1 Actually carry out the analysis in Example 6 4, where the prior g() in (6 6) is (a) the Unif(0, 1) prior used in the example, g() 1 (b) a mixture of two Beta priors, g() 5 32 5 302(1 2) What is the optimal sample size n in each case Is either prior amenable to a fully analytical solution (i e, without resort to Monte Carlo sampling)

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Question: 1. Actually carry out the analysis in Example 6.4, where the prior g() in (6.6) is (a) the Unif(0, 1) prior used in the example,

1. Actually carry out the analysis in Example 6.4, where the prior g(θ) in

(6.6) is

(a) the Unif(0, 1) prior used in the example, g(θ) = 1.

(b) a mixture of two Beta priors, g(θ) = .5 · 3θ2 + .5 · 30θ2(1 − θ2).

What is the optimal sample size ˜n in each case? Is either prior amenable to a fully analytical solution (i.e, without resort to Monte Carlo sampling)?

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