Consider the joint cumulative distribution function $\displaystyle H(x,y)$ where

$\displaystyle H(x,y) = F(x)G(y){1+\frac{1}{2}[1-F(x)][1-G(y)]}$

and $\displaystyle F(x)$ and $\displaystyle G(y)$ are both cumulative distribution function of an exponential distribution with a mean value of 1. Determine a joint probability density function of X and Y.

Not sure how to approach or do this. Thanks for the help.