# Question

With reference to Exercise 10.33, use Theorem 10.3 to show that Y1 – 1/n+1 is a consistent estimator of the parameter α.

## Answer to relevant Questions

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 ...If X1, X2, . . . , Xn constitute a random sample of size n from an exponential population, show that is a sufficient estimator of the parameter θ. Show that the estimator of Exercise 10.5 is a sufficient estimator of the variance of a normal population with the known mean µ. Exercise 10.5 Show that is a minimum variance unbiased estimator of the mean µ of a normal ...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. Given a random sample of size n from a gamma population with the known parameter α, find the maximum likelihood estimator for (a) β; (b) t = (2β – 1) 2.Post your question

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