45Covariance from E[XY]

$\displaystyle E[XY] = 10$, $\displaystyle E[X] = 2$ and $\displaystyle E[Y] = 3$. Find $\displaystyle \mathrm{Cov}(X, Y)$.

Covariance is the mean of the product minus the product of the means: Cov(X,Y) = E[XY] − E[X]E[Y]. Here that's 10 − 2·3 = 4. Check: 4 + 2·3 = 10, matching E[XY].