|
Let  be a discrete random variable. The function
![$ f_X\colon\mathbb{R} \to [0,1]$](http://images.planetmath.org:8080/cache/objects/486/l2h/img2.png "$ f_X\colon\mathbb{R} \to [0,1]$") defined as
![$ f_X(x)=P[X=x]$](http://images.planetmath.org:8080/cache/objects/486/l2h/img3.png "$ f_X(x)=P[X=x]$") is called the discrete probability function of  . Sometimes the syntax  is used, to mark the difference between this function and the continuous density function.
If  has discrete density function  , it is said that the random variable  has the distribution or is distributed  , and this fact is denoted as
 .
Discrete density functions are required to satisfy the following properties:
| 
