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 μ, which is unknown. You are interested in estimating the area of the square, which is μ². Because μ is unknown, you measure it n times, obtaining observations X₁, X₂, …., X_n. Suppose that each measurement is unbiased for μ with variance σ².

(a) Show that X̅² is a biased estimate of the area of the square.

(b) Suggest an estimator that is unbiased.