Covariance as Expectation of Product minus Product of Expectations

Theorem
Let $X$ and $Y$ be random variables.

Let the expectations of $X$ and $Y$ exist and be finite.

Then the covariance of $X$ and $Y$ is given by:


 * $\map {\operatorname {Cov} } {X, Y} = \expect {X Y} - \expect X \expect Y$