Question: 15. In the interval estimation setting involving a beta prior and a binomial likelihood, (a) Under what condition on the prior will the HPD interval

15. In the interval estimation setting involving a beta prior and a binomial likelihood,

(a) Under what condition on the prior will the HPD interval for θ be one-sided when X = n? Find this interval.

(b) Outline a specific interval-halving algorithm to find the HPD interval

(θL, θU ). Use your algorithm to find the 95% HPD interval when a = b = 1, n = 5, and x = 1. What percentage reduction in width does the HPD interval offer over the equal tail interval in this case?

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