**Problem 26-A**

You are given the following about a large portfolio of insurance policies:

- For each insurance policy, the annual number of claims follows a binomial distribution with = 3 and = 0.3.
- The claim size follows an inverse Gamma distribution with = 2.1 and = 3.
- The number of claims and the claim sizes are independent.
- The full credibility standard has been selected so that actual claim costs will be

within 10% of expected claim costs 90% of the time.

Using limited fluctuation credibility, determine the expected number of claims required for full credibility.

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**Problem 26-B**

You are given the following about a large portfolio of insurance policies:

- For each insurance policy, the annual number of claims follows a binomial distribution with = 6 and = 0.1.
- The claim size follows a Gamma distribution with = 0.8 and = 1.
- The number of claims and the claim sizes are independent.
- The full credibility standard has been selected so that actual claim costs will be

within 10% of expected claim costs 90% of the time.

Using limited fluctuation credibility, determine the expected number of exposures required for full credibility.

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Tagged: Actuarial Exam, Binomial Distribution, CAS Exam 4, CAS Exam 4 Practice Problem, Frequency, Frequency-Severity Model, Full Credibility Standard, Gamma Distribution, Inverse Gamma Distribution, Limited Fluctuation Credibility, Loss Models, Probability, Pure Premium, Severity, SOA Exam C, SOA Exam C Practice Problem

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