continuous density function
Let $X$ be a continuous random variable. The function ${f}_{X}:\mathbb{R}\to [0,1]$ 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.
${f}_{X}(x)\ge 0$ for all $x$

2.
${\int}_{x}{f}_{X}(x)\mathit{d}x=1$
Title  continuous density function 

Canonical name  ContinuousDensityFunction 
Date of creation  20130322 11:53:16 
Last modified on  20130322 11:53:16 
Owner  mathcam (2727) 
Last modified by  mathcam (2727) 
Numerical id  9 
Author  mathcam (2727) 
Entry type  Definition 
Classification  msc 6000 
Classification  msc 8100 
Classification  msc 1800 
Synonym  mass function 