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"
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 $t$.