**Both Problems 11-A and 11-B use the following information**.

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

The following provides more information about these risks:

- For each risk in Class 1, the number of claims in a year has a Poisson distribution with mean 1.
- For each risk in Class 2, the number of claims in a year has a Poisson distribution with mean 2.5.

A randomly selected risk from this portfolio has 2 claims in year 1 and 2 claims in year 2.

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**Problem 11-A**

What is the Bayesian estimate of the number of claims in the next year?

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**Problem 11-B**

What is the Buhlmann estimate of the number of claims in the next year?

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Tagged: Actuarial Exam, Bayesian Credibility, Bayesian Probability, 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

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