Andrew's git - notes.git/blob - methods/statistics.tex

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  10\pagestyle{fancy}
  11\fancyhead[LO,LE]{Unit 3 Methods Statistics}
  12\fancyhead[CO,CE]{Andrew Lorimer}
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  16\begin{document}
  17
  18  \title{Statistics}
  19  \author{}
  20  \date{}
  21  \maketitle
  22
  23  \section{Conditional probability}
  24
  25  \[ \Pr(A|B) = \frac{\Pr(A \cap B)}{\Pr(B)} \quad \text{where } \Pr(B) \ne 0 \]
  26  
  27  \[ \Pr(A) = \Pr(A|B) \cdot \Pr(B) + \Pr(A|B^{\prime}) \cdot \Pr(B^{\prime}) \tag{law of total probability} \]
  28
  29  For independent events:
  30  
  31  \begin{itemize}
  32    \item \(\Pr(A \cap B) = \Pr(A) \cdot \Pr(B)\)
  33    \item \(\Pr(A|B) = \Pr(A)\)
  34    \item \(\Pr(B|A) = \Pr(B)\)
  35  \end{itemize}
  36
  37\end{document}