$f(z) = \frac{1}{\sqrt{2\pi}} e^{-\frac{z^2}{2}}$

$f(z) = e^{-\frac{z^2}{2}}$

$f(z) = \frac{1}{2\pi} e^{-z}$

$f(z) = \frac{1}{\sqrt{\pi}} e^{-\frac{z}{2}}$