Let g and h be two probability density functions with
Chapter , Problem 20(choose chapter or problem)
Let g and h be two probability density functions with probability distribution functions G and H, respectively. Show that for 1 1, the function f (x, y) = g(x)h(y)! 1 + [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 .
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