{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction to Statistics: Probability\n",
    "### Author: Sarah Mancina"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to cover statistics, we first have to cover probability. Statistics helps us map from what we observe in our detector to the physical truth, probability helps us map from the physical truth to what we could observe in our detector."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data\n",
    "\n",
    "## Types of Data\n",
    "To start with, we'll talk about the different types of data. This is pretty simple, but it's helpful to think about the basics of data to understand probability and statitics. <br> <br>\n",
    "First we can break it down into _quantatative_ and _qualitative_.\n",
    "-  **Quantatative**: Numerical data. E.g. How tall are you? How many pairs of socks do you own?\n",
    "-  **Qualitative**: Categorical data. E.g. What is your favorite color? Do you like pizza?\n",
    "\n",
    "**_Qualitative_** data can be broken down into a couple of sub-categories:\n",
    "-  **Nominal**: The data are linked to discrete labels which cannot be ordered. E.g. What is your favorite color? [Red, orange, yellow, green, blue, purple]\n",
    "-  **Binary**: There are only two answers to the question. E.g. Do you like pizza? [no (0), yes(1)]\n",
    "-  **Oridnal**: The labels can be ordered, but the difference in values is not meaningful beyond order. E.g. How much do you like pizza? [I hate it (0), I dislike it (1), I'm neutral (2), I like it (3), I love it (4)]\n",
    "\n",
    "**_Quantatitve_** data can be broken down into two sub-categories:\n",
    "-  **Discrete**: Data that has distinct values and can be counted. E.g. How many pairs of socks do you own? [1, 2, 3, 4, ...]\n",
    "-  **Continuous**: Data that is measured on a continuum. E.g. how tall are you? [5.10 ft, 5.15 ft, 5.20 ft, ...]\n",
    "\n",
    "\n",
    "## Displaying Data\n",
    "\n",
    "How we display our data is a very important part in understanding and communicating our results. There are several ways to display data. Some tools are better suited for qualitative or quantatative data. Common ways to display qualitative data are tables, bar charts, pie charts, and more. We will focus more on quntatative data for the rest of this exercise.<br>\n",
    "\n",
    "### Histograms\n",
    "\n",
    "In physics we commonly use histograms to display our data. A histogram is a type of plot where the data is separated into discrete bins and for each bin a value proportional to the number of counts in the bin is assigned. The value assigned to the bin is usually one of the three following values:\n",
    "\n",
    "-  **Counts per Bin**: The total number of counts in the bin.\n",
    "-  **Relative Frequency**: The normalized number of counts in each bin calculated through the following formula: $$f_i = \\frac{n_i}{\\sum^{bins}_{i}n_i}$$ where $f_i$ is the frequency for bin $i$ and $n_i$ is the number of counts in bin $i$.\n",
    "-  **Density**: The frequency divided by the width of the bin as shown in the following formula: $$d_i = \\frac{n_i}{w_i \\sum^{bins}_{i}n_i}$$ where $d_i$ is the density for bin $i$, $n_i$ is the number of counts in bin $i$, and $w_i$ is the width of bin $i$. The density can be quiet useful especially when using uneven histogram bins. When using the desnsity the area of the bin, instead of the height, is proportional to the number of counts.\n",
    "\n",
    "To create and plot histograms in python we can use a couple of different tools from numpy and matplotlib. To read more about these objects you can go to their documentation sites here: [numpy.histogram](https://docs.scipy.org/doc/numpy/reference/generated/numpy.histogram.html), [numpy.histogram2d](https://docs.scipy.org/doc/numpy/reference/generated/numpy.histogram2d.html), [matplotlib.pyplot.hist](https://matplotlib.org/api/_as_gen/matplotlib.pyplot.hist.html), and [matplotlib.pyplot.hist2d](https://matplotlib.org/api/_as_gen/matplotlib.pyplot.hist2d.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#import relavent libraries\n",
    "import numpy as np\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#change pyplot defaults to make plots easier to read\n",
    "plt.rc('font', family = 'sans-serif', size = 16)\n",
    "plt.rc('legend', fontsize = 16)\n",
    "plt.rc('axes', labelsize = 24)\n",
    "plt.rc('axes', titlesize = 24)\n",
    "plt.rc('axes', linewidth = 1.5)\n",
    "plt.rc('xtick', direction = 'in', labelsize = 16)\n",
    "plt.rc('ytick', direction = 'in', labelsize = 16)\n",
    "\n",
    "#jupyter notebook magic\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's generate some random data to histogram using [numpy.random.uniform](https://docs.scipy.org/doc/numpy-1.14.5/reference/generated/numpy.random.uniform.html). This will draw random data points from a uniform distribution (a distribution where all points from the low value to the high value have the same probability) which we will discuss later."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0a14246850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#get 1000 random data points from a uniform (flat) distribution from 0 to 1\n",
    "x = np.random.uniform(low = 0.0, high = 1.0, size = 1000)\n",
    "\n",
    "#make a plot of these random variables\n",
    "fig = plt.gcf() #grab current figure\n",
    "fig.set_size_inches(8,8) #change size of figure to make larger\n",
    "\n",
    "#plot a histogram from the data in the numpy array x\n",
    "plt.hist(x)\n",
    "\n",
    "#add labels to figure\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('Counts per Bin')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the basic histogram plotted by [matplotlib.pyplot.hist](https://matplotlib.org/api/_as_gen/matplotlib.pyplot.hist.html). \n",
    "\n",
    "An important parameter in histogramming is __binning__. If the bins are too thin/too numerous, then the bins will be subject to statistical fluctuations of the small number of events in each bin. If the bins are too wide/too few, then then bins might lose some of the detail that the creator might want to show. \n",
    "\n",
    "Most python histogramming tools can take a number or an array of bin edges for the bins argument. If given a number, the histogram will bin the data points into that number of bins or even width from the minimum value in the array to the maximum value in the array. If given an array of bin edges, the histogram object will bin the data points into the bins defined by the edges."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f09f0ed3490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#make a plot of these random variables\n",
    "fig, axes = plt.subplots(nrows = 2 , ncols = 2) #grab figure and axes to make a subplot\n",
    "fig.set_size_inches(16,16) #change size of figure to make larger\n",
    "\n",
    "\n",
    "#plot a histogram from the data in the numpy array x and use 10 bins\n",
    "axes[0][0].hist(x, bins= 10)\n",
    "\n",
    "#add labels to figure\n",
    "axes[0][0].set_xlabel('x')\n",
    "axes[0][0].set_ylabel('Counts per Bin')\n",
    "axes[0][0].set_title('10 Bins')\n",
    "\n",
    "#plot a histogram from the data in the numpy array x and use 20 bins\n",
    "axes[0][1].hist(x, bins= 50)\n",
    "\n",
    "#add labels to figure\n",
    "axes[0][1].set_xlabel('x')\n",
    "axes[0][1].set_ylabel('Counts per Bin')\n",
    "axes[0][1].set_title('50 Bins')\n",
    "\n",
    "#plot a histogram from the data in the numpy array x and use 5 bins\n",
    "axes[1][0].hist(x, bins= 5)\n",
    "\n",
    "#add labels to figure\n",
    "axes[1][0].set_xlabel('x')\n",
    "axes[1][0].set_ylabel('Counts per Bin')\n",
    "axes[1][0].set_title('5 Bins')\n",
    "\n",
    "#plot a histogram from the data in the numpy array x and using set bin edges\n",
    "bin_edges = np.linspace(0, 1., 10 + 1) #make array of 11 bin edges from 0 to 1 \n",
    "axes[1][1].hist(x, bins= bin_edges)\n",
    "\n",
    "#add labels to figure\n",
    "axes[1][1].set_xlabel('x')\n",
    "axes[1][1].set_ylabel('Counts per Bin')\n",
    "axes[1][1].set_title('Array of Bin Edges')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The pyplot.hist is good for plotting the histogram; however, if you want to manipulate the output of a histogram before you plot it, you can use the returned values from numpy.histogram. The objects returned are an array of the number of counts in each bin and the bin edges. Let's take the plots above and plots the relative frequency instead of counts instead."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f09f063e7d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#make a plot of these random variables\n",
    "fig, axes = plt.subplots(nrows = 2 , ncols = 2) #grab figure and axes to make a subplot\n",
    "fig.set_size_inches(16,16) #change size of figure to make larger\n",
    "\n",
    "\n",
    "#plot a histogram from the data in the numpy array x and use 10 bins\n",
    "n, edges = np.histogram(x, bins = 10)\n",
    "freq = n / float(len(x)) #divide n by total number of data events\n",
    "x_mids = (edges[:-1] + edges[1:])/2. #calculate the middles values of each bin to give to the plot\n",
    "\n",
    "#to plot the frequency we give the frequency of each bin as a weight for the mids\n",
    "axes[0][0].hist(x_mids, weights = freq, bins = edges)\n",
    "\n",
    "#add labels to figure\n",
    "axes[0][0].set_xlabel('x')\n",
    "axes[0][0].set_ylabel('Relative Frequency')\n",
    "axes[0][0].set_title('10 Bins')\n",
    "\n",
    "#plot a histogram from the data in the numpy array x and use 20 bins\n",
    "n, edges = np.histogram(x, bins = 20)\n",
    "freq = n / float(len(x)) #divide n by total number of data events\n",
    "x_mids = (edges[:-1] + edges[1:])/2. #calculate the middles values of each bin to give to the plot\n",
    "\n",
    "#to plot the frequency we give the frequency of each bin as a weight for the mids\n",
    "axes[0][1].hist(x_mids, weights = freq, bins = edges)\n",
    "\n",
    "#add labels to figure\n",
    "axes[0][1].set_xlabel('x')\n",
    "axes[0][1].set_ylabel('Relative Frequency')\n",
    "axes[0][1].set_title('50 Bins')\n",
    "\n",
    "#plot a histogram from the data in the numpy array x and use 5 bins\n",
    "n, edges = np.histogram(x, bins = 5)\n",
    "freq = n / float(len(x)) #divide n by total number of data events\n",
    "x_mids = (edges[:-1] + edges[1:])/2. #calculate the middles values of each bin to give to the plot\n",
    "\n",
    "#to plot the frequency we give the frequency of each bin as a weight for the mids\n",
    "axes[1][0].hist(x_mids, weights = freq, bins = edges)\n",
    "\n",
    "\n",
    "#add labels to figure\n",
    "axes[1][0].set_xlabel('x')\n",
    "axes[1][0].set_ylabel('Relative Frequency')\n",
    "axes[1][0].set_title('5 Bins')\n",
    "\n",
    "#plot a histogram from the data in the numpy array x and using set bin edges\n",
    "bin_edges = np.linspace(0, 1., 10 + 1) #make array of 11 bin edges from 0 to 1 \n",
    "n, edges = np.histogram(x, bins = bin_edges)\n",
    "freq = n / float(len(x)) #divide n by total number of data events\n",
    "x_mids = (edges[:-1] + edges[1:])/2. #calculate the middles values of each bin to give to the plot\n",
    "\n",
    "#to plot the frequency we give the frequency of each bin as a weight for the mids\n",
    "axes[1][1].hist(x_mids, weights = freq, bins = edges)\n",
    "\n",
    "\n",
    "#add labels to figure\n",
    "axes[1][1].set_xlabel('x')\n",
    "axes[1][1].set_ylabel('Relative Frequency')\n",
    "axes[1][1].set_title('Array of Bin Edges')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The scale of the relative frequency is dependenent on the size of the bins. This is not the case for the density. Density can be a useful tool since integrals of the histograms can be related to the probability, we'll touch on that later.\n",
    "\n",
    "__Excersice:__ plot the density of the data array above using 10 bins from 0 to 1. There are two simple ways to do this, one using numpy.histogram and one using matplotlib.pyplot.hist. If you are stuck check the documentation for each of the histogram tools."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Descriptive Statistics\n",
    "There are a couple of different statistics you can draw from a data to help describe the set. The most common are below:\n",
    "- Aritmetic Mean: $\\bar{x} = \\sum_{i = 0}^N \\frac{1}{n}x_i$\n",
    "- Median: The value lying at the midpoint of a distribution of observed values where there is equal probability of lying above or below.\n",
    "- Standard Deviation: Measure of the spread $\\sigma = \\sqrt{\\sum_{i=0}^N \\frac{1}{N}(x_i - \\bar{x})^2}$\n",
    "- Correlation Coefficient: Measure the linear relationship between to variables $\\rho = \\frac{\\bar{xy} - \\bar{x}\\bar{y}}{\\sigma_x\\sigma_y}$. $\\rho = 0$ means there is no linear correlation, $\\rho = 1$ means a positive correlation, and $\\rho = -1$ means their is a negative correlation.\n",
    "\n",
    "__Excersice__: Calculate the probability of x, the uniformly distributed sample above. Use numpy methods to help simplify your code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Probability\n",
    "\n",
    "## Mathematical Probability\n",
    "An experiment is any activity or process where the outcome is subject to uncertainty. The sample space is the set of all possible outcomes of an experiment. An event is a set of outcomes in the sample space.\n",
    "\n",
    "Some notation for events:\n",
    "- The complement of event $A$, $\\bar{A}$, is the set of all $a$ in the sample set where $a$ is not in $A$.\n",
    "- The union of events $A$ and $B$, $A \\cup B$, is all $a$ in the sample set, $S$, if $a$ is in $A$ __or__ $B$\n",
    "- The intersection of events $A$ and $B$, $A \\cap B$, is all $a$ in the sample set, $S$, if $a$ is in $A$ __and__ $B$\n",
    "\n",
    "The foundation of probability are the Kolmogorov Axioms, which are as follows.\n",
    "1. For any event $A$ in the sample space $S$, $$P(A)\\geq0$$\n",
    "2. $P(A) + P(\\bar{A}) = 1$ where $\\bar{A}$ is the complement of $A$ in $S$\n",
    "3. For mutually exclusive events, $A_1$, $A_2$, ... in $S$, $$P(A_1 \\cup A_2 \\cup ...) = \\sum_{i=1}^{\\infty}P(A_i)$$\n",
    "\n",
    "## Frequentist Probability \n",
    "For this lecture, we will only cover the Frequentist definitions of probability and statistics. However, there is also Bayesian statistics which is a useful tool.\n",
    "\n",
    "The frequentist definition of probaility is:\n",
    "$$P(X) = \\lim_{N\\to\\infty} \\frac{n}{\\mathrm{N}}.$$\n",
    "Where $n$ is the number of times outcome $X$ occured over $N$ trials. The law of large numbers says that as N approaches infinity in an experiement, the measurement of $P(X)$ approaches it's true value.\n",
    "\n",
    "Let's test this by simulating a simple dice roll."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True probability of rolling 1 for a fair dice: 0.166666666667\n",
      "Calculated probability of rolling 1 for 10 trials: 0.0\n",
      "Calculated probability of rolling 1 for 100 trials: 0.11\n",
      "Calculated probability of rolling 1 for 1000 trials: 0.166\n",
      "Calculated probability of rolling 1 for 10000 trials: 0.1693\n",
      "Calculated probability of rolling 1 for 100000 trials: 0.16483\n",
      "Calculated probability of rolling 1 for 1000000 trials: 0.166384\n"
     ]
    }
   ],
   "source": [
    "print 'True probability of rolling 1 for a fair dice:', 1/6.\n",
    "\n",
    "sizes = [10, 100, 1000, 10000, 100000, 1000000]\n",
    "for size in sizes:\n",
    "    x = np.random.randint(1,7,size) #Randomly draw values of 1 through 6\n",
    "    p_1 = len(np.where(x == 1)[0])/float(size) #Calculated the frequentist probability estimate\n",
    "    print 'Calculated probability of rolling 1 for',size,'trials:',p_1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Probability Distributions\n",
    "\n",
    "Sometimes variables have a well defined probability distribution. If the variable is descrete it's distribution is called a __Probability Mass Functions__ (PMF), otherwise if the variable is continuous it's distribution is called a __Probability Density Function__ (PDF). For a PMF,\n",
    "$$\\sum_{i=min}^{max} PMF(x_i) = 1$$\n",
    "and for a PDF,\n",
    "$$\\int_{min}^{max} PDF(x)dx = 1.$$\n",
    "We will go through some of the most common PMF's and PDF's.\n",
    "\n",
    "We can also use probability distributions to find an __expected value__. For example if we wanted to find the mean, the expected value of $x$, we would like to find the expected variable value using the following functions\n",
    "$$\\bar{x} = \\sum_{i=min}^{max} x_i PMF(x_i)$$\n",
    "and\n",
    "$$\\bar{x} = \\int_{min}^{max} xPDF(x)dx = 1.$$\n",
    "If we wanted to find the expected value of any function of $x$, $g(x)$, we can use the same method:\n",
    "$$\\bar{x} = \\sum_{i=min}^{max} g(x_i) PMF(x_i)$$\n",
    "and\n",
    "$$\\bar{x} = \\int_{min}^{max} g(x) PDF(x)dx = 1.$$\n",
    "\n",
    "The __cummulative distribution__ is for a given value, $r$, the probability of all the outcomes $\\geq r$.\n",
    "$$CMF = \\sum_{i=r}^{max} PMF(x_i)$$\n",
    "or\n",
    "$$CDF = \\int_{r}^{max} PDF(x)dx$$\n",
    "\n",
    "## Binomial Distribution\n",
    "A binomial distribution is a PMF which describes the probability of the number of successes in a squence of independent experiments with a binary outcome (Bernoulli trial). An example would be rolling a dice and calling rolling 1 a success and rolling anything else a failure. Let's try to use this example to build the binomal distribution. \n",
    "\n",
    "If you a roll a dice 5 times, what would be the probability that you would roll a 1 twice? One way to roll a 1 twice is to roll the 1 in the first two rolls:\n",
    "$$P(\\text{1 & 1 & not 1 & not 1 & not 1}) = 1/6 \\times 1/6 \\times 5/6 \\times 5/6 \\times 5/6.$$\n",
    "But this isn't the only way to roll 1 twice. Luckily we can see if no matter what order we roll 1 twice in five rolls, the probability for each combination is the same. We must include the combinatorics to calculate the total probability \n",
    "$$P(\\text{Roll 1 twice}) = {5\\choose 2}(1/6)^2 (5/6)^3$$\n",
    "Where ${5\\choose 2} = \\frac{5!}{2!3!}$.\n",
    "\n",
    "The general form of the Binomial distribution is as follows:\n",
    "$$P(k) = {n\\choose k}p^k(1-p)^{n-k} \\text{, where } {n\\choose k} = \\frac{n!}{k!(n-k)!}.$$\n",
    "Where $k$ is the number of successes, $n$ is the number of trials, and $p$ is the probability of a single success.\n",
    "\n",
    "We can find the moments of a distribution by solving for the expectation values. For the binomial distribution, the mean is $np$ and the standard deviation is $\\sqrt{np(1-p)}$.\n",
    "\n",
    "__Excercise__: You are doing a magic trick with a normal deck of cards with no jokers. What is the probability after repeating the trick 5 times that at least one ace was drawn by the participant?\n",
    "\n",
    "\n",
    "## Poisson Distribution\n",
    "The poisson distribution is a PMF which gives the probability of a number of events occuring. The form is as follows:\n",
    "$$P(k) = \\frac{e^{\\lambda}\\lambda^k}{k!}$$ \n",
    "Where $\\lambda$ is the average number of events that occur. The mean of the distribution is therefore $\\lambda$ and the standard deviation is $\\sqrt{\\lambda}$.\n",
    "\n",
    "__Excercise__: At a bus stop, the average rate of buses is one bus per 20 minutes. What is the probability that 5 buses come within an hour??\n",
    "\n",
    "## Normal Distribution\n",
    "The normal distribution is one of the most common PDFs (partially because of the Central Limit Theorem). It is often a good assumption to assume measurements are normally distributed. The normal distribution is also known as the Gaussian distribution and has the following form:\n",
    "$$P(x) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}}e^{-(x - \\mu)^2/(2\\sigma^2)}$$\n",
    "where $\\mu$ is the mean of the distribution and $\\sigma$ is the standard deviation.\n",
    "The normal distribution has a characteristic bell curve shape which is peaked at $\\mu$ and it's width is affected by $\\sigma$.\n",
    "\n",
    "__Excersise__: Show that for large $n$ or large $\\lambda$ the binomial or Poisson distribution can be approximated by a normal distribution. Hint: use np.random.normal, np.random.poisson, and np.random.binomial. Hint 2: What should you use for the standard deviation of the normal distribution?"
   ]
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    "def plot_distribution(dist_1, dist_2, bins = 20):\n",
    "    #make a plot comparing two distributions\n",
    "    fig = plt.gcf() #grab current figure\n",
    "    fig.set_size_inches(8,8) #change size of figure to make larger\n",
    "    \n",
    "    plt.hist(dist_1, bins = bins, linewidth = 2, histtype = 'step')\n",
    "    plt.hist(dist_2, bins = bins, linewidth = 2, histtype = 'step')\n",
    "    \n"
   ]
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   "cell_type": "markdown",
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   "source": [
    "# Excersice: Making Monte Carlo Simulation\n",
    "A common tool to use in research is simulations of data which is often referred to as Monte Carlo (mc). MC relies on probability to create a fake sampling of data.\n",
    "\n",
    "Let's create a sample of neutrinos. We'll assume that the expected number of neutrinos is 100, that the neutrinos are isotropically distributed in direction, and that the neutrinos have an average energy of 1TeV with a standard deviation of 2 in log(Energy)."
   ]
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   "source": []
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   "cell_type": "code",
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