Retrieving PDF from CDF

Now is when the fundamental theorem of Calculus (discussed in the first chapter) comes into play.

• Theorem: The probability density function (PDF) and CDF satisfy:
  • $f_X(x) = \dfrac{d F_X (x)}{dx}$, is $F_X$ is differentiable at $x$ .
  • $f_X(x_0) = \mathbb{P}[X=x_0]\delta(x - x_0)$, is $F_X$ is not differentiable at $x=x_0$ .