deletions | additions       diff --git a/subsubsection_Mutual_Information_There_are__.tex b/subsubsection_Mutual_Information_There_are__.tex  index 77eccc3..6dec5b9 100644  --- a/subsubsection_Mutual_Information_There_are__.tex  +++ b/subsubsection_Mutual_Information_There_are__.tex 
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We define the Mutual Information between $X$ and $Y$, noted $MI(X,Y)$, as:  \[ MI(X,Y) = S(X) + S(Y) - S(X,Y) \]  or again equivalently  as: \[ MI(X,Y) = S(X,Y) S(X)  - S(X|Y)\] or symmetrically as:  \[ MI(X,Y) = S(X,Y) S(Y)  - S(Y|X)\] Thus it may be interpreted as the amount of information uncertainty (or information)  shared by the random variables $X$ and $Y$. The former form of mutual information contains the term $-S(X,Y)$, which means that the lower the joint entropy is and the higher the mutual information is.   Furthermore the later form of mutual information with the term $-S(X|Y)$ might be translate to "the amount of uncertainty about $X$ minus the uncertainty about $X$ when $Y$ is known".