Random variables $X$ and $Y$ are independent and have density $f_x(x)$ and $f_y(x)$:
$f_x(x)=4x^2e^{-2x}\mathbb{1}_{x>0}$
$f_y(x)=\frac{8}{3}x^3e^{-2x}\mathbb{1}_{x>0}$.
Calculate $Var(\frac{X}{X+Y})$ I tried to find density for $\frac{X}{X+Y}$, but from changing of variables I have $T(X,Y)=(\frac{X}{X+Y},Y)$. Jacobian of $T^{-1}(X,Y)$ is complicated and maybe someone can do it easier? Thanks in advance.
