\begin{definition}[Definition:Covariance]
Let $X$ and $Y$ be random variables. 
Let $\mu_X = \expect X$ and $\mu_Y = \expect Y$, the expectations of $X$ and $Y$ respectively, exist and be finite.
Then the '''covariance''' of $X$ and $Y$ is defined by: 
:$\cov {X, Y} = \expect {\paren {X - \mu_X} \paren {Y - \mu_Y} }$
where this expectation exists.
\end{definition}