SOA Exam P Sample Question 375
Study guide: Exam P-1
The length of time, T, in months, taken by relatives to file for a death benefit has density function
f(t) = \begin{cases}
\dfrac{4\beta^4}{t^5}, & \text{for } t > \beta,\ 0 < \beta < 3 \\
0, & \text{otherwise.}
\end{cases}Calculate the probability that the relatives of a policyholder will not file for the death benefit in the next four months, given that the policyholder died three months ago and the relatives have not yet filed for the death benefit.
- A)
\dfrac{81}{2401} - B)
\dfrac{256}{2401} - C)
\dfrac{81}{256} - D)
\dfrac{2401}{81}\left(\dfrac{81-\beta^4}{2401-\beta^4}\right) - E)
\dfrac{2401}{256}\left(\dfrac{256-\beta^4}{2401-\beta^4}\right)
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