Question: Consider S2, the estimator of 2, from Exercise 9.29. Analysts often use S2 rather than dividing n i=1 (Xi X) 2 by n

Consider S2, the estimator of σ2, from Exercise 9.29. Analysts often use S2 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 S2?

(b) Show that the bias of S2 approaches zero as n →
∞.

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