Problem 1 The bivariate normal distribution is frequently assumed to describe the impact points of rounds fired at a target in a two- dimensional plane. That is, if we imagine an (r, y) coordinate system centered at the target, the vertical miss distance is Y and the horizontal miss distance is X. Assume that (X, Y) are bivariate normal with Ax = 3, py = 3, Ox = .5, oy = .5 and correlation p = -.2. (a) Compute P(X 1200), the probability that the total score exceeds 1200. (b) Compute P(X2 > 550|X, = 600) and P(X, > 550| X2 = 600), the conditional probabilities that a randomly selected student scores more than 550 on a part of the test given that he/she scores 600 on the other part of the test. Problem 3 A club basketball team will play a 60-game season. Thirty-two of these games are against class A teams, and 28 are against class B teams. The outcomes of all the games are independent. The team will win each game against a class A opponent with probability .5, and it will win each game against a class B opponent with probability 65. Let X denote its total number of victories in the season. (a) Is X a binomial random variable? (b) Let XA and Xp denote, respectively, the number of victories against class A and class B teams. What are the distributions of XA and Xn? (c) What is relationship between XA, XB and X? (d) Approximate the probability that the team wins 45 or more games this season