Normal distribution
| Notation | $x\sim\mathcal{N}(\mu,\sigma)$ |
| ${1\over\sqrt{{2\pi\sigma^2}}} \operatorname{exp}\left\{-\frac{(x - \mu)^2}{2 \sigma^2}\right\}$ | |
| cdf | $\frac12\left[1 + \operatorname{erf}\left( \frac{x-\mu}{\sqrt{2\sigma^2}}\right)\right] $ |
| EV | $\mu$ |
| Var | $\sigma^2$ |
| Char. function | $\operatorname{exp}\left\{ i\mu t - \frac{1}{2}\sigma^2 t^2 \right\}$ |
| Entropy | $\frac12 \ln(2 \pi e \, \sigma^2)$ |
| Exponential family |