## Laplace Distribution

A continuous random variable $X$ is said to have a Laplace distribution, if its p.d.f. is given by $$\begin{equation*} f(x;\mu, \lambda)=\left\{ \begin{array}{ll} \frac{1}{2\lambda}e^{-\frac{|x-\mu|}{\lambda}}, & \hbox{-\infty < x< \infty;} \\ & \hbox{-\infty < \mu < \infty, \lambda >0;} \\ 0, & \hbox{Otherwise.} \end{array} \right. \end{equation*}$$

## Mean of Laplace Distribution

The mean of Laplace distribution is

## Variance of Laplace Distribution

The variance of Laplace distribution is

## Distribution Function of Laplace Distribution

The distribution function of Laplace distribution is

$$\begin{equation*} F(x) = \left\{ \begin{array}{ll} \frac{1}{2}e^{\frac{(x-\mu)}{\lambda}}, & \hbox{x< \mu;} \\ &\\ 1-\frac{1}{2}e^{-\frac{(x-\mu)}{\lambda} }, & \hbox{x\geq \mu;} \end{array} \right. \end{equation*}$$

## Quartiles of Laplace Distribution

The quartiles of Laplace distribution are

## M.G.F. of Laplace Distribution

The moment generating function of Laplace distribution is

## Characteristics Function

The characteristic function of Laplace distribution is