Exponential Distribution Formula

The exponential distribution in probability is the probability distribution that describes the time between events in a Poisson process.

Probability Density Function

Cumulative Distribution Function

$$F(x;\lambda )=\{\begin{array}{cc}1–e^{-\lambda x}& x>=0,\\ 0& x<0.\end{array}$$

where

is called the rate of the distribution.

The mean of the Exponential (

) Distribution is calculated using integration by parts as –

Simplifying further,