$f_Z(z) = z e^{-z}$ for $z \geq 0$

$f_Z(z) = e^{-z}$ for $z \geq 0$

$f_Z(z) = \frac{z^2}{2} e^{-z}$ for $z \geq 0$

$f_Z(z) = 2 e^{-2z}$ for $z \geq 0$