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

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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