Answer: Using a long rod that has length , you are going

Chapter 6, Problem 6.10

(choose chapter or problem)

Using a long rod that has length , you are going to lay out a square plot in which the length of each side is . Thus the area of the plot will be 2 . However, you do not know the value of , so you decide to make n independent measurements X1, X2, . . . Xn of the length. Assume that each Xi has mean (unbiased measurements) and variance 2 . a. Show that X2 is not an unbiased estimator for 2 . [Hint: For any rv Y, E(Y2 ) V(Y) [E(Y)]2 . Apply this with Y X.] b. For what value of k is the estimator X2 kS2 unbiased for 2 ? [Hint: Compute E(X2 kS2 ).] 11.