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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