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Besides the entropy of the probability distribution of $X$ conditionally to the probability distribution of $Y$ is defined as:  \[ S(X|Y)=-\sum_{x \in E_1}P_{X|Y}(x)log\big(P_{X|Y}(x)\big) \]  Somewhat imprecisely, we used to designate the entropy of the probability distribution of a random variable $X$ as simply \textit{the "\textit{the  entropy of $X$}. $X$}".  Hence the notation \textit{$S(X)$} for the entropy of $X$. The entropy of a probability distribution (or of a random variable) has three interpretations:   \begin{itemize}