Suppose Z and W are two standard random variables with cov(Z; W ) = 0:5: You are asked to use a linear function of Z to predict W in a repeated predictive exercise. More precisely, for each random draw (w; z) from the distribution of (W; Z) ; z is revealed, but w is not. You are asked to guess w based on a linear function of the revealed z; that is, c z d for some parameter c and d. The loss from making the wrong guess is [w (c z d)]2 : The expected loss is E [W (c Z d)]2. (a) Find f (c; d) := E [W (c Z d)]2 as a function of (c; d) : (b) Find the optimal c and d that minimize the expected loss, that is, (c; d) = arg min c;d f (c; d) : Please provide numerical answers