Suppose a certain type of fertilizer has an expected yield per acre of μ1 with variance...

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

is an unbiased estimator of σ².