Definition:Exponential Distribution

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

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

where $0 < \beta$. It is written:
 * $X \sim \Exponential \beta$

Also see

 * Expectation of Exponential Distribution: $\expect X = \beta$
 * Variance of Exponential Distribution: $\var X = \beta^2$

The probability density function of $X$ is: