**Both Problems 16-A and 16-B use the following information**.

A portfolio consists of independent risks divided into two classes. Sixty percent of the risks are in Class 1 and forty percent are in Class 2.

The following has more information about Class 1:

- The annual number of claims for a single risk in Class 1 follows a Poisson distribution with mean 1.
- The claim size follows a Gamma distribution with mean 1.6 and variance 1.28.
- The number of claims and the claim sizes are independent

The following has more information about Class 2:

- The annual number of claims for a single risk in Class 2 follows a Poisson distribution with mean 2.6.
- The claim size follows a Gamma distribution with mean 2.5 and variance 3.125.
- The number of claims and the claim sizes are independent

A risk is randomly selected from this portfolio. According to the records of the insurer, there are 4 claims for this risk in the amounts 2, 3, 5 and 5 within the last 3 years.

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**Problem 16-A**

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

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**Problem 16-B**

Determine the Buhlmann credibility estimate for the number of claims for this risk in the next year.

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Tagged: Actuarial Exam, Aggregate Claims, Buhlmann Credibility, CAS Exam 4, CAS Exam 4 Practice Problem, Frequency, Frequency-Severity Model, Gamma Distribution, Loss Models, Poisson Claim Frequency, Poisson Distribution, Poisson-Gamma Model, Probability, Pure Premium, Severity, SOA Exam C, SOA Exam C Practice Problem, Variance

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