# 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

 $\displaystyle f_{X}(x)=\frac{1}{b-a},\quad\quad x\in[a,b],$

and is denoted $X\sim U(a,b)$.

Notes:

1. 1.

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

2. 2.

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

3. 3.

$Var[X]=\frac{(b-a)^{2}}{12}$

4. 4.

$M_{X}(t)=\frac{e^{bt}-e^{at}}{(b-a)t}$

Title uniform (continuous) random variable UniformcontinuousRandomVariable 2013-03-22 11:54:18 2013-03-22 11:54:18 mathcam (2727) mathcam (2727) 10 mathcam (2727) Definition msc 60-00 uniform random variable rectangular distribution uniform distribution