A bivariate riv. (X. Y ) is said to be a bivariate standard normal r.v. if its joint pdf is given by / (z. y) = - 2pry + 12] 27 (1 - 2) 1/2 exp 2(1 ) For part (a) to (c), let p - 0. (a) Show that (b) Find fX(x) Note. By symmetry, fY (y) is the same as fX(x) with the y's replacing the x's. c) Use part (b) to justify if X and Y are independent when p = 0 For part (d) and (e), let p e (-1, 0) u (0, 1). d) Find TY (y) e) Show that Xly is a normal rv, and find its mean and variance