## 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