f(x) = \frac{\mathrm{d}}{\mathrm{d}x} F(x) . Intuitively, one can think of f ( x )&nbsp;d x as being the probability of X falling within the infinitesimal interval [ x ,&nbsp; x &nbsp;+&nbsp;d x ]. Formal definition This definition may be extended to any probability distribution using the measure-theoretic definition of probability .