There is a very common and important example of a continuous probability distribution. This is the Gaussian, or Normal distribution, also called a bell-shaped curve. It looks like this figure .

It is determined by two numbers, the location of the peak and the
width. Mathematically, the two parameters which define it are the mean
and the standard deviation . The mathematical form of
the distribution is

. The normal distribution is important because the sum of a set of independent variables drawn from almost any distribution approaches Gaussian as the number of variables goes to infinity. So, for examples, means tend to be Normally distributed. This result is called the central limit theorem.

There is a multidimensional version of the Normal distribution. It is called a multi-variant Gaussian; it is shown in two-dimensions in figure .

In this case it is defined by the centre of the peak, two directions of spread and two widths along those two special directions.