deletions | additions       diff --git a/However_the_previous_definition_are__.tex b/However_the_previous_definition_are__.tex  index ffff26a..f75aaa2 100644  --- a/However_the_previous_definition_are__.tex  +++ b/However_the_previous_definition_are__.tex 
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However the previous definition definitions  are well nigh impossible to use in practice. Hopefully it can be proved that the Mutual Information between $X$ and $Y$ can be expressed as: \[ MI(X,Y) = \sum_{(x,y) \in E_1\times E_2}P_{(X,Y)}(x,y)log\Bigg(\frac{P_{(X,Y)}(x,y)}{P_{X}(x)P_{Y}(y)}\Bigg) \]