**Problem 4-A**

You are given the following:

- The number of claims in a calendar year for a given risk follows a Poisson distribution with mean .
- The prior distribution of has a uniform distribution on .

After observing for three calendar years, this risk is found to have incurred 1 claim in year 1, 2 claims in year 2 and 3 claims in year 3.

Determine the Buhlmann credibility estimate for the expected claim frequency for the given risk in year 4.

**Problem 4-B**

You are given the following:

- The number of claims in a calendar year for a given risk follows a Poisson distribution with mean .
- The prior distribution of has the following density function.

The given risk is observed for 6 calendar years and is found to have incurred a total of 10 claims.

Determine the Buhlmann credibility estimate for the expected claim frequency for the given risk for the next calendar year.

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Tagged: Actuarial Exam, Buhlmann Credibility, CAS Exam 4, CAS Exam 4 Practice Problem, Frequency, Loss Models, Poisson Claim Frequency, Poisson Distribution, Probability, SOA Exam C, SOA Exam C Practice Problem, Uniform Distribution

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