latex.md

Moments

\operatorname{E}(X) = \mu

\operatorname{Var}(X) = \sigma^2

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Probability density function (PDF)

f(x|\mu,\sigma) = \frac{1}{\sqrt{2\pi\sigma^2}} \exp\left(-\frac{(x-\mu)^2}{2\sigma^2}\right)

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Cumulative distribution function (CDF)

F(x|\mu,\sigma) = \frac{1}{2}\left[1 + \operatorname{erf}\left(\frac{x-\mu}{\sigma\sqrt{2}}\right)\right]

\operatorname{erf}(x) = \frac{2}{\sqrt{\pi}}\int_{0}^{x} e^{-t^2} \, dt