SOA Exam FAM Sample Question 4.18
Study guide: Exam FAM
You are given that T, the time to first failure of an industrial robot, has a density f(t) given by
f(t) = \begin{cases} 0.1, & 0 \le t < 2 \\ 0.4t^{-2}, & 2 \le t < 10 \end{cases}
with f(t) undetermined on [10, \infty).
Consider a supplemental warranty on this robot that pays 100,000 at the time T of its first failure if 2 \le T \le 10, with no benefits payable otherwise.
You are also given that \delta = 5\%.
Calculate the 90th percentile of the present value of the future benefits under this warranty.
[Question 5 on the Spring 2017 exam]
- A) 82,000
- B) 84,000
- C) 87,000
- D) 91,000
- E) 95,000
Answer this question and see the worked solution