continuous density function

Let $X$ be a continuous random variable. The function $f_{X}\\colon\\mathbb{R}\\to[0,1]$ defined as $f_{X}(x)=\\frac{\\partial F_{X}}{\\partial x}$ , where $F_{X}(x)$ is the cumulative distribution function (http://planetmath.org/CumulativeDistributionFunction) of $X$ , is called the continuous density function of $X$ .Please note that if $X$ is a continuous random variable, then $f_{X}(x)$ does not equal $P[X=x]$ ; for more information read the article on cumulative distribution functions.

Analogously to the discrete case, this function must satisfy:

1.
$f_{X}(x)\\geq 0$ for all $x$
2.
$\\int_{x}{f_{X}(x)dx}=1$

单词	ContinuousDensityFunction
释义	continuous density function Let $X$ be a continuous random variable. The function $f_{X}\\colon\\mathbb{R}\\to[0,1]$ defined as $f_{X}(x)=\\frac{\\partial F_{X}}{\\partial x}$ , where $F_{X}(x)$ is the cumulative distribution function (http://planetmath.org/CumulativeDistributionFunction) of $X$ , is called the continuous density function of $X$ .Please note that if $X$ is a continuous random variable, then $f_{X}(x)$ does not equal $P[X=x]$ ; for more information read the article on cumulative distribution functions. Analogously to the discrete case, this function must satisfy: 1. $f_{X}(x)\\geq 0$ for all $x$ 2. $\\int_{x}{f_{X}(x)dx}=1$
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