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6. Sufficiency, Completeness, and Ancillarity 339

{Hint: Part (ii) follows from the Theorem 6.6.2. One may look at Lehmann
(1983, pp. 47-48) for details.}
6.6.19 Let X , ..., X be iid N(µ, σ ) where –∞ < µ < ∞, 0 < σ < ∞ are both
2
4
1
unknown parameters. Evaluate the expression for

2
where and S = 1/3 . {Note: Can Basu’s Theo-
rem be used here?}