Finding new probability density function with change of variable Y=sqrt(X) Say we have a given distribution, such as X~No(a, b). I am trying to find the pdf and mean for $Y=\sqrt{X}$. 
I know the steps for finding the PDF, but since Y can only take on positive values, then the new PDF is only valid for Y>0. 
Then how does this affect the mean, and how would I go about finding the mean? 

If $Y=\sqrt{|X|}$, then, for every $y\gt0$,
$$
f_Y(y)=2y\cdot(f_X(y^2)+f(-y^2)).$$
