1)Let three random samples of sizes n₁ = 20, n₂ = 10, and n₃ = 8 be taken from a population with mean and variance ². Let ₁², ₂², and ₃² be the sample variances. Show that ² =

(20₁² + 10₂² + 8₃²)/38 is an unbiased estimator of ². (Hint: For a population with a variance of ² , the sample variance ² is an unbiased estimator.)