Answer the following questions: a. Let X and Y follow the bivariate normal distribution with parameters , 2, 01, 02, p. Show that W = X- and Q = (Y) - p2(X-) are independent normal random variables. b. Let X and X2 be two independent normal random variables with mean zero and variance 1. Show that the vector Z (Z, Z2)', where Z Z = +X, + p62X1 + 62/1 - pX2 follows the bivariate normal distribution with parameters 1, 2, 01, 02, p. c. Let X1, X2, X3 be i.i.d. random variables N(0, 1). Show that Y X + 6X3 and Y X2 + 8X3 have bivariate normal distribution. Find the value of 8 so that the correlation coefficient between Y and Y is p = 1. = =