20. Let g and h be two probability density functions with probability distribution functions G and H, respectively. Show that for −1 ≤ α ≤ 1, the function f (x, y) = g(x)h(y)! 1 + α[2G(x) − 1][2H (y) − 1] " is a joint probability density function of two random variables. Moreover, prove that g and h are the marginal probability density functions of f . Note: This exercise gives an infinite family of joint probability density functions all with the same marginal probability density function of X and of Y .