unit2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c6602a53-290b-46de-9c0c-4f6f31e37c25",
   "metadata": {},
   "source": [
    "---\n",
    "title: \"Unit 2: Notebook\"\n",
    "math:\n",
    "  '\\trans': '^\\mathsf{T}'\n",
    "  '\\eps': '\\epsilon'\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28cedc95-6340-4cdc-9a79-e58a750146d4",
   "metadata": {},
   "source": [
    ":::{tip}\n",
    "Code cells in this notebook are executed when the file is prepared with Jupyter Notebook or Lab. They may also be executed live with JupyterLite! (although the feature is in development)\n",
    ":::"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a2bdb719-2d6f-4154-82be-e58ec6b58054",
   "metadata": {},
   "source": [
    "This is the mean of some random numbers using numpy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c62b93b2-c991-444b-9231-990d4ff8e4db",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "-0.1701530565922348"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "x = np.random.normal(size=100)\n",
    "import matplotlib.pyplot as plt\n",
    "plt.hist(x)\n",
    "plt.show()\n",
    "np.mean(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb282ac2-7116-4205-8106-38005d53a3df",
   "metadata": {},
   "source": [
    "$$\n",
    "\\theta = \\int_0^\\infty f(x,\\theta)d\\theta\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a81e150-3c48-4076-9a2d-fbf11a9a4f6a",
   "metadata": {},
   "source": [
    "Use a $\\LaTeX$ macro."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2222140-5864-4d61-a89b-2b51a7ab76a0",
   "metadata": {},
   "source": [
    "$$\n",
    "A = X \\trans Y\n",
    "$$"
   ]
  }
 ],
 "metadata": {
  "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": "3.11.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}