uniform (continuous) random variable
A random variable^{} $X$ is said to be a () random variable with parameters $a$ and $b$ if its probability density function^{} is given by
${f}_{X}(x)={\displaystyle \frac{1}{ba}},x\in [a,b],$ 
and is denoted $X\sim U(a,b)$.
Notes:

1.
They are also called rectangular distributions, considers that all points in the interval $[a,b]$ have the same mass.

2.
$E[X]=\frac{a+b}{2}$

3.
$Var[X]=\frac{{(ba)}^{2}}{12}$

4.
${M}_{X}(t)=\frac{{e}^{bt}{e}^{at}}{(ba)t}$
Title  uniform (continuous) random variable 

Canonical name  UniformcontinuousRandomVariable 
Date of creation  20130322 11:54:18 
Last modified on  20130322 11:54:18 
Owner  mathcam (2727) 
Last modified by  mathcam (2727) 
Numerical id  10 
Author  mathcam (2727) 
Entry type  Definition 
Classification  msc 6000 
Synonym  uniform random variable 
Synonym  rectangular distribution 
Synonym  uniform distribution 