diff --git a/source/statistics/probability_distribution_functions.rst b/source/statistics/probability_distribution_functions.rst
index 79208f4..c2425ed 100644
--- a/source/statistics/probability_distribution_functions.rst
+++ b/source/statistics/probability_distribution_functions.rst
@@ -1,6 +1,8 @@
 Probability Distribution Functions
 ------------------------------------
 
+.. _PDF:
+
 Probability Density Function
 =============================
 
@@ -43,4 +45,23 @@ Let's compute its CDF:
 Cumulative Distribution Function
 =================================
 
-The Cumulative Distribution Function (CDF)
+The Cumulative Distribution Function (CDF) of a random variable :math:`X` is a function :math:`F_X(x)` such that:
+
+.. math::
+   F_X(x) &= P(X \leq x)
+   
+   \lim_{x \to -\infty} F_X(x) &= 0
+
+   \lim_{x \to +\infty} F_X(x) &= 1
+   
+CDF can be used for:
+
+.. math::
+   P(X \in ]a,b]) = P(a < X \leq b) = F_X(b) - F_X(a)
+
+.. note::
+   In the definition above, the "less than or equal to" sign, ":math:`\le`", is a convention.
+   Since :math:`F_X(x)` is continuous on :math:`[0,1]` it is similar to :ref:`what is cover for the PDF <PDF>`.
+   It is not a universal convention but the distinction is important for discrete distributions.
+   More infos `here <https://en.wikipedia.org/wiki/Cumulative_distribution_function>`__.
+