Q2. a ) In a fitness program, let X denote the weight in kilograms of a male adult at the beginning of the program and Y denote his weight in kilograms at the end of the program. Assume that X and Y have a normal bivariate distribution with means Mx = 70.0 and My = 65.0, variances ox = 8.0 and or = 2.0, and unknown correlation coefficient, p. (i) Given that E(X|Y = y) = 57.0 + 0.2y, show that p = 0.1. (ii) Find E(X|Y = 75.0) and Var(X|Y = 75.0). b) Let X and Y be independent exponential random variables, both with mean 0. Find the joint pdf of U = X + Y and V = X. S 9:33 BE 2021/12/1