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 σ2. 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 σ2.
a. Show that X2 is not an unbiased estimator for σ2.
b. For what value of k is the estimator X2 - kσ2 unbiased for σ2?