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The interpretation of this form is that it measures the distance between the joint distribution and the k=joint distribution in case of independence between $X$ and $Y$. So it is a measure of \textit{dependence} between two distribution (or random variables).  \subsubsection{Properties}  Mutual information as has  the following properties: \begin{enumerate}  \item \[MI(X,Y) = MI(Y,X) (symmetry) \]  \item \[MI(X,X) = S(X) \] 
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\item \[MI(X,Y) \leq S(X),  MI(X,Y) \leq S(Y) \]  The amount of information shared by two random variable cannot be greater than the information contained in one of those single one random variables.  \item \[MI(X,Y) \meq 0 \]  The uncertainty about $X$ cannot be increased by learning about $Y$.  \item \[MI(X,Y) = 0 iff X and y are independent.\]  \end{enumerate}