Lucas Fidon edited subsection_Mutual_Information_definition_and__.tex  almost 8 years ago

Commit id: 2a51601c50ab64ac8afb6b26b20b898ed119972a

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Shannon introduced the entropy to be a measure of the quantity of information of a random variable.    Let $X: P \rightarrow E$ be a random variable with $E$ a discrete probability space.  The entropy of $X$, noted $S(X)$ $S(X)$,  is defined as: \[ S(X) = -\sum_{x \in E}P_{X}(x)*log(P_{X}(x)) \]    The entropy has three interpretations: