Ex:           Find the covariance, σXY, for the joint probability density function shown below given μX = μY = 1.6:

Sol'n:      We may express f(x, y) as a sum of two boxes:

To find the covariance, we use the following formula:

To find E(XY), we compute a double integral:

or

or

or

or

or

or

Now subtract the product of the means.