parthi2929

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "toc": true
   },
   "source": [
    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#Sampling-Distribution-of-Sample-Proportions\" data-toc-modified-id=\"Sampling-Distribution-of-Sample-Proportions-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Sampling Distribution of Sample Proportions</a></span><ul class=\"toc-item\"><li><span><a href=\"#Gumballs\" data-toc-modified-id=\"Gumballs-1.1\"><span class=\"toc-item-num\">1.1&nbsp;&nbsp;</span>Gumballs</a></span><ul class=\"toc-item\"><li><span><a href=\"#Setup\" data-toc-modified-id=\"Setup-1.1.1\"><span class=\"toc-item-num\">1.1.1&nbsp;&nbsp;</span>Setup</a></span></li><li><span><a href=\"#Statistical-Outcomes:\" data-toc-modified-id=\"Statistical-Outcomes:-1.1.2\"><span class=\"toc-item-num\">1.1.2&nbsp;&nbsp;</span>Statistical Outcomes:</a></span></li><li><span><a href=\"#Notations-and-Conditions\" data-to

parthi2929

%((*- extends 'style_ipython.tplx' -*))

% 1. CHANGE DOCUMENTCLASS TO STANDALONE
((* block docclass *))
\documentclass[float=false, crop=false, 11pt]{standalone}
((* endblock docclass *))



% 2. REMOVE PREAMBLE AND REPLACE WITH STYLE FILE INCLUSION

parthi2929

\documentclass[10pt,a4paper]{article}
    \usepackage[latin1]{inputenc}
    \usepackage{amsmath}
    \usepackage{amsfonts}
    \usepackage{amssymb}
    \usepackage{graphicx}
    \usepackage{calc}
    \usepackage{fancyvrb} % verbatim replacement that allows latex
    \usepackage[breakable]{tcolorbox}

parthi2929

parthi2929

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MLE for Normal Distribution\n",
    "\n",
    "\n",
    "$$\n",

parthi2929

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MLE for Normal Distribution\n",
    "\n",
    "\n",
    "$$\n",

parthi2929

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Maximum Likelihood Estimation of a Normal distribution involves two parameters $(\\mu, \\sigma^2)$ which we will here by refer to as $(\\theta_1, \\theta_2)$. Since the likelihood function involves two parameters, to visualize it, a 3D graph is needed. In this section, we will generate a 3D graph, for viewers to interact with it and have a look around it. Since this interactivity is not possible in pdf, this material stays as html separately. \n",
    "\n",
    "This section is not about explaining the related concepts, they are covered in the theoretical part, from which you found this reference. This section only focusses on the formula we try to graph, and how do we generate the graph (in python). We will also do not deal with any further derivation of finding the maxima. We will just stop with graphing it. The vision  is, once this is possible, any one could use it as base, to illustrate many more complex 2D Likelihoo

parthi2929

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simple Regression Model"
   ]
  },
  {

parthi2929

parthi2929