Normal distribution

probability density function

cumulative probability function

The normal distribution is a key distribution in the field of probability. It is also known as the Gaussian distribution, after mathematician Carl Gauss, and the bell curve. The normal probability density function (PDF) is

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

where $\mu$ is the mean and $\sigma ^{2}$ is the variance.

If $\mu =0$ and $\sigma =1$, the distribution is called the standard normal distribution, often denoted by $\phi$:

$\phi (x)={\frac {1}{\sqrt {2\pi }}}\exp(-{\frac {1}{2}}x^{2}).$

See also

• Central limit theorem