1)Let three random samples of sizes n 1 20, n 2 10, and n 3 8 be taken from a population with mean and variance 2 Let 1 2 , 2 2 , and 3 2 be the sample variances Show that 2 (20 1 2 10 2 2 8 3 2 ) 38 is an unbiased estimator of 2 (Hint For a population with a variance of 2 , the sample variance 2 is an unbiased estimator )

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Question: 1)Let three random samples of sizes n 1 = 20, n 2 = 10, and n 3 = 8 be taken from a population with

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 ₃²be 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.)

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