Question: (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.

(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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