Using a long rod that has length m, you are going to
Chapter 6, Problem 11(choose chapter or problem)
Using a long rod that has length m, you are going to layout a square plot in which the length of each side is m.Thus the area of the plot will be m2. However, you do notknow the value of m, so you decide to make n independentmeasurements X1, X2, , Xn of the length. Assumethat each Xi has mean m (unbiased measurements) andvariance s2.a. Show that X2 is not an unbiased estimator for m2. [Hint:For any rv Y, E(Y2) 5 V(Y) 1 [E(Y)]2. Apply this withY 5 X.]b. For what value of k is the estimator X2 2 kS2 unbiasedform2? [Hint: Compute E(X2 2 kS2).]
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