$\frac{1}{2}(1 - e^{-z})$ for $0 < z < 2$

$\frac{1}{2}(e^{-(z-2)} - e^{-z})$ for $z > 2$

$\frac{1}{2}(1 - e^{-z})$ for $0 < z < 2$ and $\frac{1}{2}(e^{2}-1)e^{-z}$ for $z > 2$

$\frac{1}{2}e^{-z}$ for all $z > 0$