# Question

If we assume in Example 9.8 that is a random variable having a uniform density with α = 0 and β = 1, show that the Bayes risk is given by

Also show that this Bayes risk is a minimum when a = 1 and b = 2, so that the optimum Bayes decision rule is given by d( x) = x+ 1 / n+ 2 .

Also show that this Bayes risk is a minimum when a = 1 and b = 2, so that the optimum Bayes decision rule is given by d( x) = x+ 1 / n+ 2 .

## Answer to relevant Questions

Verify the results given on page 273 for the marginal density of X and the conditional density of given X = x. If a random sample of size n is taken without replacement from the finite population that consists of the positive integers 1, 2, . . . , k, show that (a) The sampling distribution of the nth order statistic, Yn, is given ...Rework Example 10.5 using the alternative formula for the information given in Exercise 10.19. Example 10.5 Show that is a minimum variance unbiased estimator of the mean µ of a normal population. With reference to Example 10.3, we showed on page 281 that – 1 is an unbiased estimator of d, and in Exercise 10.8 the reader was asked to find another unbiased estimator of d based on the smallest sample value. Find the ...Substituting “asymptotically unbiased” for “ unbiased” in Theorem 10.3, show that X + 1 / n+ 2 is a consistent estimator of the binomial parameter θ.Post your question

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