Continuous Distributions

Normal Distribution

Denoted by $N(\mu, \sigma^2)$.

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

Kurtosis is 3.

Cumulative Distribution Function

Shows a dragged S shape.

Standard Normal Distribution

Denoted by $N(0, 1)$. $z$ is used to denote that it is a standard normal distribution.

$$P(z) = \frac{1}{\sqrt{2\pi}} \exp\left(-\frac{z^2}{2}\right)$$

Other continuous distributions are explained in separate pages, in detail.