SOA Exam FAM Sample Question 4.10
Study guide: Exam FAM
The present value random variable for an insurance policy on (x) is expressed as:
Z = \begin{cases} 0, & \text{if } T_{x} \le 10 \\ v^{T_{x}}, & \text{if } 10 < T_{x} \le 20 \\ 2v^{T_{x}}, & \text{if } 20 < T_{x} \le 30 \\ 0, & \text{thereafter} \end{cases}
Determine which of the following is a correct expression for E[Z].
[Question 4 on the Spring 2015 exam]
- A)
{}_{10|}\bar{A}_{x} + {}_{20|}\bar{A}_{x} - {}_{30|}\bar{A}_{x} - B)
\bar{A}_{x} + {}_{20}E_{x}\,\bar{A}_{x+20} - 2\,{}_{30}E_{x}\,\bar{A}_{x+30} - C)
{}_{10}E_{x}\,\bar{A}_{x} + {}_{20}E_{x}\,\bar{A}_{x+20} - 2\,{}_{30}E_{x}\,\bar{A}_{x+30} - D)
{}_{10}E_{x}\,\bar{A}_{x+10} + {}_{20}E_{x}\,\bar{A}_{x+20} - 2\,{}_{30}E_{x}\,\bar{A}_{x+30} - E)
{}_{10}E_{x}\left[\bar{A}_{x+10} + {}_{10}E_{x+10}\,\bar{A}_{x+20} - {}_{10}E_{x+20}\,\bar{A}_{x+30}\right]
Answer this question and see the worked solution