Exam C Practice Problem 11 – Estimating Claim Frequency

Both Problems 11-A and 11-B use the following information.

A portfolio consists of independent risks divided into two classes. Seventy percent of the risks are in Class 1 and thirty percent are in Class 2.

The following provides more information about these risks:

  • For each risk in Class 1, the number of claims in a year has a Poisson distribution with mean 1.
  • For each risk in Class 2, the number of claims in a year has a Poisson distribution with mean 2.5.

A randomly selected risk from this portfolio has 2 claims in year 1 and 2 claims in year 2.

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Problem 11-A

What is the Bayesian estimate of the number of claims in the next year?

\text{ }

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1.65

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1.66

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1.67

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1.68

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1.75

\text{ }

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\text{ }

\text{ }

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Problem 11-B

What is the Buhlmann estimate of the number of claims in the next year?

\text{ }

      \displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1.65

      \displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1.66

      \displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1.67

      \displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1.68

      \displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1.75

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\copyright \ 2013 \ \ \text{Dan Ma}

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