Problem 4 The bivariate normal distribution is frequently used to describe scores made on national standardized tests, like SAT. For concreteness assume that a particular test has two parts, labeled \"verbal\" and \"mathematics\". Furthermore, assume that a randomly selected student who takes this test will score X1 and X2 on these two parts, and that (X1, X2) are bivariate normal, with parameters m = 545, m = 555, 01 = 110, 02 = 120, and p = 0.5. (a) Compute lP(|X1 X2| > 5), the probability that the difference between the higher and the lower exceeds 5 points. (b) Compute the conditional version of the probability in (a): lP'(|X1 X2| > 5|X1 = 550) and lF'(|X1 X2| > 5|X2 = 550) i.e., the conditional probabilities that for a randomly selected student the difference between the two scores exceeds 5 points given that he / she scores 550 on one or the other part of the test