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
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.