**Problem 3-A**

A portfolio of independent risks is divided into two classes. Class 1 contains 60% of the risks in the portfolio and the remaining risks are in Class 2.

For each risk in the portfolio, the following shows the distributions of the number of claims in a calendar year.

A risk is randomly selected in the portfolio and is observed for two calendar years. The observed results are: 2 claim in the first calendar year and 3 claims in the second calendar year.

Determine the Bayesian expected number of claims for the selected risk in year 3.

**Problem 3-B**

Using the same information as in Problem 3-A, determine the Buhlmann credibility estimate for the selected risk in year 3.

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

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