Let $(X,Y,Z)$ be a continuous random vector with joint density $ f_{(X,Y,Z)}(x,y,z) = 6e^{-x-y-z},\quad 0 < x < y < z. $
What is the marginal density of $X,Y$ and $Z$?
I have calculated $f_X(x)$ here. I have calculated $f_Y(y)$ here. I have calculated $f_Z(z)$ here.
Is this right?