A point is picked randomly in space. Its three coordinates $X$, $Y$, and $Z$ are independent standard normal variables. Let $R = \sqrt{X^2+Y^2+Z^2}$ be the distance from the point from the origin. Find:
a) The density of $R^2$ (don't get how to set up the integral for this)
b) The density of $R$ (don't get part a)
c) $E(R)$
d) $\textrm{Var}(R)$
I don't get how to use the change of variables since we are dealing with $X$, $Y$ and a $Z$. Can you please explain how I can do this? Also, can it be done using spherical coordinates? I am lost on the coordinates available for us on this problem.