Suppose a certain type of fertilizer has an expected Yield per acre of 1 with variance 2,

Suppose a certain type of fertilizer has an expected Yield per acre of µ1 with variance σ2, whereas the expected Yield for a second type of fertilizer is σ2 with the same variance σ2. Let S21 and S22 denote the sample variances of Yields based on sample sizes n1 and n2, respectively, of the two fertilizers. Show that the pooled (combined) estimator

is an unbiased estimator of σ2.

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σ2 = + n2-2