Ex:           Find the covariance, σXY, for the following joint probability density function:

Sol'n:      We start with a calculation of the mean value for X.

Note that the quantity in the parentheses in the last integral is fX(x).

By symmetry we have μY = μX = 55/36.

Now we compute the covariance. The first step is to find E(XY).

or

Now subtract the product of the means.