Assume that two populations have the same variance 2. If a sample of size n1 produced a

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Assume that two populations have the same variance σ2. If a sample of size n1 produced a variance S12 from population I and a sample of size n2 produced a variance S22 from population II, show that the pooled variance
(m – 1)S; + (n2 - 1)S ni +m -2

is an unbiased estimator of σ2. Show that (S12 + S22) / 2 is also an unbiased estimator of σ2. Which of the two estimators would you prefer? Give reasons for your choice.

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Mathematical Statistics With Applications In R

ISBN: 9780124171138

2nd Edition

Authors: Chris P. Tsokos, K.M. Ramachandran

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