Consider the statistic S2 p, the pooled estimate of 2
Chapter 1, Problem 9.111(choose chapter or problem)
Consider the statistic \(S^2 _p\), the pooled estimate of \(\sigma^2\) discussed in Section 9.8. It is used when one is willing to assume that \(\sigma^2 _1\ =\ \sigma^2 _2\ =\ \sigma^2\). Show that the estimator is unbiased for \(\sigma^2\) [i.e., show that \(E(S^2 _p)\ =\ \sigma^2\)]. You may make use of results from any theorem or example in this chapter.
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