Exercise
ABy Admin
May 14'23
Answer
Key: B
First obtain the distribution of aggregate losses:
| Value | Probability |
|---|---|
| 0 | [math]1 / 5[/math] |
| 25 | [math](3 / 5)(1 / 3)=1 / 5[/math] |
| 100 | [math](1 / 5)(2 / 3)(2 / 3)=4 / 45[/math] |
| 150 | [math](3 / 5)(2 / 3)=2 / 5[/math] |
| 250 | [math](1 / 5)(2)(2 / 3)(1 / 3)=4 / 45[/math] |
| 400 | [math](1 / 5)(1 / 3)(1 / 3)=1 / 45[/math] |
[[math]]\begin{aligned}
& \mu=(1 / 5)(0)+(1 / 5)(25)+(4 / 45)(100)+(2 / 5)(150)+(4 / 45)(250)+(1 / 45)(400)=105 \\
& \sigma^{2}=(1 / 5)\left(0^{2}\right)+(1 / 5)(25)+(4 / 45)\left(100^{2}\right)+(2 / 5)\left(150^{2}\right)+(4 / 45)\left(250^{2}\right) \\
& +(1 / 45)\left(400^{2}\right)-105^{2}=8100
\end{aligned}[[/math]]
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.