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May 06'23
Exercise
Claim amounts are independent random variables with probability density function
[[math]]
f(x) = \begin{cases}
\frac{10}{x^2}, \, x \gt10 \\
0, \, \textrm{otherwise}
\end{cases}
[[/math]]
Calculate the probability that the largest of three randomly selected claims is less than 25.
- 8/125
- 12/125
- 27/125
- 2/5
- 3/5
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
May 06'23
Solution: C
The probability that a single claim is less than 25 is
[[math]]
\operatorname{P}( X \leq 25) = \int_{10}^{25} 10x^{-2} dx = 3/5.
[[/math]]
The probability that all three claims are less than 25 is (3 / 5)3 = 27 /125.
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.