**Problem 19-A**

The number of claims in a year for an insurance policy in a large pool of insurance policies has a distribution with mean and variance .

The following provides more information about the large pool of insurance policies.

- For half of the insurance policies in the large pool , while for the other half .
- For three-quarters of the insurance policies in the large pool , while for the other one-quarter .

An insurance policy is randomly selected from the large pool. Insurance company records indicate that there are 6 claims in last 5 years.

Determine the Buhlmann credibility estimate of the number of claims for the selected insurance policy in the next year.

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**Problem 19-B**

The number of claims in a year for an insurance policy in a large pool of insurance policies has a distribution with mean and variance .

The following provides more information about the large pool of insurance policies.

- For three-quarters of the insurance policies in the large pool , while for the other one-quarter .
- For one-quarter of the insurance policies in the large pool , while for the other three-quarters .

An insurance policy is randomly selected from the large pool.

Determine the Buhlmann credibility factor assigned to 5 years of claim data from the selected insurance policy.

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Tagged: Actuarial Exam, Buhlmann Credibility, CAS Exam 4, CAS Exam 4 Practice Problem, Frequency, Loss Models, Probability, SOA Exam C, SOA Exam C Practice Problem, Variance

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