Question: If X1 and X2 constitute a random sample of size
If X1 and X2 constitute a random sample of size n = 2 from an exponential population, find the efficiency of 2Y1 relative to , where Y1 is the first order statistic and 2Y1 and are both unbiased estimators of the parameter θ.
Answer to relevant QuestionsVerify the result given for var(n + 1 / n ∙ Yn) in Example 10.6. Show that if Θ is a biased estimator of θ, then Substituting “asymptotically unbiased” for “ unbiased” in Theorem 10.3, use this theorem to rework Exercise 10.35. If X1, X2, . . . , Xn constitute a random sample of size n from a geometric population, show that Y = X1 + X2 + · · · + Xn is a sufficient estimator of the parameter θ. Use the method of maximum likelihood to rework Exercise 10.54. In exercise Given a random sample of size n from a beta population with β = 1, use the method of moments to find a formula for estimating the parameter α.
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