exercise:D83ed133f2

You are given the following information about [math]N[/math], the annual number of claims for a randomly selected insured:

[[math]] \operatorname{P}[N = 0] = \frac{1}{2}, \, \operatorname{P}[N = 1] = \frac{1}{3}, \, \operatorname{P}[N \gt1] = \frac{1}{6} [[/math]]

Let [math]S[/math] denote the total annual claim amount for an insured. When [math]N = 1 [/math], [math]S[/math] is exponentially distributed with mean 5. When [math]N \gt 1 [/math], [math]S[/math] is exponentially distributed with mean 8.

Calculate [math]\operatorname{P}(4 \lt S \lt 8) [/math]

• 0.04
• 0.08
• 0.12
• 0.24
• 0.25

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.