Using a long rod that has length ft you are going to lay out

Using a long rod that has length ft, you are going to lay out a square plot in which the length of each side is ft. Thus the area of the plot will be mu^2. However, you do not know the value of ft, so you decide to make n independent measurements X1, X2, . . . , Xn of the length. Assume that each X, has mean ft (unbiased measurements) and variance pi^2 Show that X2 is not an unbiased estimator for ft2.

Solution

1/n