Question: Suppose that X and Y are random variables with expected values mX mY m and variances s2 X s2 Y s2.

Suppose that X and Y are random variables with expected values mX ¼ mY ¼ m and variances s2 X ¼ s2 Y ¼ s2. Let Z ¼ (X þ Y)/2.

(a) Find E(Z).

(b) Find varðZÞ assuming that X and Y are statistically independent.

(c) Find var(Z) assuming that cov(X, Y) ¼ 0.5s2.

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