deletions | additions       diff --git a/subsubsection_Mutual_Information_There_are__.tex b/subsubsection_Mutual_Information_There_are__.tex  index ab06e64..d479ce2 100644  --- a/subsubsection_Mutual_Information_There_are__.tex  +++ b/subsubsection_Mutual_Information_There_are__.tex 
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There are several equivalent ways to define Mutual Information.  The most intuitive definition is the following.  Let $X : P_{1} \rightarrow E_{1}$ and $Y: $Y :  P_{2} \rightarrow E_{2}$ 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 $I(X,Y)$, as:  \[ I(X,Y) = S(X) + S(Y) - S(X,Y) \]  Another definition of $I(X,Y)$ is:  \[ I(X,Y) = \sum_{(x,y) \in E_1\times E_2}P_{(X,Y)}(x,y)*log\Bigg(\frac{log(P_{(X,Y)}(x,y))}{P_{X}(x)*P_{Y}(y)}\Bigg) E_2}P_{(X,Y)}(x,y)*log\Bigg(\frac{P_{(X,Y)}(x,y)}{P_{X}(x)*P_{Y}(y)}\Bigg)  \]