diff --git a/ME3263_lab-00.ipynb b/ME3263_lab-00.ipynb index eaaa6ef..d1873e4 100644 --- a/ME3263_lab-00.ipynb +++ b/ME3263_lab-00.ipynb @@ -1,5 +1,30 @@ { "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from scipy.stats import norm, t\n", + "\n", + "import matplotlib.pyplot as plt\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "outputs": [], + "source": [ + "import pretty_plots # script to set up LaTex and increase line-width and font size" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -37,41 +62,72 @@ "\n", "$\\sigma^2 = \\frac{\\sum_{i=1}^{N}(x_{i}-\\mu)^2}{N}$,\n", "\n", - "where $x_i$ is the $i^th$ measurement in a dataset called $x$ and $N$ is the number of data points. \n", + "where $x_i$ is the $i^{th}$ measurement in a dataset called $x$ and $N$ is the number of data points. \n", "\n", - "If you know the mean and standard deviation of a normally distributed data set, then you can predict the probability a given measurement will occur. \n" + "If you know the mean and standard deviation of a normally distributed data set, then you can predict the probability a given measurement will occur. The [probability density function](https://en.wikipedia.org/wiki/Probability_density_function) for the difference between measurement $x_{i}$ and $\\mu$ is shown below for $\\sigma=1$. \n" ] }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 3, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0,0.5,'Probability of\\\\\\\\ Measurement (\\\\%)')" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n" + "x=np.linspace(-3,3)\n", + "y=norm.pdf(x,0,1)*100 # convert fraction to percent\n", + "plt.plot(x,y)\n", + "plt.xlabel('Measurement=$x_i-\\mu$')\n", + "plt.ylabel(r'Probability of\\\\ Measurement (\\%)')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Half of the measured values are above the mean, $\\mu$, and half below. To determine the number of times any given range of values would be measured, you can integrate the probability density function between two measurements, for example $\\mu\\pm\\sigma$ the mean plus or minus the standard deviation. This distribution is the [cumulative distribution function](https://en.wikipedia.org/wiki/Cumulative_distribution_function) shown below." ] }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "[]" + "Text(0,0.5,'Probability \\\\\\\\ Measurement $" + "
" ] }, "metadata": {}, @@ -79,36 +135,298 @@ } ], "source": [ - "x=np.linspace(0,1)\n", - "y=x**2\n", - "plt.plot(x,y)" + "x=np.linspace(-3,3)\n", + "y=norm.cdf(x,0,1)*100 # convert fraction to percent\n", + "plt.plot(x,y)\n", + "plt.xlabel('Measurement=$x_i-\\mu$')\n", + "plt.ylabel(r'Probability \\\\ Measurement $ helvet + r'\sansmath' # <- tricky! -- gotta actually tell tex to use! +] \ No newline at end of file diff --git a/student_error-of-mean.pdf b/student_error-of-mean.pdf new file mode 100644 index 0000000..db79085 Binary files /dev/null and b/student_error-of-mean.pdf differ