When the sample standard deviation is based on a random sample of size n from a normal population, it can be shown that S is a biased estimator for . Specifically,

(a) Use this result to obtain an unbiased estimator for = of the form cnS, when the constant cn depends on the sample size n.
(b) Find the value of cn for n = 10 and n = 25. Generally, how well does S perform as an estimator of for large n with respect to bias?

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E(S) = oV2/(n - I) I(n/2)/T[(n- 1)/2]