Let X1, X2, . . . , Xn be a random sample of size n from a population with mean µ and variance σ 2 . (a) Show that Pn i=1(Xi − X) 2/n is a biased estimator of σ 2 . (b) Find the amount of bias in the estimator. (c) What happens to the bias as the sample size n increases? (d) Using part (a) deduce that Pn i=1(Xi − X) 2/(n − 1) is an unbiased estimator for σ 2 .