SOA Exam P Sample Question 680

Study guide: Exam P-1

The loss, $X$ , subject to reimbursement under an insurance policy, has a distribution with density function

 $f(x) = \begin{cases} \left(\dfrac{1}{\beta}\right)e^{-\frac{(x-d)}{\beta}}, & \text{for } x \ge d \\[6pt] 0, & \text{otherwise,} \end{cases}$

where $d$ is the deductible, and $\beta$ is a positive constant.

Determine the 10th percentile of $X$ .

A) $\beta \ln\left(\dfrac{11}{10}\right)$
B) $\beta \ln\left(\dfrac{10}{9}\right)$
C) $\beta \ln\left(\dfrac{11}{10}\right) + d$
D) $\beta \ln\left(\dfrac{10}{9}\right) + d$
E) $\dfrac{1}{\beta}\ln\left(\dfrac{11}{10}\right)$

Concepts tested