Normal Distribution

The normal distribution is a continuous distribution. It is also referred to as the Gaussian distribution. The graph of the PDF of this distribution may be recognizable as a "bell curve". Note that a normal distribution is defined by its mean $\mu$ and variance $\sigma^2$ (standard deviation $\sigma$).

$$f(X=x) = {\displaystyle {\frac {1}{\sigma {\sqrt {2\pi }}}}e^{-{\frac {1}{2}}\left({\frac {x-\mu }{\sigma }}\right)^{2}}}$$

PDF for the normal distribution with a mean of 0 and variance of 1.

The normal distribution with a mean of 0 and variance of 1 is called the standard normal. The mean and variance of a normal distribution is often specified by the following: $N(\mu, \sigma^2)$

This distribution is important in every field of science. This is because noise, or unavoidable random error, is always present in measurements of any scientific method, and it is often normally distributed!