Actuary P/1 Exam Question

Question

Problem I am having trouble with

I was taking a practice exam and I don't understand a step in one of the solutions to the problem. I understand every part except why $f(y^{0.5})=8(y^{0.5})^{-3}$ If someone could help explain that to me it would be very helpful.

Edit: Just to be clear I am only referring to the second solution provided that starts at "Alternatively"

Basically the parameter for the function $f(y)$ was $y$, now they are just substituting $y^{0.5}$ for $y$ — Varun Iyer, Jul 17 '14 at 20:43

score 3 · Answer 1 · answered Jul 17 '14 at 20:46

3

There is a typo that may be the cause of the confusion. The density function $f(t)$ of $T$, for $t\gt 2$, is $\frac{8}{t^3}$. This is obtained by differentiating the cdf, which is $1-\frac{4}{t^2}$. After that, it is direct substitution of $y^{0.5}$ for $t$.

answered Jul 17 '14 at 20:46

André Nicolas

507,029

That explains everything, thank you. – Robert Maggio Jul 17 '14 at 21:01
You are welcome. – André Nicolas Jul 17 '14 at 21:17

Actuary P/1 Exam Question

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