uniform (discrete) random variable
$X$ is a uniform (discrete) random variable^{} with parameter $N$ if
${f}_{X}(x)=\frac{1}{N}$, $x=\{1,2,\mathrm{\dots},N\}$
Parameters:

$\star $
$N\in \{1,2,\mathrm{\dots}\}$
Syntax:
$X\sim U\{N\}$
Notes:

1.
$X$ represents the experiment in which all N outcomes are equally likely to ocurr.

2.
$E[X]=\frac{N+1}{2}$

3.
$Var[X]=\frac{{N}^{2}1}{12}$

4.
${M}_{X}(t)={\sum}_{j=1}^{N}\frac{1}{N}{e}^{jt}$
Title  uniform (discrete) random variable 

Canonical name  UniformdiscreteRandomVariable 
Date of creation  20130322 11:54:09 
Last modified on  20130322 11:54:09 
Owner  Riemann (23) 
Last modified by  Riemann (23) 
Numerical id  7 
Author  Riemann (23) 
Entry type  Definition 
Classification  msc 6000 
Classification  msc 92B05 
Classification  msc 9201 
Synonym  uniform random variable^{} 
Synonym  discrete uniform distribution^{} 