# Exponential Distribution

Exponential distribution can be viewed as the distribution of waiting time between the occurrence of events described by a Poisson variable. If T is the time elapsed before the occurrence of a Poisson event, it can also be shown that T is the recurrence time between the occurrence of any two events. This analysis will show that the distribution of the variable T is the exponential. **Definition:** If X is a continuous random variable with pdf

f(x) = $\lambda e^{-\lambda x}$ for x > 0

= 0 otherwise

then X is said to have an exponential distribution with parameter λ.The cdf of an exponential variable is F(x) = 1- $e^{-\lambda x}$

The parameter λ of the exponential distribution represents the average number of events per unit time in the corresponding Poisson Process.

Negative exponential distribution is the other name by which exponential distributions are known.