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.

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.

$Var[X]=\frac{(b-a)^{2}}{12}$
4.

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

Title	uniform (continuous) random variable
Canonical name	UniformcontinuousRandomVariable
Date of creation	2013-03-22 11:54:18
Last modified on	2013-03-22 11:54:18
Owner	mathcam (2727)
Last modified by	mathcam (2727)
Numerical id	10
Author	mathcam (2727)
Entry type	Definition
Classification	msc 60-00
Synonym	uniform random variable
Synonym	rectangular distribution
Synonym	uniform distribution