From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Mon, 22 Jul 2019 00:44:36 +0000 (+1000)
Subject: [methods] start statistics notes (conditional prob)
X-Git-Tag: yr12~85
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/54d401dc1d5c827359ef69866955bdaab0efd5ee?ds=sidebyside;hp=6bfb96829bdfbe32930fd5b49548a0d39a745cdd

[methods] start statistics notes (conditional prob)
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+\documentclass[a4paper]{article}
+\usepackage[a4paper,margin=2cm]{geometry}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{tcolorbox}
+\usepackage{fancyhdr}
+\usepackage{pgfplots}
+\usepackage{tabularx}
+
+\pagestyle{fancy}
+\fancyhead[LO,LE]{Unit 3 Methods Statistics}
+\fancyhead[CO,CE]{Andrew Lorimer}
+
+\setlength\parindent{0pt}
+
+\begin{document}
+
+  \title{Statistics}
+  \author{}
+  \date{}
+  \maketitle
+
+  \section{Conditional probability}
+
+  \[ \Pr(A|B) = \frac{\Pr(A \cap B)}{\Pr(B)} \quad \text{where } \Pr(B) \ne 0 \]
+  
+  \[ \Pr(A) = \Pr(A|B) \cdot \Pr(B) + \Pr(A|B^{\prime}) \cdot \Pr(B^{\prime}) \tag{law of total probability} \]
+
+  For independent events:
+  
+  \begin{itemize}
+    \item \(\Pr(A \cap B) = \Pr(A) \cdot \Pr(B)\)
+    \item \(\Pr(A|B) = \Pr(A)\)
+    \item \(\Pr(B|A) = \Pr(B)\)
+  \end{itemize}
+
+\end{document}