**Both Problems 17-A and 17-B use the following information**.

An insurance portfolio consists of independent risks.

For each risk in this portfolio, the number of claims in a year has a Poisson distribution with mean . The parameter follows a Gamma distribution.

A risk is randomly selected from this portfolio. Prior to obtaining any claim experience, the number of claims in a year for this risk has a distribution with mean 0.6 and variance 0.72.

After observing this risk for one year, insurance company records indicate that there are 2 claims for this risk.

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**Problem 17-A**

After knowing the insurance company records, what is the expected number of claims per year for this risk?

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**Problem 17-B**

After knowing the insurance company records, what is the variance of the number of claims per year for this risk?

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Tagged: Actuarial Exam, Bayesian Credibility, Bayesian Probability, CAS Exam 4, CAS Exam 4 Practice Problem, Frequency, Gamma Distribution, Loss Models, Poisson Claim Frequency, Poisson Distribution, Poisson-Gamma Model, Posterior Distribution, Prior Distribution, Probability, SOA Exam C, SOA Exam C Practice Problem, Variance

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