Question: 5. Let X, Y, Z be random variables. Show that (a) Cov ( X + Z, Y) = Cov (X, Y) + Cov(Z, Y), (b)

5. Let X, Y, Z be random variables. Show that (a) Cov ( X + Z, Y) = Cov (X, Y) + Cov(Z, Y), (b) Cov ( X, Y) = Cov (Y, X),(c) Cov ( X, Y + Z) = Cov(X, Y) + Cov(X, Z), (d) Cov(ax, by) = ab Cov(X, Y), Va, bER, (e) Corr(aX, by) = sgn(ab) Corr(X, Y), where son (. ) denotes the signum function or sign function

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