**Problem 7-A**

You are given the following information:

- The number of claims in a calendar year for a given risk follows a Poisson distribution with mean .
- The risk parameter follows a Gamma distribution whose coefficient of variation is 0.5.
- After observing the given risk for 5 calendar years, twelve claims are observed.
- Based on the observed data, the posterior distribution of is a continuous distribution whose mean is 2.0.

What is the Buhlmann credibility used in estimating the expected claim frequency for the given risk in the next period?

**Problem 7-B**

You are given the following information:

- The number of claims in a calendar year for a given risk follows a Poisson distribution with mean .
- The risk parameter follows a Gamma distribution with mean 1.5.
- The value of Buhlmann’s k is 8.
- After observing the given risk for 4 calendar years, the posterior distribution of is a continuous distribution whose mean is 1.75

What is the number of claims observed in the observation period?

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Tagged: Actuarial Exam, Bayesian Credibility, Buhlmann Credibility, CAS Exam 4, CAS Exam 4 Practice Problem, Coefficient of Variation, Frequency, Gamma Distribution, Loss Models, Poisson Claim Frequency, Poisson Distribution, Poisson-Gamma Model, Posterior Distribution, Prior Distribution, Probability, SOA Exam C, SOA Exam C Practice Problem

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