SOA Exam P Sample Question 496
Study guide: Exam P-1
Three identical machines are purchased simultaneously and are still operating after one year. The manufacturer then buys an insurance policy that pays 1000 if any of the three machines fails during the second year of use. The three machines operate independently.
The age at failure, in years, for each of these machines has cumulative distribution function
F(x) = \begin{cases}
1 - \left(\dfrac{1}{x}\right)^{1/4}, & \text{for } x \geq 1 \\
0, & \text{otherwise.}
\end{cases}Note that x \geq 1 because each machine has already successfully completed one year of operation.
Calculate the expected claim payment for this policy.
- A)
4 - B)
159 - C)
405 - D)
595 - E)
996
Answer this question and see the worked solution