You plan to use a rod to lay out a square, each side of which is the length of the rod. The length of the rod is , which is unknown. You are interested in estimating the area of the square, which is u. Because is unknown, you measure it a times, obtaining observations X X X Suppose that each measurement is unbiased for with variance .

(a) Show that is a biased estimate of the area of the square.

(b) Suggest an estimator that is unbiased.