# 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. 1.

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

2. 2.

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

3. 3.

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

4. 4.

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

Title uniform (discrete) random variable UniformdiscreteRandomVariable 2013-03-22 11:54:09 2013-03-22 11:54:09 Riemann (23) Riemann (23) 7 Riemann (23) Definition msc 60-00 msc 92B05 msc 92-01 uniform random variable discrete uniform distribution