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Suppose X and Y are independent variables with E(X) = E(Y ) = θ, Var(X) =...

Suppose X and Y are independent variables with E(X) = E(Y ) = θ, Var(X) = 2 and Var(Y ) = 4. The two estimators for θ, W1 = 1/2 X + 1/2 Y and W2 = 3/4 X + 1/4 Y .

(1) Are W1 and W2 unbiased? (2) Which estimator is more efficient (smaller variance)?

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