a) Consider random variables X and Y with the following joint distribution Px Y( 7, y) y -0 y=1 y=2 0 1/6 1/6 0 1/12 1/6 1/12 0 =2 0 1/6 1/6 i. (4 marks) Find the marginal distributions of X and of Y and the expectations EX and EY ii. (4 marks) Calculate the expectation E(XY ) and find the covariance Cov(X, Y). What does the sign of Cov( X, Y ) tell you about the relationship between X and Y? iii. (6 marks) Calculate the conditional distribution of X Y - 0 and hence find the conditional expectation E[X |Y - 0] Calculate the conditional distribution of Y X - 2 and hence find the conditional expectation E Y X - 2]