2 This is a more general version of Problem C.1. Let Y1, Y2, . ... Y,, be n pairwise uncorrelated random variables with common mean m and common variance o'. Let Y denote the sample average. (i) Define the class of linear estimators of u by Wa = a Y, +aYz + ... + a, Ym. where the a, are constants. What restriction on the a, is needed for W. to be an unbiased estimator of ? (ii) Find Var(Wa). (iii) For any numbers a1, d2, . .., a,,, the following inequality holds: (a, + a, + ... + a, ) ins ai+ a;+ ... + am. Use this, along with parts (i) and (ii), to show that Var(Wa) > Var(Y) whenever W. is unbiased, so that Y is the best linear unbiased estimator. [Hint: What does the inequality become when the a, satisfy the restriction from part (i)?]