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

<math>

f(x)=\frac{1}{\sqrt{2\pi\sigma^2}} \exp\left[-\frac{1}{2\sigma^2}\left(x-\mu\right)^2\right] </math> where <math>\mu</math> is the mean and <math>\sigma^2</math> is the variance.

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

<math>

\phi(x) = \frac{1}{\sqrt{2\pi}} \exp(-\frac{1}{2} x^2). </math>

See also

• Central limit theorem