9.30 Consider S 2 , the estimator of 2 , from Exercise 9.29. Analysts often use S 2 rather than dividing n i=1 (Xi

9.30 Consider S

2 , the estimator of σ2 , from Exercise 9.29. Analysts often use S

2 rather than dividing

n i=1

(Xi − ¯X )2 by n − 1, the degrees of freedom in the sample.

(a) What is the bias of S 2 ?

(b) Show that the bias of S 2 approaches zero as n →
∞.