(13) Let a, b, c, d be constants. If all of the following covariances are well defined then show that Cou(aX + by, cZ + dW) - ac Cou(X, Z) + ad Cov(X, W) + be Cou(Y, Z) + bd Cov(Y, W). The following outlines of the proofs are proposed, where U = aX + bY and V = cZ + dw. (a) Cov(U + V) = Cov(U) + Cov(V), which gives the result. (b) Since Cov(UV) = Cou(U) Cov(V), the result follows by substituting U = aX + bY and V = cZ + dw. (c) All we need to do is use the definition of covariance, then multiply out the expressions inside the expectation operation, E(UV), and then use the linearity of expectations to get this result. (d) The result, as stated, is false. (e) None of the above (a) (b) (c) (d) (e) N/A (Select One) O O O O O