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+1,37 @@ +\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} -- 2.47.1