Exam P Practice Problem 34 – Number of Claims

Problem 34A

An actuary is asked to review the claim history in a two-year period for one policyholder. The number of claims in any year for this policyholder has a Poisson distribution with mean 0.5 and is independent of the number of claims in any previous year.

The actuary finds that the policyholder has made 5 claims in the two-year period.

What is the probability that the policyholder has made more than three claims in the first year of the review period?

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Problem 34B

An actuary is asked to review the claim history in a two-year period for one policyholder. In the first year of the review period, the number of claims for this policyholder has a Poisson distribution with mean 0.3. In the second year, the number of claims for this policyholder has a Poisson distribution with mean 0.6.

The number of claims in one year is independent of the number of claims in any previous year.

The actuary finds that the policyholder has made 5 claims in the review period. What is the probability that the policyholder has made at least three claims in the first year of the review period?

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