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\begin{tabular}{lcll}\hline
Variate & $x$ & \ccode{double} & $ -\infty < x < \infty$ \\
Location & $\mu$ & \ccode{double} & $-\infty < \mu < \infty$\\
Scale & $\sigma$ & \ccode{double} & $\sigma > 0$ \\
\hline
\end{tabular}
The probability density function (PDF) is:
\begin{equation}
PDF = P(X=x) = \frac{1}{\sigma \sqrt{2\pi}} e^{\frac{-(x-\mu)^2}{2\sigma^2}}.
\end{equation}
The cumulative distribution function (CDF) does not have a convenient
closed-form expression. It is derived numerically in terms of the
error function, $\mbox{erf}()$:
\begin{equation}
CDF = P(X<x) = \frac{1}{2} + \frac{1}{2} erf(\frac{x - \mu}{\sigma \sqrt{2}}).
\end{equation}
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