Suppose that X1, , Xm form a random sample from the normal distribution with mean1 and variance 2, and Y1, , Yn form an independent random sample from the normal distribution with mean 2 and variance 22 Let a For what pairs of values of and is S2X S2Y an unbiased estimator of 2 b Determine the values of and for which S2X S2Y will be an unbiased estimator with minimum variance

Question: Suppose that X1, . . . , Xm form a random sample from the normal distribution with mean1 and variance 2, and Y1, . .

Suppose that X1, . . . , Xm form a random sample from the normal with meanμ1 and variance σ2, and Y1, . . . , Yn form an independent random sample from the normal with mean μ2 and variance 2σ2. Let
a. For what pairs of values of α and β is αS2X + βS2Y an unbiased estimator of σ2?
b. Determine the values of α and β for which αS2X + βS2Y will be an unbiased estimator with minimum variance.

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a ES 2 X S 2 Y m 1 2 n 12 2 Hence this estimator will be unbiased if m 1 2n 1 1 b Since S 2 X and ... View full answer

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