SOA Exam P Sample Question 394

Study guide: Exam P-1

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

 $f(x) = \begin{cases} \left(\dfrac{1}{\beta}\right)e^{-(x-d)/\beta}, & \text{for } x \geq d \\ 0, & \text{otherwise,} \end{cases}$

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

Determine the absolute value of the difference between the mode of $X$ and 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) $\dfrac{1}{\beta}\ln\left(\dfrac{11}{10}\right)$

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