Normal distribution

The normal distribution is a continuous probability distribution $f: \mathbb{R} \rightarrow (0,1) \subset \mathbb{R}$ specified by the mean $\mu$ and standard deviation $\sigma$ given by probability density function

$$f(x) = \frac{1}{\sigma \sqrt{2\pi}} \exp \left [ - \frac{1}{2} \left ( \frac{x - \mu}{\sigma} \right )^2 \right ].$$

Samples from the distributions would be normally referred to as $N(\mu, \sigma^2)$.