* Both Problems 24-A and 24-B use the following information*.

You are given the following information:

- The claim size of an insured has an exponential distribution with mean .
- The parameter has a Gamma distribution with mean 6 and variance 12.

A randomly selected insured has one claim of size 10.

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**Problem 24-A**

What is the Bayesian estimate of the expected amount of the next claim for this insured?

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**Problem 24-B**

What is the posterior probability that the size of the next claim for this insured will be greater than 5?

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