Question: Exercise 6.79 Let the pair (X, Y ) have the bivariate normal density function of (6.76), and let U and V be given by (6.78).

Exercise 6.79 Let the pair (X, Y ) have the bivariate normal density function of (6.76), and let U and V be given by (6.78). Show that U and V have the standard bivariate normal distribution. Hence or otherwise show that E(XY ) − E(X)E(Y ) = ρσ1σ2, and that E(Y | X = x) = μ2 + ρσ2(x − μ1)/σ1.

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