Definition:Exponential Distribution

Definition
Let $X$ be a continuous random variable on a probability space $\left({\Omega, \Sigma, \Pr}\right)$.

Then $X$ has the exponential distribution with parameter $\beta$ :
 * $X \left({\Omega}\right) = \R_{\ge 0}$
 * $\Pr \left({X < x}\right) = 1 - e^{-\frac x \beta}$

where $0 < \beta$. It is written:
 * $X \sim \operatorname{Exp} \left({\beta}\right)$

The probability density function of $X$ is:

Also see

 * Expectation of Exponential Distribution: $E \left({X}\right) = \beta$
 * Variance of Exponential Distribution: $\operatorname {var} \left({X}\right) = \beta^2$