1. Suppose that X and Y have a continuous joint distribution for which the joint p.d.f. is as follows: x+y, for 0?x? 1,0 ? y ? 1, f(x, y): 10, otherwise. (a) Find E(YX) and Var(Y|X). (b) If it is observed that X = 1/2, what predicted value of Y will have the smallest M.S.E.? (c) What will be the value of this M.S.E.? (d) If the value of Y is to be predicted from the value of X, what will be the minimum value of the overall M.S.E.? 1. Suppose that X and Y have a continuous joint distribution for which the joint p.d.f. is as follows: x+y, for 0?x? 1,0 ? y ? 1, f(x, y): 10, otherwise. (a) Find E(YX) and Var(Y|X). (b) If it is observed that X = 1/2, what predicted value of Y will have the smallest M.S.E.? (c) What will be the value of this M.S.E.? (d) If the value of Y is to be predicted from the value of X, what will be the minimum value of the overall M.S.E