## Exponential Distribution

A continuous random variable $X$ is said to have an exponential distribution with parameter $\theta$ if its p.d.f. is given by
`$$ \begin{equation*} f(x)=\left\{ \begin{array}{ll} \theta e^{-\theta x}, & \hbox{$x\geq 0;\theta>0$;} \\ 0, & \hbox{Otherwise.} \end{array} \right. \end{equation*} $$`

## Distribution Function of Exponential Distribution

The distribution function of an exponential random variable is

`$F(x)=1- e^{-\theta x},\;x\geq 0;\theta>0$`

## Mean of Exponential Distribution

The mean of an exponential random variable is

### $E(X) = \dfrac{1}{\theta}$.

## Variance of Exponential Distribution

The variance of an exponential random variable is