Overview
Given a a random variable {% X %}, the probability density function, {% f(x) %}, is defined so that the probability of some event {% A %} can be calculated as
{% \displaystyle P(A) = \int_A f(x) dx %}
Definition
Most authors utiliize the cumulative distribution function to define the density function. That is, given a cumulative distribution function {% F(x) %}, the fundamental theorem of calculus can be used to define {% f(x) %} as
{% f(x) = \frac{dF(x)}{dx} %}
Example
The density function associated with the normal distribution.