deletions | additions       diff --git a/subsection_Mutual_Information_definition_and__.tex b/subsection_Mutual_Information_definition_and__.tex  index 939ebc3..b45a534 100644  --- a/subsection_Mutual_Information_definition_and__.tex  +++ b/subsection_Mutual_Information_definition_and__.tex 
...
\[ S(X,Y)=-\sum_{(x,y) \in E_1\times E_2}P_{(X,Y)}(x,y)log\big(P_{(X,Y)}(x,y)\big) \]  Besides the entropy of the probability law of $X$ conditionally to the probability law of $Y$ is defined as:  \[ S(X|Y)=-\sum_{x \in E_1}P_{(X|Y)}(x)log\big(P_{(X|Y)}(x)\big) E_1}P_{X|Y}(x)log\big(P_{X|Y}(x)\big)  \] Somewhat imprecisely, we used to designate the entropy of the probability law of a random variable $X$ as simply \textit{the entropy of $X$}. Hence the notation \textit{$S(X)$} for the entropy of $X$.