Suppose a certain type of fertilizer has an expected yield per acre of 1 with variance s2

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Suppose a certain type of fertilizer has an expected yield per acre of 1 with variance s2

, whereas the expected yield for a second type of fertilizer is 2 with the same variance s2

.

Let and 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 s2

.

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