1 2\begin{tabular}{lcll}\hline 3Variate & $x$ & \ccode{double} & $ -\infty < x < \infty$ \\ 4Location & $\mu$ & \ccode{double} & $-\infty < \mu < \infty$\\ 5Scale & $\sigma$ & \ccode{double} & $\sigma > 0$ \\ 6\hline 7\end{tabular} 8 9The probability density function (PDF) is: 10 11\begin{equation} 12PDF = P(X=x) = \frac{1}{\sigma \sqrt{2\pi}} e^{\frac{-(x-\mu)^2}{2\sigma^2}}. 13\end{equation} 14 15The cumulative distribution function (CDF) does not have a convenient 16closed-form expression. It is derived numerically in terms of the 17error function, $\mbox{erf}()$: 18 19\begin{equation} 20CDF = P(X<x) = \frac{1}{2} + \frac{1}{2} erf(\frac{x - \mu}{\sigma \sqrt{2}}). 21\end{equation} 22 23 24 25