Question: If 1 and 2 are the means of independent random
If 1 and 2 are the means of independent random samples of sizes n1 and n2 from a normal population with the mean µ and the variance σ2, show that the variance of the unbiased estimator
Is a minimum when ω = n1 / n1 + n2
Answer to relevant QuestionsWith reference to Exercise 10.23, find the efficiency of the estimator with ω = 1/2 relative to the estimator with ω = n1/ n1 + n2. With reference to Exercise 10.12, show that 2X – 1 is also an unbiased estimator of k, and find the efficiency of this estimator relative to the one of part (b) of Exercise 10.12 for (a) n = 2; (b) n = 3. With reference to the uniform population of Example 10.4, use the definition of consistency to show that Yn, the nth order statistic, is a consistent estimator of the parameter β. Example 10.4 If X1, X2, . . . , Xn ...After referring to Example 10.4, is the nth order statistic, Yn, a sufficient estimator of the parameter β? Consider N independent random variables having identical binomial distributions with the parameters θ and n = 3. If no of them take on the value 0, n1 take on the value 1, n2 take on the value 2, and n3 take on the value 3, ...
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