14_probability_distributions_gaussian.ipynb

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    "# ICS 434: DATA SCIENCE FUNDAMENTALS\n",
    "\n",
    "## Normal (or Gaussian) Distribution\n",
    "---"
   ]
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   "source": [
    "from IPython.display import Image\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.stats import norm\n",
    "import scipy"
   ]
  },
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    "### The Normal Distribution\n",
    "\n",
    "\n",
    "* The `normal` or `Gaussian` distribution is a continuous probability distribution\n",
    "  \n",
    "* Numerous real-world phenomena can be modeled, or approximated using normal distributions\n",
    "\n",
    "* Some examples:\n",
    "  * The heights of males in a population\n",
    "  * Errors in an instrument\n",
    "  * Duration of cab rides\n",
    "    \n",
    "* Many statistical tests assume that your data is distributed according to a normal distribution\n",
    "  * More on this later"
   ]
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    "### Properties of the Normal Distribution\n",
    "\n",
    "* The normal distribution is a continuous distribution\n",
    "  * Typically graphically represented as a continuous curve\n",
    "    * As opposed to the discrete distribution, the continuous can usually take any values either in a closed or open range\n",
    "  * The probability space is uncountably infinite\n",
    "\n",
    "* The Gaussian is bell-shaped\n",
    "  * Symmetric with a mode in middle\n",
    "  \n",
    "    <img src=\"https://www.dropbox.com/scl/fi/la1c22brstj529okysrnq/gaussian.png?rlkey=pmkh6vj8q68t93c1vjuolcjg9&dl=1\" width=\"500\">\n"
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    "### Properties of the Normal Distribution -- Cont'd\n",
    "\n",
    "- The `parameters` for a normal distribution are the location of its center (mean) and spread (standard deviation)\n",
    "  - $\\mu$ is the mean; it governs where the middle of the distribution lies on the $x$-axis\n",
    "  - $\\sigma$ is the standard deviation; determines how wide the bell is and can also be referred to as the scale\n",
    "\n",
    "- To describe that a random variable is distributed according to a normal distribution with parameters $\\mu$ and $\\sigma$, we write:\n",
    "\n",
    "$$\n",
    "X \\sim \\mathcal{N} (\\mu,\\sigma)\n",
    "$$\n",
    "\n",
    "* As with the binomial, two Gaussian distributions with different parameters tell different stories:\n",
    "\n",
    "$$\n",
    "X \\sim (\\mu = 0, \\sigma = 1) \\ne Y \\sim (\\mu = 1, \\sigma = 1) \\ne Z \\sim (\\mu = 2, \\sigma = 2)\n",
    "$$\n",
    "\n"
   ]
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\n",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "\n",
    "x = np.arange(-3.5, 3.5, 0.05)\n",
    "p_x = [norm.pdf(val, 0, 1) for val in x]\n",
    "plt.plot(x, p_x, label=\"$\\mu = 0$ and $\\sigma = 1$\")\n",
    "\n",
    "x = np.arange(-13, 17, 0.05)\n",
    "p_x = [norm.pdf(val, 2, 5) for val in x]\n",
    "plt.plot(x, p_x, label=\"$\\mu = 2$ and $\\sigma = 5$\", color='r')\n",
    "\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### The Spread and Density\n",
    "\n",
    "<center><img src=\"https://www.dropbox.com/scl/fi/dkmi9sy3mffbz70olq7p3/two_gaussians.png?rlkey=1qsza099l2r8a0kq5wuq2wdeu&dl=1\" width=\"600\"></center>\n",
    "    \n",
    "- For the blue curve ($\\mu = 0$ and $ \\sigma = 1$), the range of values with high densities is small\n",
    "  \n",
    "- For the red curve ($\\mu = 2$ and $\\sigma = 5$), the range of values with low densities is larger than that of the blue curve\n",
    "  \n",
    "- Think of this in terms of the probability distribution of the biased die from the binomial example\n",
    "  - If you were to draw a random value - just like when we were sampling from the die - what do you think the values obtained from the red distribution would look like?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Properties of the Normal Distribution -- Cont'd\n",
    "\n",
    "- The probability density function for a random variable $X \\sim \\mathcal{N} (\\mu,\\sigma)$ is:\n",
    "\n",
    "\n",
    "$$ \n",
    "    p(x) = \\frac{1}{\\sqrt{2\\pi}\\sigma} e^{\\frac{(x-\\mu)^2}{2\\sigma^2}}\n",
    "$$\n",
    "\n",
    "\n",
    "- Since the sample space is uncountably infinite, the probability of a single outcom is 0\n",
    "- Therefore, instead of computing the `pmf`, continuous random variables compute the `pdf`\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# We can manually implement the CDF\n",
    "\n",
    "def computePDF_normal (x, mu, sigma):\n",
    "    return 1.0/(sigma * np.sqrt(2 * np.pi)) * np.exp(-(x - mu)**2.0 / (2 * sigma**2))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.7827254290572115e-06"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "computePDF_normal(220, 174, 11)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.7827254290572225e-06"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "norm.pdf(220, 174, 11)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[196.5637715424669,\n",
       " 160.45940027565027,\n",
       " 171.77252241712605,\n",
       " 174.11397117054383,\n",
       " 167.21475178814867]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[norm.rvs(174, 11) for _ in range(5)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([161.62096853, 156.28266459, 171.91211269, 175.48741813,\n",
       "       171.05913467])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = norm.rvs(174, 11, 5) \n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.01925357, 0.00991251, 0.03562002, 0.03593743, 0.03499423])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm.pdf(x, 174, 11)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### `pdf` versus `pmf`\n",
    "\n",
    "- A `pdf` is conceptually similar to a `pmf`, but instead of giving you a probability, it tells you the density around a particular point\n",
    "  - You can think of it as mass (as in `pmf`) normalized by a small area  \n",
    "    - Ex. in the  $x \\sim \\mathcal{N}(0, 1)$ probability density around $0$ is much higher than the density around $-2.5$\n",
    "- Since $X$ is continuous, the `pdf` is also continuous\n",
    "- The total area under the `pdf` curve sums to 1\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Data in the Distribution -- 1$\\sigma$\n",
    "\n",
    "- In the normal distribution, the area with the highest density lies close to the mean\n",
    "  - Thus, when we sample from a normal distribution, the bulk of the observations generated lie near the mean\n",
    "  \n",
    "  <img src=\"https://www.dropbox.com/s/30b7wtt7f13ybiz/dist_1_std.png?dl=1\" width=\"700px\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Data in the Distribution -- 2$\\sigma$\n",
    "\n",
    "<img src=\"https://www.dropbox.com/s/vh3l8jo1iq1bhj4/dist_2_std.png?dl=1\" width=\"700\">\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Data in the Distribution -- 3$\\sigma$\n",
    "\n",
    "<img src=\"https://www.dropbox.com/s/7oif01yvcxl4ygq/dist_3_std.png?dl=1\" width=\"700\">\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# We can manually implement the CDF\n",
    "\n",
    "def computePDF_normal (x, mu, sigma):\n",
    "    return 1.0/(sigma * np.sqrt(2 * np.pi)) * np.exp(-(x - mu)**2.0 / (2 * sigma**2))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '$\\\\mu=0$ and $\\\\sigma=2$')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 1500x1500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# We manually implement the CDF\n",
    "def computePDF_normal (x, mu, sigma):\n",
    "    return 1.0/(sigma * np.sqrt(2 * np.pi)) * np.exp(-(x - mu)**2.0 / (2 * sigma**2))\n",
    "    \n",
    "\n",
    "f, (ax1, ax2, ax3) = plt.subplots(3)\n",
    "f.set_figheight(15)\n",
    "f.set_figwidth(15)\n",
    "\n",
    "title = \"$\\mu=0$ \" + \"and \" + \"$\\sigma=2$\"\n",
    "x_values = np.array(np.arange(-6.5, 2, 0.01))\n",
    "ax1.fill_between(x=x_values, \n",
    "                 y1=computePDF_normal(x_values, 0, 2),\n",
    "                 facecolor=\"blue\",\n",
    "                 alpha=0.35)\n",
    "\n",
    "x_values = np.arange(2, 6.5, 0.01)\n",
    "ax1.fill_between(x=x_values, \n",
    "                 y1= computePDF_normal(x_values, 0, 2),\n",
    "                 facecolor=\"blue\",\n",
    "                 alpha=0.35)\n",
    "\n",
    "x_values = np.arange(-2, 2.01, 0.01)\n",
    "ax1.fill_between(x=x_values, \n",
    "                 y1= computePDF_normal(x_values, 0, 2),\n",
    "                 facecolor='red',\n",
    "                 alpha=0.35)\n",
    "ax1.text(x=-3.4, y=0.03, s=\"~15.8%\", fontsize=18)\n",
    "ax1.text(x=-0.6, y=0.1, s=\"~68.3%\", fontsize=18)\n",
    "ax1.text(x=2.2, y=0.03, s=\"~15.8%\", fontsize=18)\n",
    "ax1.set_title(title, fontsize=20)\n",
    "\n",
    "\n",
    "x_values = np.array(np.arange(-6.5, 4, 0.01))\n",
    "#print computePDF(x_values, 0, 0.1)\n",
    "ax2.fill_between(x=x_values, \n",
    "                 y1=computePDF_normal(x_values, 0, 2),\n",
    "                 facecolor=\"blue\",\n",
    "                 alpha=0.35)\n",
    "\n",
    "x_values = np.arange(4, 6.51, 0.01)\n",
    "ax2.fill_between(x=x_values, \n",
    "                 y1= computePDF_normal(x_values, 0, 2),\n",
    "                 facecolor=\"blue\",\n",
    "                 alpha=0.35)\n",
    "x_values = np.arange(-4, 4, 0.01)\n",
    "ax2.fill_between(x=x_values, \n",
    "                 y1= computePDF_normal(x_values, 0, 2),\n",
    "                 facecolor='red',\n",
    "                 alpha=0.35)\n",
    "ax2.text(x=-5, y=0.03, s=\"~2.3%\", fontsize=18)\n",
    "ax2.text(x=-0.6, y=0.1, s=\"~95.4%\", fontsize=18)\n",
    "ax2.text(x=4.1, y=0.03, s=\"~2.3%\", fontsize=18)\n",
    "ax2.set_title(title, fontsize=20)\n",
    "\n",
    "\n",
    "x_values = np.array(np.arange(-6.5, 6, 0.01))\n",
    "ax3.fill_between(x=x_values, \n",
    "                 y1=computePDF_normal(x_values, 0, 2),\n",
    "                 facecolor=\"blue\",\n",
    "                 alpha=0.35)\n",
    "\n",
    "x_values = np.arange(6, 6.51, 0.01)\n",
    "ax3.fill_between(x=x_values, \n",
    "                 y1= computePDF_normal(x_values, 0, 2),\n",
    "                 facecolor=\"blue\",\n",
    "                 alpha=0.35)\n",
    "x_values = np.arange(-6, 6, 0.01)\n",
    "ax3.fill_between(x=x_values, \n",
    "                 y1= computePDF_normal(x_values, 0, 2),\n",
    "                 facecolor='red',\n",
    "                 alpha=0.35)\n",
    "ax3.text(x=-6.9, y=0.01, s=\"~0.15%\", fontsize=18)\n",
    "ax3.text(x=-0.6, y=0.1, s=\"~99.7%\", fontsize=18)\n",
    "ax3.text(x=5.8, y=0.01, s=\"~0.15%\", fontsize=18)\n",
    "ax3.set_title(title, fontsize=20)\n",
    "\n",
    "\n",
    "# f.savefig('dist_std.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Computing the `pdf` in Python\n",
    "\n",
    "* We can easily compute the `pdf` in python using `scipy`\n",
    "```python\n",
    "import scipy.stats\n",
    "norm_0_1 = scipy.stats.norm(0, 1)\n",
    "print(norm_0_1.pdf(2))\n",
    "```\n",
    "\n",
    "* `pdf` can also take a range of values\n",
    "\n",
    "```python\n",
    "print(norm_0_1.pdf([-2, -1, 0, 1, 2]))\n",
    "```\n",
    "\n",
    "* `scipy.stats.norm` creates a frozen distribution\n",
    "  * This can be thought of a constructor in OO programming\n",
    "  * Can also invoke pdf using static methods `scipy.stats.norm.pdf(0, loc=0, scale=1)`\n",
    "\n",
    "* Which of the pdf values is larger and why?\n",
    " * Which of the `pdf`s is largest `pdf(-2)` or `pdf(2)`?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.1463837356630605e-32"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm_0_1 = scipy.stats.norm(0, 1)\n",
    "norm_0_1.pdf(12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.1463837356630605e-32"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scipy.stats.norm.pdf(12, 0, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Computing the `pdf` in Python\n",
    "\n",
    "* We can easily compute the `pdf` in python using `scipy`\n",
    "```python\n",
    "import scipy.stats\n",
    "norm_0_1 = scipy.stats.norm(0, 1)\n",
    "print(norm_0_1.pdf(2))\n",
    "```\n",
    "\n",
    "* `pdf` can also take a range of values\n",
    "\n",
    "```python\n",
    "print(norm_0_1.pdf([-2, -1, 0, 1, 2]))\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.60607868 -0.88631831 -0.72896395]\n",
      "2.1188192535093538e-27\n",
      "[2.11881925e-27 5.39909665e-02]\n"
     ]
    }
   ],
   "source": [
    "import scipy.stats\n",
    "\n",
    "norm_0_1 = scipy.stats.norm(0, 1)\n",
    "print(norm_0_1.rvs(3)) # return 3 random variates form Normal with mean 0 and std = 1\n",
    "print(norm_0_1.pdf(11)) # compute the pdf of 11 according to a Normal with mean 0 and std = 1\n",
    "print(norm_0_1.pdf([11, 2])) # compute the pdf of 11 and 2 according to a Normal with mean 0 and std = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<bound method rv_generic.rvs of <scipy.stats._continuous_distns.norm_gen object at 0x000001EE30473130>>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scipy.stats.norm.rvs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "scipy.stats.norm.rvs?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.01313812 -1.22716261 -1.60098262]\n",
      "2.1188192535093538e-27\n",
      "[2.11881925e-27 5.39909665e-02]\n"
     ]
    }
   ],
   "source": [
    "print(scipy.stats.norm.rvs(loc=0, scale=1, size=3))\n",
    "print(scipy.stats.norm.pdf(11, loc=0, scale=1))\n",
    "print(scipy.stats.norm.pdf([11, 2], loc=0, scale=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.05399097 0.24197072 0.39894228 0.24197072 0.05399097]\n"
     ]
    }
   ],
   "source": [
    "print(norm_0_1.pdf([-2, -1, 0, 1, 2]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### The Sum of PDF $\\neq$ 1\n",
    "\n",
    "```python \n",
    ">>> print(sum(norm_0_1.pdf([-2, -1, -0.5, 0, 0.5, 1, 2])))\n",
    "\n",
    "1.6949963159946946\n",
    "```\n",
    "\n",
    "* Why is the sum of the pdfs for the small subsample of the sample space greater than 1?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.05399097, 0.24197072, 0.35206533, 0.39894228, 0.35206533,\n",
       "       0.24197072, 0.05399097])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm_0_1.pdf([-2, -1, -0.5, 0, 0.5, 1, 2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.6949963159946946\n"
     ]
    }
   ],
   "source": [
    "print(sum(norm_0_1.pdf([-2, -1, -0.5, 0, 0.5, 1, 2])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.989422804014327"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scipy.stats.norm.pdf(1, 1, 0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.1188192535093538e-27\n",
      "2.1188192535093538e-27\n",
      "*************************\n",
      "[0.05399097 0.24197072 0.39894228 0.24197072 0.05399097]\n",
      "[0.05399097, 0.24197072, 0.39894228, 0.24197072, 0.05399097]\n"
     ]
    }
   ],
   "source": [
    "print(norm_0_1.pdf(11))\n",
    "print(computePDF_normal(11, 0, 1))\n",
    "\n",
    "print(\"*\" * 25)\n",
    "print(norm_0_1.pdf([-2, -1, 0, 1, 2]))\n",
    "print([float(format(computePDF_normal(x, 0, 1), \".8f\")) for x in [-2, -1, 0, 1, 2]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Plotting the `pdf`\n",
    "\n",
    "* We cannot compute the `pdf` for all the possible values\n",
    "  * Infinite number of values\n",
    "  \n",
    "* We can compute it for a sufficiently large number of values such that the plot looks continuous and smooth\n",
    "\n",
    "* We can use `np.arange` to generate values in a range with a specific step value\n",
    "\n",
    "```python\n",
    "np.arange(start, stop, step)\n",
    "```\n",
    "  * As with Python ranges, stop is not included in the range\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-2. , -1.5, -1. , -0.5,  0. ,  0.5,  1. ,  1.5])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arange(-2, 2, 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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nY2DjBkyICmFUnyB8G7ianFJEpOqq2g2q9cTknDlzCA0NxcPDg7CwMNatW3fFddevX0+/fv1o2rQpDRo0oFOnTrz22muV1omLi8NisVyyFBcXVyeeiEitdqHUyvtb0hn6xjrGzE8ice/FInRLh2YsmtiH/8wcwIToEBUhuWEsFgt9Qprw1tjerP3Drfz6F21p5OnK8XMXeH71PqJm/4c/f7yHw9mFZkcVEbmu7P5Om5CQwPTp05kzZw79+vXj3XffZejQoezdu5fWrVtfsr6XlxePPPII3bt3x8vLi/Xr1/PQQw/h5eXFgw8+WLGej48PBw4cqLSth4deFigi9cuiDam88Z9D5BaVAeDp5sw9vQOZEB1Mu+beJqcTgVaNGvDHIZ147Lb2fJJygkUb0jhwqoAlm4+xZPMxbu3YjBfv7U5zb32PFpG6z+7b5CIiIujduzdvv/12xVjnzp0ZMWIEs2fPrtI+Ro4ciZeXF0uWLAEuXhmaPn06ubm59kSpRLfJiUht9+Z/DvFK4kHg4u1HE6NDuC9ctx9J7Xa52znbNW/I+w9G4tdQL3AVkdqpRm6TKy0tZfv27QwaNKjS+KBBg9i4cWOV9pGcnMzGjRsZMGBApfHCwkKCg4MJDAzkzjvvJDk5+ar7KSkpIT8/v9IiIlJbzfnucEUR+v3gjnz/+1uZ0r+NipDUehaLheh2fswbH07ijFsI8PXgcHYhY+Zt5kxhidnxRESuiV1lKCcnB6vVir+/f6Vxf39/srKyrrptYGAg7u7uhIeH8/DDDzNlypSKr3Xq1Im4uDg+/fRT4uPj8fDwoF+/fhw6dOiK+5s9eza+vr4VS1BQkD0fRUTkhnn3+yO89MXF24B/P7gjD9/aTjN0SZ3Urrk38VMj8fdx5+CpQsbOT+Ls+VKzY4mIVFu1JlD46TsuDMP42fderFu3jm3btvHOO+/w+uuvEx8fX/G1yMhIxo0bR48ePejfvz8rVqygQ4cOvPnmm1fc35NPPkleXl7FkpGRUZ2PIiJSo+avO8rsNfsBmDmwAw/f2s7kRCLXJsTPi/ipkTTzdmd/VgHj5ieRW6RCJCJ1k11lyM/PD2dn50uuAmVnZ19yteinQkND6datG1OnTmXGjBk888wzVw7l5ESfPn2uemXI3d0dHx+fSouISG0StyGVv32+D4DHbm/PY7e3NzmRyPXRpllD4qdefGZob2Y+4xYkkffjpCAiInWJXWXIzc2NsLAwEhMTK40nJiYSHR1d5f0YhkFJyZXvMzYMg5SUFAICAuyJJyJSayzZlMYzn+0F4OFb2zLjDhUhqV/aNW9I/NQImnq5sedEPuMXJpF3QYVIROoWu6fWnjlzJrGxsYSHhxMVFcXcuXNJT09n2rRpwMXb106cOMHixYsBeOutt2jdujWdOnUCLr536OWXX+bRRx+t2Oezzz5LZGQk7du3Jz8/n3/+85+kpKTw1ltvXY/PKCJyQy1LOsafP/kBgGkD2vK7QR1/9lZikbqovb83y6dGMnreZnYez2PCwi0smdwXbw9NDCIidYPdZSgmJoYzZ87w3HPPkZmZSdeuXVm9ejXBwcEAZGZmkp6eXrG+zWbjySefJDU1FRcXF9q2bcsLL7zAQw89VLFObm4uDz74IFlZWfj6+tKrVy/Wrl1L3759r8NHFBG5cRK2pjNr1R4ApvYP5Y9DVISkfuvYwpulkyMYM38zKRm5TFy0lfce6KuXBotInWD3e4ZqK71nSETM9sG2DP6wcheGAZP6hfCXO7uoCInD2HMijzHzNpNfXE6fkMbETeqLlwqRiJikRt4zJCIil/fRjuMVRWhCVLCKkDicrq18WTYlEm8PF7amnWNS3FaKSsvNjiUiclUqQyIi1+iTlBP87oOdGAaMi2zNM7+6SUVIHFK3QF+WTI7A292FLalnmRy3jQulVrNjiYhckcqQiMg1+GznSWYkpGAzYHTfIJ77VVcVIXFoPYMa8d7ki88MbTp6hqmLt1FcpkIkIrWTypCISDWt3p3J9B+L0KjwQJ4f0Q0nJxUhkd6tGxM3qQ+ebs6sP5zDg0u2qxCJSK2kMiQiUg1f7MnisfhkrDaDe3oH8sLI7ipCIv8jPKQJcZP60sDVmbUHT/PrpdspKVchEpHaRWVIRMROiXtP8cjyHZTbDEb0bMlL96oIiVxO39AmLJzYBw9XJ749cJqHl+2gtNxmdiwRkQoqQyIidvhm/yl+s2w75TaDu3q05OX7euCsIiRyRVFtm7JgQh/cXZz4el82jyzfQZlVhUhEageVIRGRKvruQDbTluygzGowrFsAr43qgYuz/hkV+Tn92vkxb3w4bi5OfLX3FI/FJ6sQiUitoO/iIiJVsO7QaR5csp1Sq40hN7Xg9ft7qgiJ2OGWDs2YGxuGm7MTa/ZkMT0hhXIVIhExmb6Ti4j8jI2Hc5jy3jZKy20M7OLPP0f3wlVFSMRuv+jYnHdie+PqbOHzXZnMXLFThUhETKXv5iIiV7HpyBkeeG8rJeU2bu/UnLfG9MbNRf90ilTXbZ38mTM2DFdnC5/uPMnvP9yF1WaYHUtEHJS+o4uIXMGW1LM8ELeV4jIbt3ZsxpxxKkIi18PALv68Obo3Lk4WViWf4A8f7sKmQiQiJtB3dRGRy9iWdpaJi7ZwocxK//Z+vD0uDHcXZ7NjidQbQ7q24J+je+HsZGHljuM88ZEKkYjceCpDIiI/sSP9HBMXbaWo1Eq/dk2ZNz4cD1cVIZHr7ZfdAng9pidOFlix7TizPt6tQiQiN5TKkIjI/0jJyGXCgi0UlpQT1aYp88f3URESqUF39WjJaz8WovgtGfzl0z0YhgqRiNwYKkMiIj/afTyP2AVJFJSU0ze0CQsmhtPATUVIpKYN79mKl+/rgcUCSzen8+xne1WIROSGUBkSEQH2nMhj3IIkCorLCQ9uzKKJffB0czE7lojDGNk7kJfu6Y7FAnEb0/jrv/epEIlIjVMZEhGHt/dkPuMWJJF3oYzerRsR90BfvNxVhERutPvCg3hhZDcAFm5I5e+rVYhEpGapDImIQ9uflc/Y+ZvJLSqjZ1Aj3nugLw1VhERME9OnNX+/+2IhmrculRe/OKBCJCI1RmVIRBzWoVMFjJ2XxLmiMroH+vLeA33x9nA1O5aIwxsT0Zq/Dr8JgHe+P8IrXx1UIRKRGqEyJCIO6XB2IaPnJXHmfCk3tfRhyQMR+DZQERKpLWKjQnj6ri4A/Ovbw7z+9SGTE4lIfaQyJCIO58jpQkbP20xOYQmdA3xYOjkCX08VIZHaZlK/UJ4a1hmAN/5ziH/+R4VIRK4vlSERcShpOecZM28zpwtK6NTCm2VTImjs5WZ2LBG5gin92/CnX3YC4NXEg7z17WGTE4lIfaIyJCIOI/1MEaPnbeZUfgkd/BuybEoETVSERGq9B29pyx+GdATgH18e4N3vj5icSETqC5UhEXEIGWcvFqHMvGLaNvNi2ZRImjZ0NzuWiFTRb37Rjt8O7ADA7DX7mb/uqMmJRKQ+UBkSkXrv+LmLRehE7gXa+HkRPzWSZt4qQiJ1zaO3t+fx29sD8LfP97FoQ6rJiUSkrlMZEpF67WTuBcbMS+L4uQuE+nkR/2AkzX08zI4lItU0/Y72PHpbOwCe/WwvizelmRtIROo0lSERqbey8ooZPW8z6WeLaN3Ek+VTI/BXERKp0ywWCzMHduDXv2gLwF8++YGlm4+ZnEpE6iqVIRGpl7LzLxahY2eKCGrSgPgHIwnwbWB2LBG5DiwWC38Y3JEHb2kDwFMf7+H9LekmpxKRukhlSETqneyCi0UoNec8rRo1IH5qJK0aqQiJ1CcWi4Unh3Zi8s2hADy5ajcrtmWYnEpE6ppqlaE5c+YQGhqKh4cHYWFhrFu37orrrl+/nn79+tG0aVMaNGhAp06deO211y5Zb+XKlXTp0gV3d3e6dOnCqlWrqhNNRBxcTmEJY+clceT0eVr6ehA/NZLAxp5mxxKRGmCxWHhqWGcmRodgGPDHlbtYuf242bFEpA6xuwwlJCQwffp0Zs2aRXJyMv3792fo0KGkp1/+8rSXlxePPPIIa9euZd++fTz11FM89dRTzJ07t2KdTZs2ERMTQ2xsLDt37iQ2NpZRo0aRlJRU/U8mIg7nzI9F6FB2IS18PFg+NZLWTVWEROozi8XC03d1YVxkawwDfvfhTj5OPmF2LBGpIyyGYRj2bBAREUHv3r15++23K8Y6d+7MiBEjmD17dpX2MXLkSLy8vFiyZAkAMTEx5Ofns2bNmop1hgwZQuPGjYmPj6/SPvPz8/H19SUvLw8fHx87PpGI1Afnzpcyet5m9mcV0NzbnYSHogj18zI7lojcIDabwayP9xC/JR0nC7xxfy/u6tHS7FgiYpKqdgO7rgyVlpayfft2Bg0aVGl80KBBbNy4sUr7SE5OZuPGjQwYMKBibNOmTZfsc/DgwVfdZ0lJCfn5+ZUWEXFMuUWljJ2fxP6sAvwauhP/YKSKkIiDcXKy8PyIrsSEB2EzYHpCCp/vyjQ7lojUcnaVoZycHKxWK/7+/pXG/f39ycrKuuq2gYGBuLu7Ex4ezsMPP8yUKVMqvpaVlWX3PmfPno2vr2/FEhQUZM9HEZF6Iq+ojNgFW9ibmY9fQzfip0bQtllDs2OJiAmcnCzMHtmNe8MCsdoMHns/mS/2qBCJyJVVawIFi8VS6c+GYVwy9lPr1q1j27ZtvPPOO7z++uuX3P5m7z6ffPJJ8vLyKpaMDM0gI+Jo8ovLGL8wid0n8mji5cayKZG09/c2O5aImMjJycKL93RnZK9WWG0GjyxP5qsfrv4LWxFxXC72rOzn54ezs/MlV2yys7MvubLzU6GhF6e+7NatG6dOneKZZ55h9OjRALRo0cLufbq7u+Pu7m5PfBGpRwqKy5iwcAs7j+fR2NOVZVMi6NhCRUhEwNnJwj/u64HVMPgk5SQPL9/BO+PCuL3z1X9WERHHY9eVITc3N8LCwkhMTKw0npiYSHR0dJX3YxgGJSUlFX+Oioq6ZJ9fffWVXfsUEcdRWFLOxEVbSU7PxbeBK0unRNA5QBOniMj/c3ay8Mp9PRjWPYAyq8Gvl+7g2wPZZscSkVrGritDADNnziQ2Npbw8HCioqKYO3cu6enpTJs2Dbh4+9qJEydYvHgxAG+99RatW7emU6dOwMX3Dr388ss8+uijFft8/PHHueWWW3jxxRcZPnw4n3zyCV9//TXr16+/Hp9RROqR8yXlPLBoK9uPncPHw4VlUyK4qaWv2bFEpBZycXbi9Zie2GwGa/Zk8dCS7cwfH84tHZqZHU1Eagm7y1BMTAxnzpzhueeeIzMzk65du7J69WqCg4MByMzMrPTOIZvNxpNPPklqaiouLi60bduWF154gYceeqhinejoaN5//32eeuop/vznP9O2bVsSEhKIiIi4Dh9RROqLotJyHojbypa0s3h7uLBkcgRdW6kIiciVuTo78c/RvXh42Q6+2nuKqYu3sWBCH25u72d2NBGpBex+z1BtpfcMidRvF0qtTH5vKxuPnKGhuwtLJvelV+vGZscSkTqitNzGb5Zt5+t92Xi4OrFwYh+i26oQidRXNfKeIRERMxSXWXlwyTY2HjmDl5sz7z3QR0VIROzi5uLEW2N7c2vHZhSX2Zgct42ko2fMjiUiJlMZEpFarbjMykNLtrPuUA6ebs7EPdCXsOAmZscSkTrI3cWZt8eFcUuHZlwoszIpbivb0s6aHUtETKQyJCK1Vkm5ld8s28H3B0/TwNWZhRP70CdERUhEqs/D1Zm5sWH0b+9HUamVCQu3sP3YObNjiYhJVIZEpFYqLbfx8LJkvtl/8f7+BRPDiWzT1OxYIlIPXCxE4US3bcr5HwtRcroKkYgjUhkSkVqnzGrj0fgdfL3vFO4uTswfrwedReT6auDmzPwJ4USENqGwpJzxC7ew63iu2bFE5AZTGRKRWqXMauOx+GS+/OEUbi5OzB0frilwRaRGeLq5sHBiH/qGNKGguJxx85PYcyLP7FgicgOpDIlIrVFutTEjIYU1e7Jwc3bi3XFhDNDLEUWkBnm5u7BwUh/CghuTX1zO2PlJ/HBShUjEUagMiUitYLUZ/PaDnfx7VyauzhbmjO3NrZ2amx1LRBxAQ3cX4ib1oWdQI/IulDFufhL7s/LNjiUiN4DKkIiYzmoz+P0HO/kk5SQuThb+NaY3d3TxNzuWiDgQbw9XFk/uS49AX84VlTF2XhIHTxWYHUtEapjKkIiYymYz+OPKXXyUfAJnJwtvju7F4JtamB1LRByQj4crix+IoGsrH86cL2XMvM0czlYhEqnPVIZExDQ2m8GfVu3mw+3HcXay8M/7ezG0W4DZsUTEgfl6urJ0cgRdAnzIKSxl9LwkjpwuNDuWiNQQlSERMYXNZvDUJ3t4f2sGThZ4dVQPhnVXERIR8zXydGPZlAg6tfDmdEEJo+duJjXnvNmxRKQGqAyJyA1nGAZPf/oDy5PSsVjglVE9GN6zldmxREQqNPa6WIg6+nuT/WMhOnZGhUikvlEZEpEbyjAMnv1sL0s2H8NigX/c24O7ewWaHUtE5BJNG7qzbGoE7Zs3JCu/mNFzN5NxtsjsWCJyHakMicgNYxgGf/t8H3Eb0wB4cWR37g1TERKR2svvx0LUppkXJ/OKuX/uZo6fUyESqS9UhkTkhjAMg9lr9rNgfSoAf7+7G6P6BJmcSkTk5zX39iB+aiShfl6cyL3A6HmbOZF7wexYInIdqAyJSI0zDIOXvjzA3LVHAfjriK6MiWhtcioRkarz97lYiIKbepJx9gJj5m0mM0+FSKSuUxkSkRr3WuJB3v7uCADP/uomYiODTU4kImK/Fr4XC1FQkwYcO1PEmHlJnMovNjuWiFwDlSERqVGvf32Qf35zGIA/39mFCdEh5gYSEbkGLRs1IH5qJK0aNSA15zyj520mu0CFSKSuUhkSkRrz5n8O8frXhwCY9cvOTL451OREIiLXLrCxJ+8/GElLXw+Onj7PmHlJnC4oMTuWiFSDypCI1Ig53x3mlcSDAPxxSCem3tLG5EQiItdPUBNP4h+MJMDXg8PZhYydv5kzhSpEInWNypCIXHdz1x7hpS8OAPD7wR359S/ampxIROT6C27qxfKpkfj7uHPwVCFj5ydx9nyp2bFExA4qQyJyXc1fd5S/r94PwIw7OvDwre1MTiQiUnNC/S4Wombe7uzPKmDc/CRyi1SIROoKlSERuW7iNqTyt8/3AfDYbe14/I72JicSEal5bZs1JH5qBH4N3dmbmc+4BUnkFZWZHUtEqkBlSESuiyWb0njms70APHxrW2YM7GByIhGRG6ddc2+WT42gqZcbe07kE7swibwLKkQitZ3KkIhcs+VJ6fz5kx8AeGhAG343qCMWi8XkVCIiN1YHf2+WTY2gsacru47nMWHhFgqKVYhEajOVIRG5Jglb0/nTqt0ATLk5lCeGdFIREhGH1amFD8umRNLI05WUjFwmLNxCYUm52bFE5ApUhkSk2j7YlsETH10sQpP6hTBrWGcVIRFxeF1a+rB0cgQ+Hi7sSM9l0qItnFchEqmVVIZEpFo+2nGcP6zchWHA+Khg/nJnFxUhEZEfdW3ly9IpEXh7uLA17RyT4rZSVKpCJFLbVKsMzZkzh9DQUDw8PAgLC2PdunVXXPejjz5i4MCBNGvWDB8fH6Kiovjyyy8rrRMXF4fFYrlkKS4urk48Ealhn6Sc4Hcf7MQwYGxEa5791U0qQiIiP9E9sBFLJkfg7e7CltSzTI7bxoVSq9mxROR/2F2GEhISmD59OrNmzSI5OZn+/fszdOhQ0tPTL7v+2rVrGThwIKtXr2b79u3ceuut3HXXXSQnJ1daz8fHh8zMzEqLh4dH9T6ViNSYz3aeZEZCCjYD7u8TxF+Hd1UREhG5gp5BjYh7oC9ebs5sOnqGqYu3UVymQiRSW1gMwzDs2SAiIoLevXvz9ttvV4x17tyZESNGMHv27Crt46abbiImJoa//OUvwMUrQ9OnTyc3N9eeKJXk5+fj6+tLXl4ePj4+1d6PiFzZmt2ZPBKfjNVmcF9YIC/e0x0nJxUhEZGfsy3tLOMXbqGo1MotHZoxNzYMD1dns2OJ1FtV7QZ2XRkqLS1l+/btDBo0qNL4oEGD2LhxY5X2YbPZKCgooEmTJpXGCwsLCQ4OJjAwkDvvvPOSK0c/VVJSQn5+fqVFRGrOF3uyePTHIjSydyteUBESEamy8JAmLJrYhwauzqw9eJpfL91OSbmuEImYza4ylJOTg9Vqxd/fv9K4v78/WVlZVdrHK6+8wvnz5xk1alTFWKdOnYiLi+PTTz8lPj4eDw8P+vXrx6FDh664n9mzZ+Pr61uxBAUF2fNRRMQOiXtP8cjyHZTbDIb3bMk/7u2Bs4qQiIhdIto0ZeHEPni4OvHtgdP8ZukOSsttZscScWjVmkDhp88HGIZRpWcG4uPjeeaZZ0hISKB58+YV45GRkYwbN44ePXrQv39/VqxYQYcOHXjzzTevuK8nn3ySvLy8iiUjI6M6H0VEfsY3+0/xm2XbKbcZ3NWjJa/cpyIkIlJdUW2bsmBCH9xdnPjP/mweXr6DMqsKkYhZ7CpDfn5+ODs7X3IVKDs7+5KrRT+VkJDA5MmTWbFiBXfcccfVQzk50adPn6teGXJ3d8fHx6fSIiLX13cHspm2ZAdlVoNh3QJ4bVQPXJw1I7+IyLXo186PeePDcXNxInHvKR6LT1YhEjGJXT/VuLm5ERYWRmJiYqXxxMREoqOjr7hdfHw8EydOZPny5QwbNuxn/x7DMEhJSSEgIMCeeCJyHa07dJoHl2yn1Gpj8E3+vH5/TxUhEZHr5JYOzXg3Ngw3ZyfW7Mli+vsplKsQidxwdv9kM3PmTObPn8/ChQvZt28fM2bMID09nWnTpgEXb18bP358xfrx8fGMHz+eV155hcjISLKyssjKyiIvL69inWeffZYvv/ySo0ePkpKSwuTJk0lJSanYp4jcWBsP5zDlvW2UltsY2MWfN0f3xlVFSETkurq1Y3PeHtcbV2cLn+/OZMaKnSpEIjeY3T/dxMTE8Prrr/Pcc8/Rs2dP1q5dy+rVqwkODgYgMzOz0juH3n33XcrLy3n44YcJCAioWB5//PGKdXJzc3nwwQfp3LkzgwYN4sSJE6xdu5a+ffteh48oIvbYfPQMD7y3lZJyG7d3as5bY3rj5qIiJCJSE27v7M+csWG4OFn4bOdJfvfBTqw2u956IiLXwO73DNVWes+QyLX73/dg/KLjxVs43F30HgwRkZr2xZ4sHl6+Q+9xE7lOauQ9QyJSf+06nsukRVspKrVyczs/3hmnIiQicqMM6dqCf97fCycLfLD9OH/5dA/15PfVIrWaypCIsPdkPrELtlBQUk7f0CbMGx+uN6OLiNxgw7oH8MqoHlgssHRzOs9/vk+FSKSGqQyJOLhDpwqIXZBE3oUyerVuxMKJfWjgpiIkImKGu3sFMvvubgDMX5/KK18dNDmRSP2mMiTiwNJyzjN2fhJnzpfStZUPcZP60tDdxexYIiIO7f6+rXn2VzcB8K9vD/Ovb6783kURuTYqQyIOKuNsEWPmbSa7oISO/t4seSAC3wauZscSERFgQnQITw7tBMDLXx1k/rqjJicSqZ9UhkQcUFZeMWPnJ3Eyr5g2zbxYOiWCxl5uZscSEZH/8dCAtsy4owMAf/t8H0s2pZkbSKQeUhkScTCnC0oYM38z6WeLaN3Ek+VTImnm7W52LBERuYzHbm/Hr3/RFoA/f/IDK7ZmmJxIpH5RGRJxIGfPlzJufhJHT5+npa8Hy6dG0MLXw+xYIiJyBRaLhT8M7sikfiEA/PGjXXyScsLcUCL1iMqQiIPIu1BG7IIkDpwqoLm3O8unRhLY2NPsWCIi8jMsFgt/ubMLYyJaYxgwc8VO1uzONDuWSL2gMiTiAApLypm4aAs/nMynqZcby6dGEOLnZXYsERGpIovFwt+Gd+We3oFYbQaPvZ/MN/tPmR1LpM5TGRKp5y6UWnkgbivJ6bn4NnBlyeQI2jX3NjuWiIjYycnJwkv3dufO7gGUWQ2mLd3B+kM5ZscSqdNUhkTqseIyK1MXb2NL6lm83V1YMrkvXVr6mB1LRESqydnJwmsxPRnUxZ/SchtTFm8l6egZs2OJ1FkqQyL1VGm5jd8s28H6wzl4ujkT90Afugc2MjuWiIhcI1dnJ94c04sBHZpRXGbjgbit7Eg/Z3YskTpJZUikHiq32nj8/WS+2Z+Nu4sTCyb0ISy4idmxRETkOnF3cebd2DCi2zblfKmVCQu3sOdEntmxROoclSGResZqM/jtBztZsycLN2cn5o4PJ6ptU7NjiYjIdebh6sz8CeGEBzemoLj84oyhWQVmxxKpU1SGROoRm83gyY928UnKSVycLLw1tjcDOjQzO5aIiNQQTzcXFk3qQ49AX84VlTF2/maOnC40O5ZInaEyJFJPGIbB05/+wIptx3GywBv392JgF3+zY4mISA3z9nDlvQf60jnAh5zCUsbOSyL9TJHZsUTqBJUhkXrAMAz+vnofSzYfw2KBl+/rwbDuAWbHEhGRG6SRpxtLJ/elffOGZOUXM3reZk7kXjA7lkitpzIkUg+8mniQeetSAfj73d0Y2TvQ5EQiInKjNW3ozrIpEYQ09eRE7gXGztvMqfxis2OJ1GoqQyJ13FvfHubNbw4D8MxdXRjdt7XJiURExCzNfTxYPjWSwMYNSDtTxNj5SeQUlpgdS6TWUhkSqcPmrzvKP748AMATQzsxsV+oyYlERMRsLRs1IH5qJC18PDicXci4+UnkFpWaHUukVlIZEqmjlmw+xt8+3wfA9DvaM21AW5MTiYhIbRHUxJPlUyPwa+jO/qwCxi/cQn5xmdmxRGodlSGROmjFtgz+/PEeAKYNaMvjt7c3OZGIiNQ2bZo1ZNmUCBp7urLreB6TFm3lfEm52bFEahWVIZE65pOUE/xx5S4AJkaH8MchHbFYLCanEhGR2qhjC2+WTI7Ax8OF7cfOMeW9bRSXWc2OJVJrqAyJ1CFf7Mlk5oqdGAaM7tuap+/qoiIkIiJX1bWVL+890JeG7i5sOnqGB5dsp6RchUgEVIZE6oxv92fzaHwyVpvByN6teH5EVxUhERGpkl6tG7NwYh8auDqz9uBpHlmeTJnVZnYsEdOpDInUAesP5fDQ0u2UWQ2GdQ/gpXu64+SkIiQiIlXXN7QJ8yeE4+biROLeU0xPSKFchUgcnMqQSC23JfUsUxZvpbTcxsAu/rwe0xMXZ/2vKyIi9uvXzo93x4Xh6mzh812Z/OHDXdhshtmxREyjn6hEarHk9HNMWrSF4jIbAzo0419jeuGqIiQiItfg1k7NeXN0b5ydLHyUfIJZH+/BMFSIxDHppyqRWmrPiTwmLNzC+VIrUW2a8m5sGO4uzmbHEhGRemBI1xa8OqoHFgvEb0nn2c/2qhCJQ6pWGZozZw6hoaF4eHgQFhbGunXrrrjuRx99xMCBA2nWrBk+Pj5ERUXx5ZdfXrLeypUr6dKlC+7u7nTp0oVVq1ZVJ5pIvXAgq4DYBUnkF5cTHtyY+RPC8XBVERIRketneM9WvHRPdwDiNqbx4hcHVIjE4dhdhhISEpg+fTqzZs0iOTmZ/v37M3ToUNLT0y+7/tq1axk4cCCrV69m+/bt3Hrrrdx1110kJydXrLNp0yZiYmKIjY1l586dxMbGMmrUKJKSkqr/yUTqqKOnCxk7P4lzRWV0D/Rl4aQ+eLm7mB1LRETqofvCg/jriK4AvPP9Ed74zyGTE4ncWBbDzl8BRERE0Lt3b95+++2Ksc6dOzNixAhmz55dpX3cdNNNxMTE8Je//AWAmJgY8vPzWbNmTcU6Q4YMoXHjxsTHx1dpn/n5+fj6+pKXl4ePj48dn0ik9kg/U8SodzeRlV9M5wAf4qdG0MjTzexYIiJSz81fd5S/fb4PgCeGdmLagLYmJxK5NlXtBnZdGSotLWX79u0MGjSo0vigQYPYuHFjlfZhs9koKCigSZMmFWObNm26ZJ+DBw++6j5LSkrIz8+vtIjUZSdzLzBm/may8otp17whSyf3VRESEZEbYkr/Nvx+cEcAXlizn0UbUk1OJHJj2FWGcnJysFqt+Pv7Vxr39/cnKyurSvt45ZVXOH/+PKNGjaoYy8rKsnufs2fPxtfXt2IJCgqy45OI1C7Z+cWMmbeZ4+cuENLUk+VTImja0N3sWCIi4kAevrUdj97WDoBnP9vL8qTLPwIhUp9UawKFn7713jCMS8YuJz4+nmeeeYaEhASaN29+Tft88sknycvLq1gyMjLs+AQitceZwhLGzk8i7UwRrRo1YNnUSJr7eJgdS0REHNDMgR2Y2j8UgFkf7+ajHcdNTiRSs+x6KtvPzw9nZ+dLrthkZ2dfcmXnpxISEpg8eTIffPABd9xxR6WvtWjRwu59uru74+6u35xL3ZZbVMq4BVs4lF1ICx8P4qdG0qpRA7NjiYiIg7JYLPzpl50pKbexeNMxfvfBTtxcnLize0uzo4nUCLuuDLm5uREWFkZiYmKl8cTERKKjo6+4XXx8PBMnTmT58uUMGzbskq9HRUVdss+vvvrqqvsUqevyi8uYsHAL+zLz8WvozrKpEbRu6ml2LBERcXAWi4Vn7rqJmPAgbAZMfz+Fr36o2uMQInWN3fP1zpw5k9jYWMLDw4mKimLu3Lmkp6czbdo04OLtaydOnGDx4sXAxSI0fvx43njjDSIjIyuuADVo0ABfX18AHn/8cW655RZefPFFhg8fzieffMLXX3/N+vXrr9fnFKlVzpeU88Cirew8nkdjT1eWTYmgbbOGZscSEREBwMnJwt9HdqO43MonKSd5ZHky8yaEM6BDM7OjiVxXdj8zFBMTw+uvv85zzz1Hz549Wbt2LatXryY4OBiAzMzMSu8cevfddykvL+fhhx8mICCgYnn88ccr1omOjub9999n0aJFdO/enbi4OBISEoiIiLgOH1GkdikuszLlvW1sO3YObw8XlkyOoGMLb7NjiYiIVOLsZOGV+3owtGsLSq02Hly8jY1HcsyOJXJd2f2eodpK7xmSuqCk3MqDi7fz/cHTeLk5s3RKBL1aNzY7loiIyBWVltv49dLt/Gd/Np5uzix+oC/hIU1+fkMRE9XIe4ZEpPrKrDYeWZ7M9wdP08DVmUWT+qoIiYhIrefm4sRbY3vTv70fRaVWJi3ayq7juWbHErkuVIZEbgCrzWBGQgqJe0/h5uLE/Anh9A3Vb9VERKRu8HB1Zm7sxe9dBSXlxC7Ywt6TeuG91H0qQyI1zGYz+P2HO/n3rkxcnS28Oy6Mfu38zI4lIiJilwZuziyc2IderRuRd6GM2AVJHDpVYHYskWuiMiRSgwzD4KlP9vDRjhM4O1l4c3Rvbu3U/Oc3FBERqYUaursQN6kvXVv5cOZ86cWXhuecNzuWSLWpDInUEMMweO7fe1melI7FAq+O6sGQri3MjiUiInJNfBu4suSBCDr6e5NdUMKYeZvJOFtkdiyRalEZEqkBhmHw0pcHWLQhDYCX7unO8J6tzA0lIiJynTT2cmPplAjaNPPiZF4xY+cnkZVXbHYsEbupDInUgH/+5zBvf3cEgL+O6Mp94UEmJxIREbm+mnm7s3xKJK2beJJ+togx8zdzuqDE7FgidlEZErnO3v3+CK99fRCAp4Z1JjYy2OREIiIiNaOFrwfLp0bQ0teDo6fPM25+EmfPl5odS6TKVIZErqO4DanMXrMfgN8P7siU/m1MTiQiIlKzAht7snxqJM293TlwqoDYBUnkXSgzO5ZIlagMiVwn8VvSeeazvQA8els7Hr61ncmJREREbowQPy+WT42gqZcbP5zMZ+KiLRSWlJsdS+RnqQyJXAerko/zp1W7AZjaP5SZAzuYnEhEROTGatfcmyWTI/Bt4Epyei4PxG3lQqnV7FgiV6UyJHKNPt+VyW9X7MQwYHxUMH/6ZWcsFovZsURERG64Li19WDK5L97uLmxJPcvUxdsoLlMhktpLZUjkGiTuPcXj7ydjMyAmPIhn7rpJRUhERBxa98BGxD3QB083Z9YfzuE3y3ZQWm4zO5bIZakMiVTT9wdP8/CyHZTbDIb3bMnfR3bDyUlFSEREJCy4CQsm9MHdxYlv9mfz+PvJlFtViKT2URkSqYZNR87w4OJtlFptDO3aglfu64GzipCIiEiFqLZNmTs+HDdnJ9bsyeK3H+zEajPMjiVSicqQiJ22HzvH5Pe2UlJu4/ZOzXnj/l64OOt/JRERkZ8a0KEZb43tjYuThU9STvKnj3ZjUyGSWkQ/wYnYYffxPCYu3EJRqZX+7f14a2xv3Fz0v5GIiMiVDOzizxv398LJAgnbMnjmsx8wDBUiqR30U5xIFe3LzCd2YRIFJeX0DW3C3NhwPFydzY4lIiJS6w3rHsDL9/XAYoHFm44xe81+FSKpFVSGRKrgcHYh4+YnkVtURq/WjVg4sQ8N3FSEREREqmpk70D+fnc3AOauPcpriQdNTiSiMiTys46dOc/Y+Zs5c76Urq18iJvUl4buLmbHEhERqXNG923NM3d1AeCf3xzmrW8Pm5xIHJ3KkMhVHD9XxJh5SZzKL6GjvzdLHrj4Zm0RERGpnon9QnliaCcA/vHlARasTzU5kTgylSGRK8jKK2bs/CRO5F6gTTMvlk6JoLGXm9mxRERE6rxpA9oy/Y72APz133tZuvmYyYnEUakMiVxGTmEJY+dv5tiZIlo38WT5lEiaebubHUtERKTeePz29kwb0BaApz7ewwfbMkxOJI5IZUjkJ86dL2Xc/CSOnD5PS18Plk+NoIWvh9mxRERE6hWLxcIfh3RkYnQIAH9cuYtPd540N5Q4HJUhkf+Rd6GM8Qu3sD+rgObe7iyfGklgY0+zY4mIiNRLFouFp+/qwui+rbEZMCMhhS/2ZJkdSxyIypDIjwpLypm0aAu7T+TR1MuN5VMjCPHzMjuWiIhIvWaxWHh+RFdG9m6F1WbwaPwOvt2fbXYscRAqQyLAhVIrk+O2siM9F98GriyZHEG75t5mxxIREXEITk4WXrqnO8O6B1BmNXho6XY2HM4xO5Y4AJUhcXjFZVYeXLKNpNSzeLu7sGRyX7q09DE7loiIiENxcXbi9ZieDOziT2m5jSnvbWNL6lmzY0k9pzIkDq203MYjy3ew7lAOnm7OxD3Qh+6BjcyOJSIi4pBcnZ3415heDOjQjAtlVh6I20pKRq7ZsaQeUxkSh1VutTE9IZmv92Xj7uLEggl9CAtuYnYsERERh+bu4sy7sWFEtWlKYUk54xcksedEntmxpJ6qVhmaM2cOoaGheHh4EBYWxrp16664bmZmJmPGjKFjx444OTkxffr0S9aJi4vDYrFcshQXF1cnnsjPstoMfv/hLlbvzsLN2Ym548OJatvU7FgiIiICeLg6M39COOHBjckvLid2QRIHTxWYHUvqIbvLUEJCAtOnT2fWrFkkJyfTv39/hg4dSnp6+mXXLykpoVmzZsyaNYsePXpccb8+Pj5kZmZWWjw89G4Xuf5sNoNZq3azKvkELk4W3hrbmwEdmpkdS0RERP6Hl7sLCyf1oXugL+eKyhgzL4mjpwvNjiX1jN1l6NVXX2Xy5MlMmTKFzp078/rrrxMUFMTbb7992fVDQkJ44403GD9+PL6+vlfcr8VioUWLFpWWqykpKSE/P7/SIvJzDMPg2c9+4P2tGThZ4I37ezGwi7/ZsUREROQyfDxcWfxAXzoH+JBTWMLY+UlknC0yO5bUI3aVodLSUrZv386gQYMqjQ8aNIiNGzdeU5DCwkKCg4MJDAzkzjvvJDk5+arrz549G19f34olKCjomv5+qf8Mw+CFNft5b9MxLBZ4+b4eDOseYHYsERERuYpGnm4sndyXds0bkplXzOh5mzmZe8HsWFJP2FWGcnJysFqt+PtX/k26v78/WVnVf1twp06diIuL49NPPyU+Ph4PDw/69evHoUOHrrjNk08+SV5eXsWSkZFR7b9fHMNrXx/i3bVHAfj73d0Y2TvQ5EQiIiJSFU0burN8SgQhTT05fu4CY+cnkZ2vZ8vl2lVrAgWLxVLpz4ZhXDJmj8jISMaNG0ePHj3o378/K1asoEOHDrz55ptX3Mbd3R0fH59Ki8iVzPnuMP/8z8Vy/cxdXRjdt7XJiURERMQezX08WDY1klaNGpCac56x85M4U1hidiyp4+wqQ35+fjg7O19yFSg7O/uSq0XXFMrJiT59+lz1ypBIVS1Yn8pLXxwA4ImhnZjYL9TkRCIiIlIdrRo1IH5qJC18PDiUXUjsgi3kFZWZHUvqMLvKkJubG2FhYSQmJlYaT0xMJDo6+rqFMgyDlJQUAgL0PIdcm2VJx/jrv/cCMP2O9kwb0NbkRCIiInItWjf1ZNnUCPwaurM3M5/xi7ZQUKxCJNVj921yM2fOZP78+SxcuJB9+/YxY8YM0tPTmTZtGnDxWZ7x48dX2iYlJYWUlBQKCws5ffo0KSkp7N27t+Lrzz77LF9++SVHjx4lJSWFyZMnk5KSUrFPker4cPtxZq3aA8C0AW15/Pb2JicSERGR66Fts4YsmxJBY09Xdmbk8kDcVopKy82OJXWQi70bxMTEcObMGZ577jkyMzPp2rUrq1evJjg4GLj4ktWfvnOoV69eFf+9fft2li9fTnBwMGlpaQDk5uby4IMPkpWVha+vL7169WLt2rX07dv3Gj6aOLLPdp7kDx/uBGBidAh/HNLxmp5rExERkdqlYwtvlkyOYPS8zWxNO8eU97axcGIfPFydzY4mdYjFMAzD7BDXQ35+Pr6+vuTl5WkyBQf35Q9Z/GbZDqw2g9F9W/P3u7uqCImIiNRTO9LPETs/ifOlVn7RsRnvxobh7qJC5Oiq2g2qNZucSG317YFsHll+sQiN7N2K50eoCImIiNRnvVs3/vGKkBPfHTjNo8uTKbPazI4ldYTKkNQbGw/nMG3JdsqsBsO6B/DSPd1xclIREhERqe8i2jRl/vg+uLk48dXeU8xcsROrrV7c/CQ1TGVI6oWtaWeZ/N42SsptDOziz+sxPXFx1uktIiLiKG5u78c743rj6mz58dnhXdhUiORn6KdFqfNSMnKZtGgrF8qsDOjQjH+N6YWripCIiIjDua2TP2+O7oWzk4WVO47z50/2UE8ej5caop8YpU774WQe4xckUVhSTlSbpnpoUkRExMEN6RrAq6N6YLHAsqR0/vrvfSpEckUqQ1JnHTxVQOyCLeQXlxMe3Jj5E8I1naaIiIgwvGcrXrynOwALN6Tyjy8PqBDJZakMSZ2UmnOesfOTOHu+lO6Bviyc1Acvd7tfmyUiIiL11KjwIP46/CYA5nx3hDe/OWxyIqmNVIakzsk4W8SYeZs5XVBC5wAfFj/QFx8PV7NjiYiISC0TGxXCU8M6A/Bq4kHmrj1iciKpbVSGpE7ZdOQMo97dRGZeMe2aN2Tp5L408nQzO5aIiIjUUlP6t+F3gzoA8PfV+/nrv/dSXGY1OZXUFipDUicUl1l5/vO9jJm/mcy8Yto082L5lAiaNnQ3O5qIiIjUco/c1p7Hbm8PwIL1qfzqX+vZezLf5FRSG6gMSa23LzOfEW9tYN66VAwDRvcN4rNHbqa5j4fZ0URERKSOmDmwAwsmhOPX0I2DpwoZ/tZ63vn+iF7O6uAsRj2ZWiM/Px9fX1/y8vLw8fExO45cB1abwfx1R3nlq4OUWm34NXTjhZHduaOLv9nRREREpI46U1jCEx/tJnHvKQD6hjThlVE9CGriaXIyuZ6q2g1UhqRWyjhbxG8/2MmW1LMA3NHZnxfu6YafbosTERGRa2QYBh9sO86zn/3A+VIrDd1dePquLtwbFojFYjE7nlwHKkNSJxmGwcodJ3jm0x8oLCnHy82Zp++6ifvC9Y+TiIiIXF/pZ4qYuSKFbcfOATD4Jn9mj+xOEy9NzlTXqQxJnXP2fCmzVu1mzZ4sAMKDG/PqqJ60bqrL1iIiIlIzrDaDd9ce4bXEg5RZDfwauvOPe7tza6fmZkeTa6AyJHXKtwey+cOHuzhdUIKLk4UZAzswbUBbnJ10NUhERERq3p4TecxISOFQdiEAYyNaM2tYZzzd9FL3ukhlSOqEotJy/r56H0s3pwPQrnlDXo/pSddWviYnExEREUdTXGblpS8OsHBDKgChfl68OqoHvVo3NjmZ2EtlSGq9lIxcZiSkkJpzHoBJ/UL445BOeLg6m5xMREREHNmGwzn87oOdZOYV4+xk4ZFb2/HIbe1wddZbaeoKlSGptcqsNt769jBvfnMYq82ghY8HL9/Xg5vb+5kdTURERASAvKIy/vLpHj5JOQlAj0BfXo3pSdtmDU1OJlWhMiS10tHThcxYsZOdGbkA3NWjJX8b3hVfT1dzg4mIiIhcxqc7T/LUqt3kF5fj4erErF92ZlxksGa5reVUhqRWMQyDpUnpPP/5XorLbPh4uPDXEV0Z3rOV2dFERERErioz7wK/+2AnGw6fAWBAh2b8497uNPfxMDmZXInKkNQa2fnF/GHlLr47cBqAfu2a8o97e9CyUQOTk4mIiIhUjc1m8N6mNF5Ys5+SchuNPF2ZfXc3hnYLMDuaXIbKkNQKX+zJ5MmPdnOuqAw3FyeeGNKJidEhOGnKbBEREamDDp0qYHpCCj+czAdgZO9WPPOrm/Dx0C3/tYnKkJgqv7iMZz/dy8odxwHoEuDDG/f3pL2/t8nJRERERK5NabmNN/5zkLe/O4LNgFaNGvDKqB5EtmlqdjT5kcqQmCbp6BlmrtjJidwLOFlg2oC2TL+jA24umo5SRERE6o9taWeZuWIn6WeLsFjgwf5tmDmoA+4uek2I2VSG5IYrKbfy6lcHmbvuKIYBQU0a8OqonvQJaWJ2NBEREZEaUVhSzt/+vZf3t2YA0KmFN6/f35NOLfTzqJlUhuSG2p+Vz/T3U9ifVQBATHgQf76rCw3dXUxOJiIiIlLzEvee4omVuzhzvhQ3Zyd+P7gjk28O1XPSJlEZkhvCZjNYsD6Vf3x5gFKrjSZebswe2Y3BN7UwO5qIiIjIDXW6oIQnVu7iP/uzAYhs04SX7+tBYGNPk5M5HpUhqXEnci/w2xUpbD56FoDbOzXnhXu608zb3eRkIiIiIuYwDIOErRk89++9FJVa8XZ34dnhN3F3r1Z6UesNVNVuUK0n2ufMmUNoaCgeHh6EhYWxbt26K66bmZnJmDFj6NixI05OTkyfPv2y661cuZIuXbrg7u5Oly5dWLVqVXWiyQ1gGAarko8z5LW1bD56Fk83Z2aP7Mb8CeEqQiIiIuLQLBYL9/dtzerH+tO7dSMKSsqZuWInDy/fwbnzpWbHk5+wuwwlJCQwffp0Zs2aRXJyMv3792fo0KGkp6dfdv2SkhKaNWvGrFmz6NGjx2XX2bRpEzExMcTGxrJz505iY2MZNWoUSUlJ9saTGpZbVMojy5OZkbCTgpJyerVuxOrH+jO6b2v9tkNERETkRyF+Xqx4KIrfDeqAi5OF1buzGPz6Wr4/eNrsaPI/7L5NLiIigt69e/P2229XjHXu3JkRI0Ywe/bsq277i1/8gp49e/L6669XGo+JiSE/P581a9ZUjA0ZMoTGjRsTHx9fpVy6Ta7mfX/wNL//YCfZBSW4OFmYfkd7pg1oi4uzpswWERERuZLdx/OYnpDMkdPnARgfFcyTQzvTwE1TcNeUGrlNrrS0lO3btzNo0KBK44MGDWLjxo3VS8rFK0M/3efgwYOvus+SkhLy8/MrLVIzLpRaefqTPUxYuIXsghLaNPPio99E88ht7VWERERERH5Gt0BfPn+sPxOjQwBYvOkYw/65jp0ZuabmEjvLUE5ODlarFX9//0rj/v7+ZGVlVTtEVlaW3fucPXs2vr6+FUtQUFC1/365sl3Hcxn25jre23QMgInRIXz+aH+6BzYyN5iIiIhIHeLh6swzv7qJxQ/0xd/HnaM55xn59kbe+PoQ5Vab2fEcVrV+rf/TZ0MMw7jm50Xs3eeTTz5JXl5exZKRkXFNf79UVm618eZ/DjFyzkaOnj6Pv487ix/oyzO/ukmXdEVERESq6ZYOzfhy+i0M6x6A1Wbw2tcHufedTaTmnDc7mkOy642Yfn5+ODs7X3LFJjs7+5IrO/Zo0aKF3ft0d3fH3V0zl9WEtJzzzFiRQnJ6LgDDugXw/N1daeTpZm4wERERkXqgkacb/xrdi0Fd/Hnq4z2kZOTyyzfW8dSdnRmjSaluKLuuDLm5uREWFkZiYmKl8cTERKKjo6sdIioq6pJ9fvXVV9e0T7GfYRgsT0pn6BvrSE7PxdvDhddjevKvMb1UhERERESuI4vFwvCerfhy+i1EtWnKhTIrs1bt4YG4rWQXFJsdz2HYdWUIYObMmcTGxhIeHk5UVBRz584lPT2dadOmARdvXztx4gSLFy+u2CYlJQWAwsJCTp8+TUpKCm5ubnTp0gWAxx9/nFtuuYUXX3yR4cOH88knn/D111+zfv366/ARpSp++sbkqDZNeXlUD1o1amByMhEREZH6q2WjBiybEsHCDam89OUBvj1wmiGvr2P2yG4MvqmF2fHqPbun1oaLL1196aWXyMzMpGvXrrz22mvccsstAEycOJG0tDS+++67//9LLnOpLzg4mLS0tIo/f/jhhzz11FMcPXqUtm3b8vzzzzNy5MgqZ9LU2tX35Q9ZPPnRbs6eL8XN2Yk/DOnIA/1CcXLSJVoRERGRG+VAVgHTE1LYl3lxluT7wgL5y11d8PZwNTlZ3VPVblCtMlQbqQzZr7CknOc++4EV244D0DnAh9djetKxhbfJyUREREQcU0m5lde/PsQ73x/BMCCwcQNeHdWTvqFNzI5Wp6gMyVVtTTvLzBUpZJy9gMUCD97ShpkDO+DuopniRERERMy2JfXiz2rHz138WW3agLbMuKMDbi56x2NVqAzJZZWW23jt64MVv21o1agBr47qQUSbpmZHExEREZH/UVBcxnOf7eWD7f9/F88b9/ekg7/u4vk5KkNyiYOnCpj+fgp7f7wP9d6wQJ7WfagiIiIitdoXe7L406ofn+92ceIPg/V8989RGZIKNpvBoo1pvPjFfkrLbTT2dGX2yG4M6RpgdjQRERERqYLsgmKeWLmbb36c+Te6bVNevq8HLTXz72WpDAkAJ3Mv8LsPdrLxyBkAftGxGS/d253m3h4mJxMRERERexiGwfIt6fzt3/u4UGbF28OFv43oyq96tNSLWn9CZUj4JOUEf/54D/nF5TRwdWbWsM6MjdBbjUVERETqstSc88xISCElIxeAO7sH8LcRXWnk6WZusFpEZciB5RWV8dQne/hs50kAegQ14rVRPWjTrKHJyURERETkeii32pjz3RHe+M8hrDaDFj4e/OO+7vRv38zsaLWCypCDWn8oh999sJOs/GKcnSw8dlt7Hr61LS7OmoZRREREpL7ZmZHLjIQUjuacB2BidAhPDO2Eh6tjvy5FZcjBFJdZeWHNfuI2pgEQ6ufFazE96RnUyNRcIiIiIlKzLpRamb1mH4s3HQOgbTMvXo/pRbdAX5OTmUdlyIHsOZHH9IQUDmcXAhAbGcyTv+yEp5uLyclERERE5Eb57kA2v/9wF6cLSnBxsjD9jvZMG+CYdwipDDkAq83gne+P8FriQcptBs283Xnp3u7c2rG52dFERERExATnzpfyp1W7WbMnC4Cw4Ma8OqoHwU29TE52Y6kM1XPpZ4qYsSKF7cfOATC0awuev7sbTbw0i4iIiIiIIzMMg1XJJ3j6kx8oKCnH082Zv9zZhZg+QQ4zq7DKUD1lGAYrtmXw3Gd7OV9qxdvdhWeH38TdvVo5zMktIiIiIj/v+LkifrtiJ0mpZwG4o3NzZo/sTjNvd5OT1TyVoXoop7CEJ1bu5ut9pwDoG9qEV0f1ILCxp8nJRERERKQ2stkM5q8/ystfHqTUaqOplxsv3NOdgV38zY5Wo1SG6pmv957iiY92kVNYipuzE78b3IHJN7fB2UlXg0RERETk6vZl5jMjIYX9WQUA3N8niKfu7EJD9/o54ZbKUD1xvqScv32+l/gtGQB0auHNazE96RxQfz6jiIiIiNS8knIrr351kLnrjmIY0LqJJ6/F9CAsuInZ0a47laF6YPuxs8xI2En62SIsFpjavw0zB3Zw+JdoiYiIiEj1bT56ht+u2MmJ3As4WeDXv2jL47d3wM2l/kzBrTJUh5VZbbzx9SHmfHcYmwGtGjXg5ft6ENW2qdnRRERERKQeyC8u45lPf+CjHScA6NrKh9djetKuubfJya4PlaE66nB2ATMSdrL7RB4AI3u14pnhN+Hj4WpyMhERERGpb1bvzuRPq3aTW1SGu4sTTwztxISoEJzq+HPpKkN1jM1msHhTGrPX7Kek3EYjT1eeH9GNYd0DzI4mIiIiIvVYdn4xv/9wF98fPA3Aze38+Md93QnwbWBysupTGapDsvKK+f2HO1l3KAeAWzo04x/3dsffx8PkZCIiIiLiCAzDYGlSOs9/vpfiMhs+Hi48f3c37urR0uxo1aIyVEd8tvMkT328h7wLZXi4OvGnX3YmNjJYL1AVERERkRvuyOlCZiaksPP4xUc2hvdsyXO/6oqvZ916ZENlqJbLu1DG05/s4eOUkwB0D/Tl1VE9ade8ocnJRERERMSRlVlt/Oubw/zr28NYbQYBvh68fF8P+rXzMztalakM1WIbD+fw2w92kplXjLOThYdvbcejt7XD1bn+TGcoIiIiInVbcvo5Zq7YSWrOeQAm3xzK7wd3rBOveVEZqoWKy6z848sDLFifCkBIU09ejelJ79aNTU4mIiIiInKpotJynv98H8uS0gFo37whr8X0pGsrX5OTXZ3KUC3zw8k8ZiSkcPBUIQBjIlrz1LDOeLq5mJxMREREROTqvt2fze8/3EVOYQmuzhZmDOzAQ7e0xbmWTsGtMlRLWG0Gc9ce5dXEA5RZDfwauvPSvd24rZO/2dFERERERKrsTGEJf1q1my9/OAVAn5DGvDqqJ0FNPE1OdimVoVog42wRM1eksDXtHACDuvgze2Q3mjZ0NzmZiIiIiIj9DMPgw+3HefazvRSWlOPl5szTv7qJ+8ICa9VsyCpDJjIMgw+2H+fZT3/gfKmVhu4uPH1XF+6tZSeJiIiIiEh1ZJwt4rcrdrIl7SxQ+37przJkkrp0+VBEREREpLqsNoN5647yylf/fRzEjZfu7V4rHgepajeo1lzOc+bMITQ0FA8PD8LCwli3bt1V1//+++8JCwvDw8ODNm3a8M4771T6elxcHBaL5ZKluLi4OvFMlZlXzDf7s3F1tvDHIZ14/8EoFSERERERqXecnSxMG9CWTx6+mQ7+DckpLOXLPafMjmUXu6cyS0hIYPr06cyZM4d+/frx7rvvMnToUPbu3Uvr1q0vWT81NZVf/vKXTJ06laVLl7JhwwZ+85vf0KxZM+65556K9Xx8fDhw4EClbT08PKrxkczVtZUvf7+7G11a+nBTy9o95aCIiIiIyLXq0tKHTx+5mblrj/LAzaFmx7GL3bfJRURE0Lt3b95+++2Ksc6dOzNixAhmz559yfp//OMf+fTTT9m3b1/F2LRp09i5cyebNm0CLl4Zmj59Orm5udX8GLXnNjkRERERETFXjdwmV1payvbt2xk0aFCl8UGDBrFx48bLbrNp06ZL1h88eDDbtm2jrKysYqywsJDg4GACAwO58847SU5OvmqWkpIS8vPzKy0iIiIiIiJVZVcZysnJwWq14u9f+aEof39/srKyLrtNVlbWZdcvLy8nJycHgE6dOhEXF8enn35KfHw8Hh4e9OvXj0OHDl0xy+zZs/H19a1YgoKC7PkoIiIiIiLi4Ko1gcJPp4c2DOOqU0Zfbv3/HY+MjGTcuHH06NGD/v37s2LFCjp06MCbb755xX0++eST5OXlVSwZGRnV+SgiIiIiIuKg7JpAwc/PD2dn50uuAmVnZ19y9ee/WrRocdn1XVxcaNq06WW3cXJyok+fPle9MuTu7o67e+2Yx1xEREREROoeu64Mubm5ERYWRmJiYqXxxMREoqOjL7tNVFTUJet/9dVXhIeH4+rqetltDMMgJSWFgIAAe+KJiIiIiIhUmd23yc2cOZP58+ezcOFC9u3bx4wZM0hPT2fatGnAxdvXxo8fX7H+tGnTOHbsGDNnzmTfvn0sXLiQBQsW8Lvf/a5inWeffZYvv/ySo0ePkpKSwuTJk0lJSanYp4iIiIiIyPVm93uGYmJiOHPmDM899xyZmZl07dqV1atXExwcDEBmZibp6ekV64eGhrJ69WpmzJjBW2+9RcuWLfnnP/9Z6R1Dubm5PPjgg2RlZeHr60uvXr1Yu3Ytffv2vQ4fUURERERE5FJ2v2eottJ7hkREREREBGroPUMiIiIiIiL1hcqQiIiIiIg4JLufGaqt/nu3X35+vslJRERERETETP/tBD/3RFC9KUMFBQUABAUFmZxERERERERqg4KCAnx9fa/49XozgYLNZuPkyZN4e3tjsVhMzZKfn09QUBAZGRmazKEG6PjWLB3fmqXjW7N0fGuWjm/N0vGtWTq+Nau2HV/DMCgoKKBly5Y4OV35yaB6c2XIycmJwMBAs2NU4uPjUytOhvpKx7dm6fjWLB3fmqXjW7N0fGuWjm/N0vGtWbXp+F7titB/aQIFERERERFxSCpDIiIiIiLikFSGaoC7uztPP/007u7uZkepl3R8a5aOb83S8a1ZOr41S8e3Zun41iwd35pVV49vvZlAQURERERExB66MiQiIiIiIg5JZUhERERERBySypCIiIiIiDgklSEREREREXFIKkMiIiIiIuKQVIaug7S0NCZPnkxoaCgNGjSgbdu2PP3005SWll51O8MweOaZZ2jZsiUNGjTgF7/4BT/88MMNSl23PP/880RHR+Pp6UmjRo2qtM3EiROxWCyVlsjIyJoNWkdV5/jq/K26c+fOERsbi6+vL76+vsTGxpKbm3vVbXT+XtmcOXMIDQ3Fw8ODsLAw1q1bd9X1v//+e8LCwvDw8KBNmza88847Nyhp3WTP8f3uu+8uOU8tFgv79++/gYnrjrVr13LXXXfRsmVLLBYLH3/88c9uo/O36uw9vjp/q2727Nn06dMHb29vmjdvzogRIzhw4MDPblcXzl+Voetg//792Gw23n33XX744Qdee+013nnnHf70pz9ddbuXXnqJV199lX/9619s3bqVFi1aMHDgQAoKCm5Q8rqjtLSU++67j1//+td2bTdkyBAyMzMrltWrV9dQwrqtOsdX52/VjRkzhpSUFL744gu++OILUlJSiI2N/dntdP5eKiEhgenTpzNr1iySk5Pp378/Q4cOJT09/bLrp6am8stf/pL+/fuTnJzMn/70Jx577DFWrlx5g5PXDfYe3/86cOBApXO1ffv2Nyhx3XL+/Hl69OjBv/71ryqtr/PXPvYe3//S+fvzvv/+ex5++GE2b95MYmIi5eXlDBo0iPPnz19xmzpz/hpSI1566SUjNDT0il+32WxGixYtjBdeeKFirLi42PD19TXeeeedGxGxTlq0aJHh6+tbpXUnTJhgDB8+vEbz1DdVPb46f6tu7969BmBs3ry5YmzTpk0GYOzfv/+K2+n8vby+ffsa06ZNqzTWqVMn44knnrjs+n/4wx+MTp06VRp76KGHjMjIyBrLWJfZe3y//fZbAzDOnTt3A9LVL4CxatWqq66j87f6qnJ8df5WX3Z2tgEY33///RXXqSvnr64M1ZC8vDyaNGlyxa+npqaSlZXFoEGDKsbc3d0ZMGAAGzduvBERHcJ3331H8+bN6dChA1OnTiU7O9vsSPWCzt+q27RpE76+vkRERFSMRUZG4uvr+7PHSudvZaWlpWzfvr3SeQcwaNCgKx7LTZs2XbL+4MGD2bZtG2VlZTWWtS6qzvH9r169ehEQEMDtt9/Ot99+W5MxHYrO3xtD56/98vLyAK76s25dOX9VhmrAkSNHePPNN5k2bdoV18nKygLA39+/0ri/v3/F1+TaDB06lGXLlvHNN9/wyiuvsHXrVm677TZKSkrMjlbn6fytuqysLJo3b37JePPmza96rHT+XionJwer1WrXeZeVlXXZ9cvLy8nJyamxrHVRdY5vQEAAc+fOZeXKlXz00Ud07NiR22+/nbVr196IyPWezt+apfO3egzDYObMmdx888107dr1iuvVlfNXZegqnnnmmcs+WPe/y7Zt2yptc/LkSYYMGcJ9993HlClTfvbvsFgslf5sGMYlY/VVdY6vPWJiYhg2bBhdu3blrrvuYs2aNRw8eJDPP//8On6K2qumjy/o/K3q8b3cMfm5Y+Xo5+/V2HveXW79y43LRfYc344dOzJ16lR69+5NVFQUc+bMYdiwYbz88ss3IqpD0Plbc3T+Vs8jjzzCrl27iI+P/9l168L562J2gNrskUce4f7777/qOiEhIRX/ffLkSW699VaioqKYO3fuVbdr0aIFcLE1BwQEVIxnZ2df0qLrK3uP77UKCAggODiYQ4cOXbd91mY1eXx1/lb9+O7atYtTp05d8rXTp0/bdawc7fy9HD8/P5ydnS+5SnG1865FixaXXd/FxYWmTZvWWNa6qDrH93IiIyNZunTp9Y7nkHT+3ng6f6/u0Ucf5dNPP2Xt2rUEBgZedd26cv6qDF2Fn58ffn5+VVr3xIkT3HrrrYSFhbFo0SKcnK5+0S00NJQWLVqQmJhIr169gIv3a3///fe8+OKL15y9LrDn+F4PZ86cISMjo9IP7/VZTR5fnb9VP75RUVHk5eWxZcsW+vbtC0BSUhJ5eXlER0dX+e9ztPP3ctzc3AgLCyMxMZG77767YjwxMZHhw4dfdpuoqCg+++yzSmNfffUV4eHhuLq61mjeuqY6x/dykpOTHfo8vZ50/t54On8vzzAMHn30UVatWsV3331HaGjoz25TZ85fs2ZuqE9OnDhhtGvXzrjtttuM48ePG5mZmRXL/+rYsaPx0UcfVfz5hRdeMHx9fY2PPvrI2L17tzF69GgjICDAyM/Pv9EfodY7duyYkZycbDz77LNGw4YNjeTkZCM5OdkoKCioWOd/j29BQYHx29/+1ti4caORmppqfPvtt0ZUVJTRqlUrHd/LsPf4GobOX3sMGTLE6N69u7Fp0yZj06ZNRrdu3Yw777yz0jo6f6vm/fffN1xdXY0FCxYYe/fuNaZPn254eXkZaWlphmEYxhNPPGHExsZWrH/06FHD09PTmDFjhrF3715jwYIFhqurq/Hhhx+a9RFqNXuP72uvvWasWrXKOHjwoLFnzx7jiSeeMABj5cqVZn2EWq2goKDi31fAePXVV43k5GTj2LFjhmHo/L1W9h5fnb9V9+tf/9rw9fU1vvvuu0o/5xYVFVWsU1fPX5Wh62DRokUGcNnlfwHGokWLKv5ss9mMp59+2mjRooXh7u5u3HLLLcbu3btvcPq6YcKECZc9vt9++23FOv97fIuKioxBgwYZzZo1M1xdXY3WrVsbEyZMMNLT0835ALWcvcfXMHT+2uPMmTPG2LFjDW9vb8Pb29sYO3bsJVO56vyturfeessIDg423NzcjN69e1ea2nXChAnGgAEDKq3/3XffGb169TLc3NyMkJAQ4+23377BiesWe47viy++aLRt29bw8PAwGjdubNx8883G559/bkLquuG/Uzn/dJkwYYJhGDp/r5W9x1fnb9Vd6efc//25oK6evxbD+PFJJhEREREREQei2eRERERERMQhqQyJiIiIiIhDUhkSERERERGHpDIkIiIiIiIOSWVIREREREQcksqQiIiIiIg4JJUhERERERFxSCpDIiIiIiLikFSGRERERETEIakMiYiIiIiIQ1IZEhERERERh/R/nKp0hJJ8LrAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 4))\n",
    "\n",
    "norm_0_1 = scipy.stats.norm(0, 1)\n",
    "x_axis = np.arange(-2, 2.5, 0.5)\n",
    "y_axis = norm_0_1.pdf(x_axis)\n",
    "\n",
    "_ = plt.plot(x_axis, y_axis)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-2. , -1.5, -1. , -0.5,  0. ,  0.5,  1. ,  1.5,  2. ])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_axis = np.arange(-2, 2.5, 0.5)\n",
    "x_axis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.05399097, 0.1295176 , 0.24197072, 0.35206533, 0.39894228,\n",
       "       0.35206533, 0.24197072, 0.1295176 , 0.05399097])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_axis = norm_0_1.pdf(x_axis)\n",
    "y_axis\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 4))\n",
    "\n",
    "norm_0_1 = scipy.stats.norm(0, 1)\n",
    "x_axis = np.arange(-4,  , 0.05)\n",
    "y_axis = norm_0_1.pdf(x_axis)\n",
    "\n",
    "_ = plt.plot(x_axis, y_axis)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Illustrating Density\n",
    "\n",
    "* To illustrate the idea that dense regions contribute more random samples, we sample 1,000 values from a normal distribution $\\mathcal{N}(\\mu=0, \\sigma=2)$\n",
    "\n",
    "* We will plot the values as a histogram\n",
    "  * We bin the values into 20 bins and plot them as a histogram\n",
    "  * Counts for each bin are shown on the $y$-axis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4.6118764 ,  0.2139341 ,  1.9731058 , -0.63778838,  1.45090739,\n",
       "        3.34333852, -0.68827856, -0.69840683,  0.54869204,  0.86717192])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Ex. sampling 10 values from Gaussian with mean 0 and standard deviation 2\n",
    "\n",
    "# np.random.seed(211)\n",
    "\n",
    "gaussianSamples = np.random.normal(0, 2, 10)\n",
    "gaussianSamples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.normal(0, 2, 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.39836355,  2.04043556, -0.1931295 ,  3.61519792, -0.99823001,\n",
       "        1.86644274,  1.45753349, -1.35890528,  1.03753143, -2.56553234])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(211)\n",
    "gaussian_samples = np.random.normal(0, 2, 1000)\n",
    "gaussian_samples[0:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1000"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(gaussian_samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the counts rathe than the density\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "_ = plt.hist(gaussian_samples, bins=20, edgecolor=\"k\", linewidth=2, alpha=0.4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Comparing the Density Curve and the Histogram\n",
    "\n",
    "- We plot the pdf over the histogram to see if it matches the sequence data\n",
    "- Should the histogram match the density curve exactly?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 4))\n",
    "\n",
    "normal_0_2 = scipy.stats.norm(0, 2)\n",
    "x_axis = np.linspace(-8, 8, 100)\n",
    "y_axis = normal_0_2.pdf(x_axis)\n",
    "\n",
    "plt.plot(x_axis, y_axis, color=\"k\")\n",
    "\n",
    "# Note that the param density=True is necessary here\n",
    "_ = plt.hist(gaussianSamples, bins=20, edgecolor=\"k\", color='#80d4ff', linewidth=2, alpha=0.2, density=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.19947114020071635"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "\n",
    "# we don't need to create the `frozen` distribution beforehand\n",
    "norm.pdf(0, loc=0, scale=2)    # equivalent to norm.pdf(0, 0, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For mu=0 and sigma=2:\n",
      "\tThe probability density of x =   -2 is  0.1209854\n",
      "\tThe probability density of x =   -1 is  0.1760327\n",
      "\tThe probability density of x = -0.5 is  0.1933341\n",
      "\tThe probability density of x = -0.2 is  0.1984763\n",
      "\tThe probability density of x =    0 is  0.1994711\n",
      "\tThe probability density of x =    1 is  0.1760327\n",
      "\tThe probability density of x =    0 is  0.1994711\n",
      "\tThe probability density of x =  0.1 is  0.1992220\n",
      "\tThe probability density of x =  0.2 is  0.1984763\n",
      "\tThe probability density of x =  0.5 is  0.1933341\n",
      "\tThe probability density of x =    1 is  0.1760327\n",
      "\tThe probability density of x =    2 is  0.1209854\n"
     ]
    }
   ],
   "source": [
    "some_vals = [-2, -1, -0.5, -0.2, -0,1, 0, 0.1, 0.2, 0.5, 1, 2]\n",
    "\n",
    "mu = 0\n",
    "sigma = 2\n",
    "\n",
    "print(f\"For mu={mu} and sigma={sigma}:\")\n",
    "\n",
    "for val in some_vals:\n",
    "    print(f\"\\tThe probability density of x = {val: >4} is {norm.pdf(val, 0, 2): .7f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The sum of the probability densities computed above is: 2.1518536163942685\n"
     ]
    }
   ],
   "source": [
    "print(\"The sum of the probability densities computed above is: \", end=\"\")\n",
    "print(sum([norm.pdf(x, 0, 2) for x in some_vals]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### The Sum of `pdf`s\n",
    "\n",
    "- Why is the sum here greater than 1? Aren't the probabilities of the elements in the sample space supposed to sum to 1?\n",
    "\n",
    "- Remember that the probability at a single point is 0\n",
    "  * The sample space is infinite\n",
    "  \n",
    "- Therefore, `pdf` computes the probability of small interval (Ex. $x-0.01 < x <  x+0.01$)\n",
    "\n",
    "\n",
    "* We know that:\n",
    "$$\n",
    "  density = \\frac{mass}{area}\n",
    "$$\n",
    "\n",
    "  So, we can convert back to mass such that\n",
    "$$\n",
    "  mass = density * area\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The sum of the probability densities computed above is: 0.9999366575184352\n"
     ]
    }
   ],
   "source": [
    "norm_cdf_sum = 0\n",
    "\n",
    "for x in np.arange(-8, 8, 0.0001):\n",
    "    norm_cdf_sum += computePDF_normal(x, 0, 2) * 0.0001\n",
    "    \n",
    "    \n",
    "print(\"The sum of the probability densities computed above is: %s\" % norm_cdf_sum)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### QQ-Plots\n",
    "* A QQ-Plot is used to visually determine how close a sample is to a specified distribu‐ \n",
    "tion—in this case, the normal distribution. \n",
    "\n",
    "* Recall that: \n",
    "  - A quantile is a split point that divides the range of the data into continuous intervals. \n",
    "In the context of the normal distribution:\n",
    "    \n",
    "    - The median (the middle score) is a quantile that divides the data so that 50% of the scores are below it and 50% are above it.\n",
    "    - The 25th percentile (a type of quantile) is the score below which 25% of the scores fall.\n",
    "    - Similarly, the 75th percentile (another quantile) is the score below which 75% of the scores fall, and so on.\n",
    "\n",
    "    - Theoretical quantiles don't come from the data itself but from a theoretical (or ideal) distribution that we're comparing our data to. Fo\n",
    "  * For the normal distribution, these quantiles are points on the x-axis (the horizontal line) of the bell curve that correspond to certain probabilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "n = 100\n",
    "data = np.random.normal(0, 1, n)\n",
    "\n",
    "data_sorted = np.sort(data)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculate ranks for each data point\n",
    "ranks = np.arange(1, n+1)\n",
    "ranks[0:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1 , 0.11,\n",
       "       0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.2 , 0.21, 0.22,\n",
       "       0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.3 , 0.31, 0.32, 0.33,\n",
       "       0.34, 0.35, 0.36, 0.37, 0.38, 0.39, 0.4 , 0.41, 0.42, 0.43, 0.44,\n",
       "       0.45, 0.46, 0.47, 0.48, 0.49, 0.5 , 0.51, 0.52, 0.53, 0.54, 0.55,\n",
       "       0.56, 0.57, 0.58, 0.59, 0.6 , 0.61, 0.62, 0.63, 0.64, 0.65, 0.66,\n",
       "       0.67, 0.68, 0.69, 0.7 , 0.71, 0.72, 0.73, 0.74, 0.75, 0.76, 0.77,\n",
       "       0.78, 0.79, 0.8 , 0.81, 0.82, 0.83, 0.84, 0.85, 0.86, 0.87, 0.88,\n",
       "       0.89, 0.9 , 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98, 0.99,\n",
       "       1.  ])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ranks/n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-2.2619852 , -2.01691896, -1.84368767, -1.70067971, -1.61647972,\n",
       "       -1.53657403, -1.45862466, -1.39228265, -1.31620565, -1.25255694,\n",
       "       -1.20015449, -1.15227935, -1.10976141, -1.06926172, -1.03408786,\n",
       "       -0.99559336, -0.95737835, -0.92198543, -0.88299068, -0.85089725,\n",
       "       -0.82144242, -0.78106141, -0.74265416, -0.71400644, -0.6781344 ,\n",
       "       -0.64459496, -0.61011934, -0.57804776, -0.54344064, -0.51421746,\n",
       "       -0.48801169, -0.46252076, -0.43258044, -0.40131459, -0.37545248,\n",
       "       -0.34630304, -0.32088249, -0.29003382, -0.26637189, -0.23958171,\n",
       "       -0.21608154, -0.19233644, -0.16851791, -0.14471075, -0.12061805,\n",
       "       -0.09414866, -0.06564708, -0.04236556, -0.01625263,  0.00897443,\n",
       "        0.03228957,  0.05992043,  0.0836036 ,  0.10578042,  0.13094812,\n",
       "        0.15541609,  0.17827555,  0.20000463,  0.22713782,  0.24906295,\n",
       "        0.27569628,  0.30051872,  0.32730119,  0.35219967,  0.37828766,\n",
       "        0.40492822,  0.43191255,  0.45624657,  0.48513994,  0.51384861,\n",
       "        0.54631825,  0.57292088,  0.59811839,  0.62516543,  0.65381069,\n",
       "        0.67864857,  0.71278479,  0.74575716,  0.77831025,  0.81723157,\n",
       "        0.85712156,  0.89371488,  0.93055334,  0.96887118,  1.0118805 ,\n",
       "        1.05506497,  1.11115149,  1.16913805,  1.22505074,  1.28805105,\n",
       "        1.34219543,  1.4058755 ,  1.46979537,  1.53846843,  1.6226212 ,\n",
       "        1.72423727,  1.85021145,  2.04089897,  2.30497337,  3.54846138])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theoretical_quantiles = np.quantile(np.random.normal(0, 1, 10000), q=ranks/n)\n",
    "\n",
    "theoretical_quantiles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the sorted data against the theoretical quantiles\n",
    "plt.scatter(theoretical_quantiles, data_sorted)\n",
    "# plt.plot(np.unique(theoretical_quantiles), np.poly1d(np.polyfit(theoretical_quantiles, data_sorted, 1))(np.unique(theoretical_quantiles)), color='red') \n",
    "\n",
    "plt.title('QQ-Plot')\n",
    "plt.xlabel('Theoretical Quantiles')\n",
    "plt.ylabel('Sample Quantiles')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'n' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn [21], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m data \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mrandom\u001b[38;5;241m.\u001b[39mnormal(\u001b[38;5;241m0\u001b[39m, \u001b[38;5;241m1\u001b[39m, \u001b[43mn\u001b[49m)\n\u001b[1;32m      3\u001b[0m plt\u001b[38;5;241m.\u001b[39mscatter(theoretical_quantiles, data_sorted)\n\u001b[1;32m      4\u001b[0m plt\u001b[38;5;241m.\u001b[39mplot(np\u001b[38;5;241m.\u001b[39munique(theoretical_quantiles), np\u001b[38;5;241m.\u001b[39mpoly1d(np\u001b[38;5;241m.\u001b[39mpolyfit(theoretical_quantiles, data_sorted, \u001b[38;5;241m1\u001b[39m))(np\u001b[38;5;241m.\u001b[39munique(theoretical_quantiles)), color\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mred\u001b[39m\u001b[38;5;124m'\u001b[39m) \n",
      "\u001b[0;31mNameError\u001b[0m: name 'n' is not defined"
     ]
    }
   ],
   "source": [
    "data = np.random.normal(0, 1, n)\n",
    "\n",
    "plt.scatter(theoretical_quantiles, data_sorted)\n",
    "plt.plot(np.unique(theoretical_quantiles), np.poly1d(np.polyfit(theoretical_quantiles, data_sorted, 1))(np.unique(theoretical_quantiles)), color='red') \n",
    "\n",
    "plt.title('QQ-Plot')\n",
    "plt.xlabel('Theoretical Quantiles')\n",
    "plt.ylabel('Sample Quantiles')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Actual data quantiles')"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import scipy.stats as stats\n",
    "n= 100\n",
    "data = np.random.normal(0, 1, n)\n",
    "\n",
    "stats.probplot(data, dist=\"norm\", plot=plt)\n",
    "\n",
    "plt.title('QQ-Plot')\n",
    "plt.xlabel('Expected quantiles')\n",
    "plt.ylabel('Actual data quantiles')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "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": "3.9.16"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}