10. Using a long rod that has length m, you are going to lay out a square plot in which the length of each side is m. Thus the area of the plot will be m2. However, you do not know the value of m, so you decide to make n independent measurements X1, X2, . . . Xn of the length. Assume that each Xi has mean m (unbiased measurements) and variance s2.

a. Show that is not an unbiased estimator for m2.

(Hint: For any rv Y, E(Y 2)V(Y)[E(Y)]2. Apply this with Y  .)

b. For what value of k is the estimator  kS2 unbiased for m2? [Hint: Compute E(  kS2).]