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 $x$
•
$\\sum_{x}f_{X}(x)=1$

单词	DiscreteDensityFunction
释义	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 $x$ • $\\sum_{x}f_{X}(x)=1$
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