Question: 5. Variance and correlation (20 points). Let X and Y be two r.V.s. (a) If Var(X + 3Y) = Var(X - 3Y), must X and

5. Variance and correlation (20 points). Let X and Y be

5. Variance and correlation (20 points). Let X and Y be two r.V.s. (a) If Var(X + 3Y) = Var(X - 3Y), must X and Y be uncorrelated? (b) If Var(X) = Var(Y), must X and Y be uncorrelated? (c) Find the sense of the following inequality: 2, =, or 0. (d) Let X and Y have correlation coefficient px,y. What is the correlation coefficient between X and al + b, where a, b are constants with a > 0

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