When the sample standard deviation S is based on a random sample from a normal population distribution,

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When the sample standard deviation S is based on a random sample from a normal population distribution, it can be shown that
E(S) = √2/(n - 1)Γ(n/2)σ/Γ((n - 1)/2)
Use this to obtain an unbiased estimator for s of the form cS. What is c when n = 20?
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