With reference to Exercise 10.23, find the efficiency of the estimator with ω = 1/2 relative to the estimator with ω = n1/ n1 + n2.
Answer to relevant QuestionsIf X1, X2, and X3 constitute a random sample of size n = 3 from a normal population with the mean µ and the variance σ2, find the efficiency of X1 + 2X2 + X3 / 4 relative to X1 + X2 + X3 / 3 as estimates of µ. Use the formula for the sampling distribution of 8 X on page 253 to show that for random samples of size n = 3 the median is an unbiased estimator of the parameter θ of a uniform population with α = θ – 12 and β = θ + ...Substituting “asymptotically unbiased” for “ unbiased” in Theorem 10.3, show that X + 1 / n+ 2 is a consistent estimator of the binomial parameter θ. If X1 and X2 constitute a random sample of size n = 2 from a Poisson population, show that the mean of the sample is a sufficient estimator of the parameter λ. Use the method of maximum likelihood to rework Exercise 10.53. In exercise Given a random sample of size n from a Poisson population, use the method of moments to obtain an estimator for the parameter λ.
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