\(\DeclarePairedDelimiterX{\Set}[2]{\{}{\}}{#1 \nonscript\;\delimsize\vert\nonscript\; #2}\) \( \DeclarePairedDelimiter{\set}{\{}{\}}\) \( \DeclarePairedDelimiter{\parens}{\left(}{\right)}\) \(\DeclarePairedDelimiterX{\innerproduct}[1]{\langle}{\rangle}{#1}\) \(\newcommand{\ip}[1]{\innerproduct{#1}}\) \(\newcommand{\bmat}[1]{\left[\hspace{2.0pt}\begin{matrix}#1\end{matrix}\hspace{2.0pt}\right]}\) \(\newcommand{\barray}[1]{\left[\hspace{2.0pt}\begin{matrix}#1\end{matrix}\hspace{2.0pt}\right]}\) \(\newcommand{\mat}[1]{\begin{matrix}#1\end{matrix}}\) \(\newcommand{\pmat}[1]{\begin{pmatrix}#1\end{pmatrix}}\) \(\newcommand{\mathword}[1]{\mathop{\textup{#1}}}\)
Needs:
Correlation ›
Multivariate Normals ›
Needed by:
Multivariate Normal Mutual Informations ›
Links:
Sheet PDF ›
Graph PDF ›

Normal Correlation

Why

What is the correlation between components of a normal density.

Result

Let $g \sim \normal{\mu }{\Sigma }$. Then the correlation between the $i$th and $j$th component random variables is

\[ \frac{\Sigma _{ij}}{\sqrt{\Sigma _{ii}\Sigma _{jj}}} \]

 Copyright © 2023 The Bourbaki Authors — All rights reserved — Version 13a6779cc — About — Show the old page view