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.

$\int_{x}{f_{X}(x)dx}=1$

Title	continuous density function
Canonical name	ContinuousDensityFunction
Date of creation	2013-03-22 11:53:16
Last modified on	2013-03-22 11:53:16
Owner	mathcam (2727)
Last modified by	mathcam (2727)
Numerical id	9
Author	mathcam (2727)
Entry type	Definition
Classification	msc 60-00
Classification	msc 81-00
Classification	msc 18-00
Synonym	mass function