uniform (discrete) random variable

$X$ is a uniform (discrete) random variable with parameter $N$ if

$f_X(x) = \frac{1}{N}$ , $x=\{1,2,...,N\}$

Parameters:

$\star$

$N \in \{1,2,...\}$

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