Question: (a) For random variables X and Y , show that Cov(X + Y, X Y ) = Var(X) Var(Y) (b) Suppose that Cov(X,

(a) For random variables X and Y , show that
Cov(X + Y, X − Y ) = Var(X) − Var(Y)
(b) Suppose that Cov(X, Y) = 0. Prove that
ρ(X + Y, X − Y ) = Var(X) − Var(Y)/Var(X) + Var(Y)

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