf33wdjONP5Xfqv6E9Y4TDqFKljdyrl7ZxOmDTJmjxr5kx6V+lNwcwF+Xn3z3YnSxU82SsqvmYKJim3FZFWQCuAfPnyJT6Z8hxjIEsWaN+eoNAitC7Tmtcffd3uVMpXhIZaQ9yHhJAGWP/GerKmzWp3qlTBk8XiKJA3zusQ4NhdbFvtlm2X37qSMWYc7s6BZcqUSWwhUp4kAh98AEB64IOaH9ibR/mekBDr69atZPX3hxJZ2X12N4JQJKvOyeYpnhzfaQNQRERCRSQAaAzMSeS2C4FaIpLZfWO7lnuZSsl274bFizEuF23mtWHxvsV2J1K+KioK6teHV14h6uplqk2sRss5LXGZW29/qqTisWJhjIkB2mD9kd8FTDfG7BCRASLSAEBEyorIUayhz78QkR3ubc8BA7EKzgZgwI2b3SoF69ULGjVi/tYfGLthLDtOa78K5SEBAdaYY1u3EjBwMAOrD+S3w78x4Q8dCsRTPDqSmzFmHrcMOGiM6RPn+QasS0zxbfs18LUn86kktGULzJhBdO8edFrdl6JZi/JO2XfsTqV8Wf36Vl+eYcNo8cwyJuWrTOfFnalfrD4PpHvA7nQ+R4cZV0mjd2/InJnPawTz15m/GFFrBAHOALtTKV83ahTkz4+jWXO+qD6SiKgIwheG253KJ+kY0er+rV0Lv/zCuUG96LtuCDUL1qRukUT0x1DqfmXIAN98A/Pn82DukvSq0osL1y/gMi4cop+Fk5IWC3X/Tp6ERx4huM17DNmTlwohFXSAN5V84szr3qdKb6tFnkpyWnrV/WvYELZuxZkxmFaPt+KRHI/YnUilRqtWQdmycOoUKw6u4JP1n9idyKdosVD3zhiYPRtiYmj+UwsmbpldgRY0AAAWVklEQVRodyKVmgUHw/bt0KoVE7dMpOPCjvx56k+7U/kMLRbq3i1YAM89x8LxXZm0dZKOAKrs9fDDMHgw/PQTH54pTXBgMG/98pb2vUgiWizUvTEGevUiJjQ/4a75FMpciLbl2tqdSqV2HTtCtWpkC+/FyMe6s/rIasZvGm93Kp+gxULdm9mzYfNmxnesys4zuxheaziBfoF2p1KpncMBEyeCCK8vOU2N0Bp0/bUrJyNO2p3M62lrKHX3YmOhd28iHipC72tzqV6gOg2LNbQ7lVKW/Plh/XqkaFE+P7eXeXvmkS1tNrtTeT0tFuruHT8OIqTv/T5TH89E7gy5tamsSlmKFQOgyJVA2meqDQ4nxhj9d3oftFiouxcSgtmyBRGhlkOvZKoUyuWC2rXB3585U/sycM0QljdbTrqAdHYn80r6P13dnU2b4OJFXv6xCf1XDrQ7jVK353DA8OGwfTuZp8xk47GN9F/R3+5UXkuLhUq0gJhoaNSIJW8+xYydMwjyC7I7klJ3VrcutGpF5WHTeCNXXUauGcnWE1vtTuWVtFioRGu8dQGxRw7Tsew5QjOF0v6J9nZHUiphI0ZAwYIMHb6VrGmy0OqXVsS6Yu1O5XX0noVKlKDo67RZM52vXi7C9qt7mFFXzyyUZxXoNjfBdQ4OScSAlenTw+TJZBk3jlFVK/Hq/DeYv3c+9YrWS4KUqYcWC5Uor2+eR+Zr5+lf0knlnJV5/sHn7Y6kVOJVqAAVKtDEGPLlLEalfJXsTuR1tFioRHnw9AFW53+MX9+YgkGbICrvJLt2UaldP/j2W46ljSV3htx2R/IaWixUonSs146gaBd/Z3/Q7ihK3Z/ff2dVh0Y89dAmpr84nQbFGtidyCvoDW51RxmvRxBy4QSnA4bxT9rP7I6j1P0pUQKGDKHc9NUUkWy0mdeGiKgIu1N5BS0W6o7eWjeT3ovf4ppzDf4ml91xlLp/7drhX60G4yad5cilI/Re2tvuRF5Bi4W6raxXLtB080+0rp8Gpys7GWKetTuSUvfP4YAJE6hwMoC3I4rz8fqP2XRsk92pUjwtFuq2Wq+dwXcPR3MgcwSZY1rgQEeVVT4iXz5YtowPei0nd4bcrD6y2u5EKZ7e4FbxKnvkT17f/DMFO6YhMDY/aWMr2x1JqaT12GNkAv56bS3pLl6zO02Kp8VCxavEqQMcyZSb4Ng+EG0QtKms8kHGkK7+8xARwYofRxGaoxj5gvPZnSpF0stQKl7jy5TgmRYjuRqYG3+Tx+44SnmGCPTrx7n9O6g7tS5t5rXBGGN3qhRJi4X6lzH0XPolDx7/hROBXTmRZordiZTyvLAwsjRvTb/F0fy8+2dm/TXL7kQpkhYLddNrW+ZTY+9sfs8zAYcJJjj6RbsjKZU8PvyQDmcK8+hZf9rObcOlyEt2J0pxtFgoy++/03r151RtEcjVgAByRPXHSWa7UymVPNKlw++bKYw79jjHr5yg55KedidKcfQGt4J//oEXXuDll/w4lsFFjqg++JsQu1MplbzKl6fcD2votqSHjhkVDz2zUPDVV3DlCtEBncgW1YNAl47/pFKvwcXfpc3wldZc8+omLRapnDGGRa+Uh02bOBn8JGldZe2OpJS9Ll/G/DyHyV3r8PkGHQ/tBi0Wqdn06fSf1Z7a34YxX/bZnUaplKF4cRg6jB+itxI+rz0Hzh+wO1GKoMUitVq1ivHDX6H/9jE0L9WcsMJhdidSKsWQNm345FIlHFHRvDOjufa9QItF6nTsGL+E1+PtOrHUyV+TcfXG6WRGSsXlcJD3i+94f00QC46vZPqO6XYnsp0Wi9QmMpLTjRvQuOYFHsv6ENNfmYW/09/uVEqlPCEhtB2wkMcfKEX7Be1T/bwX2nQ2tRk+nOy/bWJqi6488VI46QPS251IqRTLWakKXxaewOGz+0h//CzkT73/Xzx6ZiEiYSLyt4jsFZFu8bwfKCLfu99fJyIF3MsLiMg1EdnifnzuyZypxYmIEyxtVBpmzKBBiyE8kO4BuyMpleKVylmKBl0nQJ06xF5JvWcXHisWIuIExgJ1gBJAExEpcctqLYHzxpjCwChgaJz39hljSrkfb3sqZ2px+Y911J0cRqOfXuFCvZp2x1HKu7Rrx6fpd1F+SCGiYqPsTmMLT55ZlAP2GmP2G2OigGlAw1vWaQhMcj//AXhK9E5rkos+eogXxlZh68ltfNvoWzIFZbI7klLepVYt8lWqyya/U7z5SS2iY6PtTpTsPFks8gBH4rw+6l4W7zrGmBjgIpDV/V6oiPwhIitEJN6Zd0SklYhsFJGNp0+fTtr0PsJcv84bA8qyKG8UXzzej7pF69odSSmvVO/96fTbnYdvLqzg2RFluBJ1xe5IycqTxSK+M4RbGyvfbp3jQD5jTGkgHJgqIhn/s6Ix44wxZYwxZbJnz37fgX3Rj90a8E2e0/TP/hIt6/exO45S3ittWvp+uYfPL1VlwfU/qTm5JjGuGLtTJRtPtoY6CuSN8zoEOHabdY6KiB8QDJwzVg+YSABjzCYR2QcUBTZ6MK+tCnSbm6j1Dg65izODCRNo9NFiZvVoRMPW0+4xmVLqpjRpeGvEcnL8NZsjFw7j17svtG0LOXPanczjPHlmsQEoIiKhIhIANAbm3LLOHKCZ+/kLwFJjjBGR7O4b5IhIQaAIsN+DWX3O/D3z2VuuMNKpE88OmK6d7pRKQs8Wf5a2aavB6NEsb1CSLSu+tzuSx3nszMIYEyMibYCFgBP42hizQ0QGABuNMXOAr4DJIrIXOIdVUACqAANEJAaIBd42xpzzVFZfs2rnAhrNasTTBZ9mzvBb67NSKrESOuMv8dIgDmfszJGFjZl96C+qN+2bTMmSn0c75Rlj5gHzblnWJ87z68B/pmMzxswEZnoym6/adWwr9afWJ68riK8bfm13HKV82s4cRfit5RrCvqhC2J5+TB5+kJfem2B3LI/Q4T58yLHLxwj7vBIBkTEsKDGYbGmz2R1JKZ+Xt0gZfu+5l3IxOWh8ZRIfr/vY7kgeocXCh/T5/GXOxUQwz68ZBV9ra3ccpVKNzJlzs2jAAZ4t/iwbj23EfPGFz02epGND+Yq1a/m43zreCivPY9O/sjuNUqlOGv80zHhxBq5jR5HiD3FsRD+yT52Nf5nydkdLEnpm4eVcxsWHqz7kUswV0pYuR9nx88DptDuWUqmS0+HEPyQ/11YuoWq9M9QfU5GI7yfbHStJaLHwcl0Xd6HLr134Ps1++O03yJLF7khKpXppHitP1wZDWRzqovqSppwa1MPuSPdNi4UXG712NMPXjOCd2Md4o3RL0L4USqUYb1QLZ/YLP7Ajl5Mn+Yr95727q5gWCy81fcd0wheG89wu+Ph6dcShh1KplKb+w8+zpOVKzvnH0GFBB5g/H/75x+5Y90RvcHuhqNgous3tSMUj8O356jinDLE7klLqNirkq8iq/1tFVhMED5XD+Pshs3+CsmXtjnZX9OOoFwo4fY7lX8Uy57cQ0kydAX5a85VKyYpnK0727AWIWryABnUu8N1bT8L33jVEiBYLLxIjp+m/vD+ujRvIdzqKLN/PgaxZE95QKZUiXC9emMvlS/NKw2hGftQY+vQBc+tg3CmTFgsv4SKCUwF9Gbl2JAcqloCDB6FUKbtjKaXuQsbAjCxosYQXijeiU214L2Yerv/M3JAyabHwAoYoTgW8TyxHmZW9LYWyFIKM/5neQynlBYL8gpj24nTalH2XEYGbCF8YDtu2wZEjCW9sI73YncIZXJzxH0mk808m/eigRva10MIF2vpJKa/ldDj5uM4Y8mcqQM0CNaBmYzh/HmbPhvIps8e3/sVJ4aLlINec6+izPC01DmaDadO0UCjlA0SE9yq+R6ncj8GMGYwpHcXJOlVg6lS7o8VL/+qkcGlj8vHD9AJ0/T2GVo16QTYdSVYpX3MwTzq6PXmdiq0c7G37KvTsCS6X3bH+hxaLFMgQy2XnXCKcS6i5dx2Ndu2hW5127MxR0O5oSikPKJCpAEubLeVilnRUfDeIjbuWaLFQt2eIJcK5hGOB73Au4DOuOJcxv1gF6jcdxZwS1eyOp5TyoPIh5VndcjXpsuakWpk/WXhwCZw8CYcP2x0N0GKRYlxzbOFY4FucDRiF4M/jJ5tR43BTBAfbcxWxO55SKhkUzVqU1f+3mmLZinEp8hI0b2719F6zxu5oWizsFBkTyblr1tTiDpMOB+kpce4dvplViLWfT+bjn0ficMXanFIplZxyZcjFujfW8eJDL8LIkewMCcRUqwqT7R3qXIuFDa7HXOfTDZ9SZEwROi3qBEDRc+mYOjOEbWM+59ldvzH5sbo0bjIYl0PnplAqtfFzWL0a/sh0nUefPU540xy4mjWFbt1su5eh/SyS0bXoa4zfPJ6hq4Zy7PIxKuatSJOHGgNQ4Pxx6uxew5dln+XLss9xOn1mm9Mqpez2aM5Hebfsu4x2fcTxLoWYNOsHArt3h+DgZM+ixSIZ9VnWh+FrhlM1f1UmP9yH6p8vQHYvgyG1WRH6GBVbT+BCGu2ZrZSyOMTBqNqjyJ0hN11/7crpLlWYFSTY8VdCL0N5UERUBMNWDWPNEevmVPsn2rO83Gcsn5mBGrXfRpYug8zuMwgRLRRKqf8QEbo82YVJz05i5bHVTNoyyZYcembhAZciL/HJ+k8YuWYkZ6+dpWflnlTIW4GQsZMJ6dHDmvp04EBo29aW00mllPdp+mhTSuUsxSMPPGLLz9dikcQ+WvsR/Vb048L1C9QtUpfe6Z+hfN6nrTfr1QOnE1q3hgwZ7A2qlPI6JXOUtO1n62WoJHDu2jli3U1cr0ZfpWr+qmws+Qm/fHaR8g3fhREjrBUfeQS6dNFCoZTyOlos7sPpK6fp/mt38o/Oz4ydMwDodqU0s0ef4PFGbaw5J8aMgVGj7A2qlFL3SS9D3YOTEScZvno4n278lGvR13ipxIs8+oB1eiiLFlld9D//3Op9GRhob1illEoCWizukjGGsG/D2HZyG6881IQeVx/jwYETIctxeKoE9O8PQ4eCv7/dUZVSPqBAt7kJrnNwSF2P59DLUIlw9NJRuizuwpWoK4gIY2qNZle+YUzuvZkHm3aC6Oh/e1VmyKCFQinlc/TM4g4OXTjEkN+H8PWWr3EZF0+FPkXtwrWp1LwPrFwJDz8M338Pzz9vtXJSSikfpcUiHpExkbSZ14aJWyciCC0fbU63Mw+Sv8BT1gpvvw0dOkDDhjprnVIqVdBiEY9Av0AOXzrM26XeoMuBPORtMw6OjIesBa0C0aSJ3RGVUipZabGIT3Q080/XxtFlOBw/Dk8+CePHQ61adidTSilbaLGIj9OJ46uvoVgx+PZbqFYNROxOpZRStvFosRCRMOAjwAl8aYwZcsv7gcA3wOPAWeBlY8xB93vdgZZALNDOGLPQk1lvbZ6WsWZvLgWlh4VXYeE8IHmapymlVErksbuzIuIExgJ1gBJAExEpcctqLYHzxpjCwChgqHvbEkBj4CEgDPjU/f2SzaWg9Mn545RSKkXzZFOecsBeY8x+Y0wUMA1oeMs6DYEb4+3+ADwlIuJePs0YE2mMOQDsdX8/pZRSNvBkscgDHInz+qh7WbzrGGNigItA1kRuq5RSKpl48p5FfHeETSLXScy2iEgroJX7ZYSI/H1XCe8sG3Dmf37e0CT87vcoiTP8Zx+T+effk7vIcNf754EMHuPO4LF9vIsMnnTH/UtBx+F+3PcxvM8M+ROzkieLxVEgb5zXIcCx26xzVET8gGDgXCK3xRgzDhiXhJlvEpGNxpgynvjeKYWv76Ov7x/4/j76+v6B9+yjJy9DbQCKiEioiARg3bCec8s6c4Bm7ucvAEuNMca9vLGIBIpIKFAEWO/BrEoppe7AY2cWxpgYEWkDLMRqOvu1MWaHiAwANhpj5gBfAZNFZC/WGUVj97Y7RGQ6sBOIAd41xsR6KqtSSqk782g/C2PMPGDeLcv6xHl+HXjxNtsOAgZ5Ml8CPHJ5K4Xx9X309f0D399HX98/8JJ9FOuqj1JKKXV7OmSqUkqpBGmxAETkaxE5JSJ/xlnWT0T+EZEt7sczdma8HyKSV0SWicguEdkhIu3dy7OIyGIR2eP+mtnurPfqDvvoE8dRRIJEZL2IbHXvX3/38lARWec+ht+7G5N4pTvs40QRORDnGJayO+v9EBGniPwhIr+4X3vFMdRiYZmINazIrUYZY0q5H/Pied9bxACdjDEPAk8A77qHVOkGLDHGFAGWuF97q9vtI/jGcYwEahhjHgVKAWEi8gTWEDmj3MfwPNYQOt7qdvsI0DnOMdxiX8Qk0R7YFee1VxxDLRaAMWYlVmssn2SMOW6M2ex+fhnrH2oe/ne4lUnAs/YkvH932EefYCwR7pf+7ocBamANlQPefwxvt48+Q0RCgLrAl+7XgpccQy0Wd9ZGRLa5L1N57SWauESkAFAaWAfkMMYcB+uPLfCAfcmSzi37CD5yHN2XL7YAp4DFwD7ggnuoHPCBYXFu3UdjzI1jOMh9DEe5R6v2VqOBLoDL/TorXnIMtVjc3mdAIazT4ePACHvj3D8RSQ/MBDoYYy7ZnccT4tlHnzmOxphYY0wprBENygEPxrda8qZKWrfuo4g8DHQHigNlgSxAVxsj3jMRqQecMsZsirs4nlVT5DHUYnEbxpiT7n+4LmA8Xj7qrYj4Y/0R/dYY86N78UkRyeV+PxfWpzmvFd8++tpxBDDGXACWY92byeQeKgduMyyON4qzj2HuS4zGGBMJTMB7j+GTQAMROYg1CncNrDMNrziGWixu48YfUbfngD9vt25K574u+hWwyxgzMs5bcYdbaQb8lNzZksrt9tFXjqOIZBeRTO7naYCaWPdllmENlQPefwzj28e/4nygEazr+V55DI0x3Y0xIcaYAlijVSw1xryKlxxD7ZQHiMh3QDWs0R9PAn3dr0thnRIeBN66cX3f24hIJeA3YDv/XivtgXVNfzqQDzgMvGiM8cob/XfYxyb4wHEUkZJYNz+dWB/yphtjBohIQaxPqVmAP4DX3J/Avc4d9nEpkB3rks0W4O04N8K9kohUA94zxtTzlmOoxUIppVSC9DKUUkqpBGmxUEoplSAtFkoppRKkxUIppVSCtFgopZRKkBYLpe6DiMS6R0LdKiKbRaSie3luEfkhoe2V8hbadFap+yAiEcaY9O7ntYEexpiqNsdSKsnpmYVSSScj1hDTiEiBG/OjiEhzEflRRBa45ywY5l7udM/V8KeIbBeRjjZmV+qOPDoHt1KpQBr3KKlBQC6s8X7iUwprJNxI4G8RGYM1ym8eY8zDADeGulAqJdIzC6XuzzX3hDzFsSbQ+sY9htGtlhhjLhpjrgM7gfzAfqCgiIwRkTDAJ0cCVr5Bi4VSScQYswZrfLHs8bwdd6yfWMDPGHMeeBRrdNV3cU+Io1RKpJehlEoiIlIcaxC8s0DaRKyfDYgyxswUkX1Y0/sqlSJpsVDq/ty4ZwHWqKjNjDGx8V+J+o88wAQRuXGG390TAZVKCtp0VimlVIL0noVSSqkEabFQSimVIC0WSimlEqTFQimlVIK0WCillEqQFgullFIJ0mKhlFIqQVoslFJKJej/AWl98YAHG5v4AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.bar (bins2, hist2norm)\n",
    "plt.plot(bins2, P2,'r--')\n",
    "plt.plot(bins2, Gaussian2, 'g--')\n",
    "plt.xlabel ('Bins')\n",
    "plt.ylabel ('Counts')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3. The Poisson and the Gaussian both fit the high activity data but not the low activity data because it is not symmetrical.\n",
    "\n",
    "4. This appears to be true because the standard deviations for each distribution are close. High activity: sigma p = 5.39, sigma g = 5.40. Low activity: sigma p was .59 and the sigma g was .57."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}