Let Y1, Y2,..., Yn denote a random sample of size n from a population whose density is

Chapter 8, Problem 8.14

(choose chapter or problem)

Let Y1, Y2,..., Yn denote a random sample of size n from a population whose density is given by f (y) = $ y1/ , 0 y , 0, elsewhere, where > 0 is a known, fixed value, but is unknown. (This is the power family distribution introduced in Exercise 6.17.) Consider the estimator = max(Y1, Y2,..., Yn ). a Show that is a biased estimator for . b Find a multiple of that is an unbiased estimator of . c Derive MSE().

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