Minor changes

source/statistics/introduction.rst

@@ -10,4 +10,25 @@ Metrics
 Variance
 ^^^^^^^^^^^^^^
 
-Variance can be seen as the expected squared deviation from the mean of a random variable :math:`X`.
+Variance can be seen as the expected squared deviation from the expected value of a random variable :math:`X`.
+
+.. math::
+   \mathbb{V}[X]=\mathbb{E}[X-\mathbb{E}[X]]^2=\frac{\sum_{i=1}^n (x_i - \mathbb{E}[X])^2}{n}=\mathrm{Cov}(X,X)
+
+Covariance
+^^^^^^^^^^^^^^
+
+Covariance is a way to quantify the relationship between two random variables :math:`X` and
+:math:`Y` (`source <https://www.youtube.com/watch?v=qtaqvPAeEJY>`_). Covariance **DOES NOT**
+quantify how strong this correlation is! If covariance is:
+
+Positive
+    For large values of :math:`X`, :math:`Y` is also taking large values
+Negative
+    For large values of :math:`X`, :math:`Y` is also taking low values
+Null
+    No correlation
+
+.. math::
+   \mathrm{Cov}(X,Y)=\mathbb{E}[(X-\mathbb{E}[X])(Y-\mathbb{E}[Y])]=\frac{\sum_{i=1}^n (x_i - \mathbb{E}[X])(y_i - \mathbb{E}[Y])}{n}
+