The exponential distribution is a one-sided distribution completely specified by one parameter 
; the density of this distribution is
The mean of the exponential distribution is 
.
The exponential distribution is a model for the length of intervals between two consecutive random events in time, or between a given point and the next nearest point. In this case is the rate of events – that is, the average number of events per a unit interval. (For details on what “random events” means here see Poisson process.
An important property of the exponential distribution is
Because of this property, the exponential distribution is also referred to as a ’memory-less distribution’. One of the applications of the exponential distribution is in queuing theory.