12. 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 S2 1 and S2 2 denote the sample variances of yields based on sample sizes n1 and n2, respectively, of the two fertilizers.

Show that the pooled (combined) estimator

ˆ 2

is an unbiased estimator of 2

.