deletions | additions       diff --git a/subsubsection_Mutual_Information_There_are__.tex b/subsubsection_Mutual_Information_There_are__.tex  index d920b15..4ba640f 100644  --- a/subsubsection_Mutual_Information_There_are__.tex  +++ b/subsubsection_Mutual_Information_There_are__.tex 
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The most intuitive definition is the following.  Let $X : P_{1} \rightarrow E_{1}$ and $Y : P_{2} \rightarrow E_{2}$ be two random variables, where $E_{1}$ and $E_{2}$ are two discrete probability spaces.   We define the Mutual Information of $X$ and $Y$, noted $I(X,Y)$, $MI(X,Y)$,  as: \[ I(X,Y) MI(X,Y)  = S(X) + S(Y) - S(X,Y) \] or again as:  \[ MI(X,Y) = S(X,Y) - S(X|Y)\]  or symmetrically as:  \[ MI(X,Y) = S(X,Y) - S(Y|X)\]  Thus it may be interpreted as the amount of information shared by the random variables $X$ and $Y$.