## The Exponential Distribution

The probability distribution for the exponential function, withprobability distribution functionisillustrated below.

A number of situations can be modelled by the exponentialdistribution. In these examples it must be assumed however that eachevent is independent.

The lifetimes of electric bulbs. Some bulbs will fail almostimmediately 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