# Exam P Practice Problem 22 – Poisson Number of Claims

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Problem 22A
Ten percent of the policyholders for an auto insurance company are considered high risk and ninety percent of its policyholders are considered low risk. The number of claims made by a policyholder in a calendar year follows a Poisson distribution with mean $\lambda$.

For high risk policyholders, $\lambda=0.9$. For low risk policyholders, $\lambda=0.1$. An actuary selects one policyholder at random. What is the expected number of claims made by this policyholder in the next calendar year?

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Problem 22B
Use the same information as in Problem 22A. What is the variance of the number of claims made by this randomly selected policyholder?

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