Category:Definitions/Gaussian Distribution

This category contains definitions related to Gaussian Distribution.
Related results can be found in Category: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:

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