# Normal cdf

The normal cumulative distribution function $F \colon \mathbb{R} \rightarrow \mathbb{R}$ is defined for $\mu \in \mathbb{R}$ and $\sigma^2 >0$ by $$F(x) = \dfrac{1}{2} \left[ 1 + \mathrm{erf} \left( \dfrac{x-\mu}{\sigma \sqrt{2}} \right) \right],$$ where $\mathrm{erf}$ denotes the error function and $\exp$ denotes the exponential function.