Let be a continuous random variable. The function defined as , where is the cumulative distribution function of , is called the continuous density function of . Please note that if is a continuous random variable, then does not equal ; for more information read the article on cumulative distribution functions.
Analogously to the discrete case, this function must satisfy:
![$f_X\colon\mathbb{R} \to [0,1]$](http://images.planetmath.org:8080/cache/objects/496/l2h/img2.png "$f_X\colon\mathbb{R} \to [0,1]$"){kind=small}
![$P[X=x]$](http://images.planetmath.org:8080/cache/objects/496/l2h/img9.png "$P[X=x]$"){kind=small}
