# Category:Gaussian Distribution

This category contains results about the Gaussian distribution.

Let $X$ be a continuous random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.

Then $X$ has a Gaussian distribution if and only if the probability density function of $X$ is:

$\map {f_X} x = \dfrac 1 {\sigma \sqrt {2 \pi} } \map \exp {-\dfrac {\paren {x - \mu}^2} {2 \sigma^2} }$

for $\mu \in \R, \sigma \in \R_{> 0}$.

This is written:

$X \sim \Gaussian \mu {\sigma^2}$

## Subcategories

This category has the following 2 subcategories, out of 2 total.

## Pages in category "Gaussian Distribution"

The following 13 pages are in this category, out of 13 total.