Problem 2. [23 points] 111 a. hierarchical model Y|X = 1' N Normal {a + bit, J3} and suppose X m Normal (#,Jg). (a) [7 points] Calculate the marginal mean and marginal variance of Y. (b) (T point-o) Calculate the cavarianee between X and. Y. [e] [7 points] What is the joint distribution of X and Y? [o] [7 points] What in the conditional distribution X|YT