Find the value of θ that maximizes the risk function of Example 9.8, and then find the values of a and b that minimize the risk function for that value of θ. Compare the results with those given on page 272.
Answer to relevant QuestionsIf 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 ...If X is a random variable having the binomial distribution with the parameters n and θ, show that n ∙ X/n ∙ (1 – X/n) is a biased estimator of the variance of X. The information about θ in a random sample of size n is also given by Where f (x) is the value of the population density at x, provided that the extremes of the region for which f(x) ≠ 0 do not depend on θ. The ...Verify the result given for var(n + 1 / n ∙ Yn) in Example 10.6. 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 ...
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