Question: Suppose that X and Y are random variables for which E(X) = 3, E(Y) = 1, Var(X) = 4, and Var(Y) = 9. Let Z

Suppose that X and Y are random variables for which E(X) = 3, E(Y) = 1, Var(X) = 4, and Var(Y) = 9. Let Z = 5X − Y + 15. Find E(Z) and Var(Z) under each of the following conditions:
(a) X and Y are independent.
(b) X and Y are uncorrelated.
(c) The correlation of X and Y is 0.25.

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