SOA Exam P Sample Question 589
Study guide: Exam P-1
In a one-year period, the number of fires that occur in buildings insured by ABC insurance is Poisson distributed with mean 12. The resulting losses are independent random variables that are also independent of the number of losses, each having density function
f(x) = \begin{cases}
\dfrac{8-x}{32}, & \text{for } 0 < x < 8 \\
0, & \text{otherwise.}
\end{cases}The payment for any loss is equal to the amount of the loss in excess of a deductible of 2.
Calculate the expected total payment that ABC must make for losses due to fire that occur in a one-year period.
- A)
8.0 - B)
13.5 - C)
16.5 - D)
30.0 - E)
32.0
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