Question: Suppose that X and Y are random variables for which E(X) = 3, E(Y ) = 1, V ar(X) = 4, and V ar(Y )

Suppose that X and Y are random variables for which E(X) = 3, E(Y ) = 1, V ar(X) = 4, and V ar(Y ) = 9. Let Z = 5X Y + 15. Find E(Z) and V ar(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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