From 9e279ad51d27634529f288e10bbe7ae489fadc75 Mon Sep 17 00:00:00 2001
From: Loic Guegan <manzerbredes@mailbox.org>
Date: Sun, 15 Oct 2023 16:41:28 +0200
Subject: [PATCH] Minor changes

---
 source/statistics/notations.rst | 20 ++++++++++++++++++--
 1 file changed, 18 insertions(+), 2 deletions(-)

diff --git a/source/statistics/notations.rst b/source/statistics/notations.rst
index ae9e53d..ce304b6 100644
--- a/source/statistics/notations.rst
+++ b/source/statistics/notations.rst
@@ -39,7 +39,23 @@ Two different notation conventions are used. The one to use depends if you are w
 Operators
 ==========
 
-Var esperance etc.. + remove in metrics esperence
-   
+Expected value
+^^^^^^^^^^^^^^^
 
+The expected value (*esperance*) of a random variable :math:`X` is noted :math:`\mathbb{E}[X]`.
+It as the following linerarity  properties:
 
+.. math::
+   \mathbb{E}[X+Y]=\mathbb{E}[X] + \mathbb{E}[Y]
+.. math::
+   \mathbb{E}[\alpha X]=\alpha\mathbb{E}[X]
+
+Variance
+^^^^^^^^
+
+The variance operator of a random variable :math:`X` is noted :math:`\mathbb{V}[X]` or :math:`\mathrm{Var}[X]`.
+
+Coraviance
+^^^^^^^^^^
+The covariance operator of a random variable :math:`X` and :math:`Y`
+is noted :math:`\mathrm{Cov}[X,Y]`.