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\subsubsection{Properties}  Mutual information as the following properties:  \begin{enumerate}  \item  \[MI(X,Y) = MI(Y,X) (symmetry) \] \item  \[MI(X,X) = S(X) \] The amount of information a random variable shared with itself is simply the entropy of $X$.  \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.  \end{enumerate}  \[