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:

• $N\in \{1,2,\mathrm{\dots }\}$

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. $M_X(t)={\sum }_{j=1}^N\frac{1}{N}{e}^{jt}$