Please answer the following question(s). Please show all your working/solution(s).

Let Y], . . . , Yn be independent, uniformly distributed random variables on the interval [01 9], and Y\") = max(Y1, Y2, .. . , Y") be the largest order statistic of those random variables. (a) Find an estimator 91, a function h(Y(n)) of the largest order statistic, so that 91 is an unbiased estimator of 0. (b) What is the MSE of your estimator 91? (c) Is 91 a consistent estimator for 6? ((1) Another seemingly reasonable estimator of 0 is twice the empirical mean, 27. We'll call this 92. Is it unbiased? (e) What is the MSE of 62? (f) Is 92 a consistent estimator for I9? (g) 90mpare the results from parts (b) and ((1). Under what circumstances, if any, would you prefer 31 to 62? (h) Compute the relative efciency of 5'2 relative to l