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Lucas Fidon edited However_the_previous_definitions_are__.tex
almost 8 years ago
Commit id: 251702aaa5ba1a38f2530a8052a937d68c3b360e
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diff --git a/However_the_previous_definitions_are__.tex b/However_the_previous_definitions_are__.tex
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\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 \[MI(X,Y) \leq
S(X),
MI(X,Y) S(X),\]
\[MI(X,Y) \leq S(Y) \]
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 \[MI(X,Y)
\meq \geq 0 \]
The uncertainty about $X$ cannot be increased by learning about $Y$.
\item \[MI(X,Y) = 0 iff X and y are independent.\]
\end{enumerate}