Question: Suppose that y1 and y2 are random variables from population with mean µ and variance σ2. Suppose we have the following estimators:
(i) X =1/2 ×y1 +1/2 ×y2,
(ii) Z =1/4 × y1 +3/4 × y2 and
(iii) S =1/3 × y1 + y2.
(a) Are X, Z and S unbiased?
(b) Which one is the most efficient estimator?