# 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. 1.

$f_{X}(x)\geq 0$ for all $x$

2. 2.

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

Title continuous density function ContinuousDensityFunction 2013-03-22 11:53:16 2013-03-22 11:53:16 mathcam (2727) mathcam (2727) 9 mathcam (2727) Definition msc 60-00 msc 81-00 msc 18-00 mass function