Given
Z = $X_1^2$ + $X_2^2$
how can I find the joint probability density function of Z?
$X_1$ and $X_2$ are independent random variables so I know $fx(x)*fy(y)=fx,y(x,y)$ but how do I get to the point where I find the marginal density functions?
I tried solving this by glancing at a similar question posed on this forum here: Finding the joint probability density function of two random variables
It suggests using transformations and a jacobian coupled with the density function of the standard normal distribution. But the transformations dont make any sense in my problems context, they need different input. Could someone shed some light on this? And what is the jacobian doing there?