Revision as of 23:12, 18 January 2024 by Admin (Created page with "'''Answer: A''' <math>E(Y)=\bar{a}_{10}+e^{-\delta(10)} e^{-\mu(10)} \bar{a}_{x+10}</math> <math>=\frac{\left(1-e^{-0.6}\right)}{0.06}+e^{-0.7} \frac{1}{0.07}</math> <math>=14.6139</math> <math>Y > E(Y) \Rightarrow\left(\frac{1-e^{-0.06 T}}{0.06}\right)>14.6139</math> <math>\Rightarrow T >34.90</math> <math>\operatorname{Pr}[Y > E(Y)]=\operatorname{Pr}(T>34.90)=e^{-34.90(0.01)}=0.705</math> {{soacopyright|2024}}")
Exercise
Jan 18'24
Answer
Answer: A
[math]E(Y)=\bar{a}_{10}+e^{-\delta(10)} e^{-\mu(10)} \bar{a}_{x+10}[/math]
[math]=\frac{\left(1-e^{-0.6}\right)}{0.06}+e^{-0.7} \frac{1}{0.07}[/math]
[math]=14.6139[/math]
[math]Y \gt E(Y) \Rightarrow\left(\frac{1-e^{-0.06 T}}{0.06}\right)\gt14.6139[/math]
[math]\Rightarrow T \gt34.90[/math]
[math]\operatorname{Pr}[Y \gt E(Y)]=\operatorname{Pr}(T\gt34.90)=e^{-34.90(0.01)}=0.705[/math]
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.