. (8 marks) Let #, !, ... , $ be n pairwise uncorrelated random variables with common mean and common variance !. Let A denote the sample average. Define the class of linear estimators of by = ## + !! + + $$, where #, !, ... , $ are constants. a. (2 marks) What restrictions on the constants are necessary to ensure that W is an unbiased estimator of ? (Do not just state your answer; prove it.) b. (2 marks) Calculate the variance of W. (Your answer will be a function of the constants and !). It can be shown (which means I will not do so) that # $ ( " $ "&# )! " $ ! "&# . c. (2 marks) Use this fact to help prove that, whenever W is unbiased, (A) (). 6 d. (2 marks) Briefly explain what weights are used to calculate the sample average, A, and what part (c) implies when choosing among linear unbiased estimators.