Question: Problem 5.5 Let X, Y, Z be random variables. Show that (i) Cov(X + Z,Y)= Cov(X,Y) + Cov(Z,Y) (ii) Cov(X,Y)= Cov(Y, X) (iii) Cov(X,

Problem 5.5 Let X, Y, Z be random variables. Show that (i) Cov(X + Z,Y)= Cov(X,Y) + Cov(Z,Y) (ii) Cov(X,Y)= Cov(Y, X) (iii) Cov(X, Y + Z) = Cov(X, Y) + Cov(X, Z) (iv) Cov(aX, bY) = abCov(X, Y), Va, b = R (v) Corr(aX, bY) = sgn(ab)Corr(X,Y)

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