The probability distribution for the exponential function, with probability distribution functionis illustrated below.

A number of situations can be modelled by the exponential distribution. In these examples it must be assumed however that each event is independent.

The lifetimes of electric bulbs. Some bulbs will fail almost immediately and some will last a very long time.

The time intervals between cars passing a certain point.

The the time intervals between earthquakes or volcanoes.

The mean of the exponential distribution is

and the variance is