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ME3263_lab-00.ipynb

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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# ME 3263\n",
+    "## Laboratory # 0\n",
+    "## Introduction to the Student t-test"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We use statistics to draw conclusions from limited data. No measurement is exact. Every measurement you make has two types of uncertainties, *systematic* and *random*. *Systematic* uncertainties come from faults in your assumptions or equipment. \n",
+    "*Random* uncertainties are associated with unpredictable (or unforeseen at the\n",
+    "time) experimental conditions. These can also be due to simplifications of your\n",
+    "model. Here are some examples for caliper measurements:\n",
+    "\n",
+    "In theory, all uncertainies could be accounted for by factoring in all physics\n",
+    "in your readings. In reality, there is a diminishing return on investment\n",
+    "for this practice. So we use some statistical insights to draw conclusions. "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Mean and standard deviation\n",
+    "\n",
+    "If the same measurement is taken multiple times, then there should be some average value, the mean, $\\mu$. If there is an average value, then that means there is also a measure of deviation from the average value, standard deviation, $\\sigma$. The definitions for mean and standard deviation are as such\n",
+    "\n",
+    "$\\mu = \\sum_{i=1}^{N}\\frac{x_{i}}{N}$\n",
+    "\n",
+    "and\n",
+    "\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",
+    "\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"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x77232c5850>]"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<matplotlib.figure.Figure at 0x7735fea490>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "x=np.linspace(0,1)\n",
+    "y=x**2\n",
+    "plt.plot(x,y)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.13"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}