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 μ2 with the same variance σ2. let s12 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 below is an unbiased estimator of σ2. sigma hat2 = (n1 − 1)s12 + (n2 − 1)s22 n1 + n2 − 2 e (n1 − 1)s12 + (n2 − 1)s22 n1 + n2 − 2 = n1 − 1 n1 + n2 − 2 e + n2 − 1 n1 + n2 − 2 e = n1 − 1 n1 + n2 − 2 + n2 − 1 n1 + n2 − 2 = σ2