Solution-Suppose that y1 and y2 are random variables from

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?

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