Suppose that two independent random samples of n1 and n2 observations are selected from
Chapter 8, Problem 8.133(choose chapter or problem)
Suppose that two independent random samples of n1 and n2 observations are selected from normal populations. Further, assume that the populations possess a common variance 2. Let S2 i = ni j=1(Yi j Yi)2 ni 1 , i = 1, 2. a Show that S2 p, the pooled estimator of 2 (which follows), is unbiased: S2 p = (n1 1)S2 1 + (n2 1)S2 2 n1 + n2 2 . b Find V(S2 p).
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