discrete density function

Let $X$ be a discrete random variable. The function $f_X:ℝ\to [0,1]$ 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	2013-03-22 11:53:14
Last modified on	2013-03-22 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 00-02
Synonym	discrete probability function
Related topic	Distribution