Suppose a certain type of fertilizer has an expected Yield per acre of 1 with variance 2, whereas the expected Yield for a second type of fertilizer is 2 with the same variance 2 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 2 2 n2 2

Question: Suppose a certain type of fertilizer has an expected Yield per acre of 1 with variance 2, whereas the expected Yield for a second type

Suppose a certain type of fertilizer has an expected Yield per acre of Âµ1 with variance Ïƒ2, whereas the expected Yield for a second type of fertilizer is Ïƒ2 with the same variance Ïƒ2. 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 Ïƒ2.

2 = + n2-2

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