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Question: specifically suppose that xi x2 xn denote n payments...

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Specifically, suppose that Xi, X2, .., Xn denote n payments, modeled as iid random variables with common Weibull pdf 0, otherwise, where m > 0 is known and θ is unknown. In turn, suppose that θ ~ IG(α, β), that is, θ has an inverted gamma (prior) pdf 0, otherwise (a) Prove that the inverted gamma IG(α, β) prior is a conjugate prior for the Weibull family above. (b) Suppose that m-2, α-05, and β-2. Here are n-10 insurance payments (measured in $10,000s): 0.2697 0.0719 0.4698 0.8192 3.9700 0.2681 0.2415 2.8351 0.0885 0.1180 Find the posterior mean of

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