discrete density function

Let $X$ be a discrete random variable. The function $f_{X}\colon\mathbb{R}\to[0,1]$ 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:

• $f_{X}(x)\geq 0$ for all $x$

• $\sum_{x}f_{X}(x)=1$

Title discrete density function DiscreteDensityFunction 2013-03-22 11:53:14 2013-03-22 11:53:14 drini (3) drini (3) 16 drini (3) Algorithm msc 60E99 msc 00-02 discrete probability function Distribution