discrete density function
Let $X$ be a discrete random variable. The function^{} ${f}_{X}:\mathbb{R}\to [0,1]$ defined as ${f}_{X}(x)=P[X=x]$ is called the discrete probability function of $X$. Sometimes the syntax ${p}_{X}(x)$ is used, to mark the difference^{} between this function and the continuous density function.
If $X$ has discrete density function ${f}_{X}(x)$, it is said that the random variable $X$ has the distribution^{} or is distributed ${f}_{X}(x)$, and this fact is denoted as $X\sim {f}_{X}(x)$.
Discrete density functions are required to satisfy the following properties:

•
${f}_{X}(x)\ge 0$ for all $x$

•
${\sum}_{x}{f}_{X}(x)=1$
Title  discrete density function 

Canonical name  DiscreteDensityFunction 
Date of creation  20130322 11:53:14 
Last modified on  20130322 11:53:14 
Owner  drini (3) 
Last modified by  drini (3) 
Numerical id  16 
Author  drini (3) 
Entry type  Algorithm 
Classification  msc 60E99 
Classification  msc 0002 
Synonym  discrete probability function 
Related topic  Distribution 