I am having problem with a probablity theory question.
Given that $X$ is a $N(0,1)$-distributed (normal) random variable. Find the density funciton of $X^2$.
So, i put $X^2 = Y$.
$F_Y(y) = P(Y \le y) = P(X^2 \le y) = P(X \le\sqrt y) = F_X(\sqrt y)$
This is where i get stuck. How do i differentiate $F_X(\sqrt y)$ in order to find $f_Y(y)$?
Thanks and best regards!