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Let X1, X2, ..... , Xn be a random sample of size I/ from a normal distribution.
(a) Show that an unbiased estimator for σ is cS, where
c = [√(n - 1) τ{(n - 1) / 2} / √2 τ(n/2)]
HINT: Recall that the distribution of (n - 1)S2 / σ2 χ2 (n - 1).
(b) Find the value of c when n = 5, n = 6.
(c) Graph c as a function of n. What is the limit of c as n increases without bound?
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