## Continuous Uniform Distribution

A continuous random variable $X$ is said to have a Uniform distribution (or rectangular distribution) with parameters $\alpha$ and $\beta$ if its p.d.f. is given by $$\begin{equation*} f(x)=\left\{ \begin{array}{ll} \dfrac{1}{\beta - \alpha}, & \hbox{\alpha \leq x\leq \beta;} \\ 0, & \hbox{Otherwise.} \end{array} \right. \end{equation*}$$

## Distribution Function

The distribution function of continuous uniform distribution $U(\alpha,\beta)$ is $F(x)=\dfrac{x-\alpha}{\beta - \alpha},\;\alpha \leq x\leq \beta$

## Mean of Uniform Distribution

The mean of continuous uniform distribution is

## Variance of Uniform Distribution

The variance of continuous uniform distribution is

## Mean deviation about mean of Uniform Distribution

The mean deviation about mean of continuous Uniform Distribution is

## M.G.F. of Uniform Distribution

The moment generating function of continuous uniform distribution is