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 \(p_X(x) >0\).