**Problem 15-A**

You are given the following:

- The annual number of claims generated for a single risk follows a Poisson distribution with mean .
- The claim size follows a uniform distribution on .
- The risk parameter is a random variable with density function where .
- Given , the number of claims and the claim sizes are independent.

According to the records of the insurer, there are 4 claims in the amounts 5, 5, 15 and 20 within the last 5 years.

Determine the Buhlmann credibility estimate for total claim costs in the next year.

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**Problem 15-B**

You are given the following:

- The annual number of claims generated for a single risk follows a Poisson distribution with mean .
- The claim size follows a uniform distribution on .
- The prior distribution of has a uniform distribution on .
- Given , the number of claims and the claim sizes are independent.

According to the records of the insurer, there are 5 claims in the total amount of 360 within the last 3 years.

Determine the Buhlmann credibility estimate for total claim costs in the next year.

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