Revision as of 19:19, 15 January 2024 by Admin (Created page with "You are given the following survival function of a newborn: <math display="block"> S_{0}(x)= \begin{cases}1-\frac{x}{250}, & 0 \leq x<40 \\ 1-\left(\frac{x}{100}\right)^{2}, & 40 \leq x \leq 100\end{cases} </math> Calculate the probability that (30) dies within the next 20 years. <ul class="mw-excansopts"><li> 0.13</li><li> 0.15</li><li> 0.17</li><li> 0.19</li><li> 0.21</li></ul>")
Jan 15'24
Exercise
You are given the following survival function of a newborn:
[[math]]
S_{0}(x)= \begin{cases}1-\frac{x}{250}, & 0 \leq x\lt40 \\ 1-\left(\frac{x}{100}\right)^{2}, & 40 \leq x \leq 100\end{cases}
[[/math]]
Calculate the probability that (30) dies within the next 20 years.
- 0.13
- 0.15
- 0.17
- 0.19
- 0.21
Jan 15'24
Answer: B
[[math]]
\begin{aligned}
& { }_{20} q_{30}=\frac{S_{0}(30)-S_{0}(50)}{S_{0}(30)}=\frac{\left(1-\frac{30}{250}\right)-\left(1-\left[\frac{50}{100}\right]^{2}\right)}{1-\frac{30}{250}}=\frac{\frac{220}{250}-\frac{3}{4}}{\frac{220}{250}} \\
& =\frac{440-375}{440}=\frac{65}{440}=\frac{13}{88}=0.1477
\end{aligned}
[[/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.