Definition:Gaussian Distribution

Definition
Let $X$ be a continuous random variable on a probability space $\left({\Omega, \Sigma, \Pr}\right)$.

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


 * $f_X \left({x}\right) = \dfrac 1 {\sigma \sqrt{2 \pi} } \, \exp \left({-\dfrac { \left({x - \mu}\right)^2} {2 \sigma^2} }\right)$

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

This is written:


 * $X \sim N \left({\mu, \sigma^2}\right)$

Also known as
The Gaussian distribution is also commonly known as the normal distribution.

Both terms may be found on.

Also see

 * Expectation of Gaussian Distribution: $E \left({X}\right) = \mu$
 * Variance of Gaussian Distribution: $\operatorname {var} \left({X}\right) = \sigma^2$