Revision as of 19:18, 15 January 2024 by Admin (Created page with "You are given the survival function: <math display = "block">S_{0}(x)=\left(1-\frac{x}{60}\right)^{\frac{1}{3}}, \quad 0 \leq x \leq 60</math>. Calculate <math>1000 \mu_{35}</math>. <ul class="mw-excansopts"><li> 5.6</li><li> 6.7</li><li> 13.3</li><li> 16.7</li><li> 20.1</li></ul>")
Jan 15'24
Exercise
You are given the survival function:
[[math]]S_{0}(x)=\left(1-\frac{x}{60}\right)^{\frac{1}{3}}, \quad 0 \leq x \leq 60[[/math]]
.
Calculate [math]1000 \mu_{35}[/math].
- 5.6
- 6.7
- 13.3
- 16.7
- 20.1
Jan 15'24
Answer: C
[[math]]
\begin{aligned}
\mu_{x} & =-\frac{d}{d_{x}} \ln S_{0}(x)=-\frac{1}{3} \frac{d}{d_{x}} \ln \left(1-\frac{x}{60}\right) \\
& =\frac{1}{180}\left(1-\frac{x}{60}\right)^{-1}=\frac{1}{3(60-x)}
\end{aligned}
[[/math]]
Therefore, [math]1000 \mu_{35}=(1000) \frac{1}{3(25)}=\frac{1000}{75}=13.3[/math].
Copyright 2024 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.