Properties of the CDF

• Theorem: If $X$ is a discrete random variable, itd CDF satisfies the following:
  1. The CDF is a sequence of increasing unit steps.
  2. The CDF achieves a maximum at $F_X (\infty) = 1$.
  3. The CDF achieves a minimum at $F_X (-\infty) = 0$.
  4. The unit steps have jumps at positions $x$ where $p_X(x) >0$.