**Problem 6-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 the Gamma distribution with mean 2 and variance 1.

After observing this risk for five calendar years, a total of 12 claims are observed.

Which of the following is the moment generating function of the posterior distribution of ?

**Problem 6-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 Gamma distribution with mean 4 and variance .

After observing this risk for eight calendar years, a total of 32 claims are observed.

Determine the coefficient of variation of the posterior distribution of .

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Tagged: Actuarial Exam, Bayesian Credibility, CAS Exam 4, CAS Exam 4 Practice Problem, Coefficient of Variation, Frequency, Gamma Distribution, Moment Generating Function, Poisson Claim Frequency, Poisson Distribution, Poisson-Gamma Model, Posterior Distribution, Prior Distribution, SOA Exam C, SOA Exam C Practice Problem

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