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→Motivation
:<math>\Eta(Y) = \sum_{y\in\mathcal Y} {\mathrm{Pr}(Y=y)\,\mathrm{I}(y)}
:<math>\H(Y) = \sum_{y\in\mathcal Y} {\mathrm{Pr}(Y=y)\,\mathrm{I}(y)}
= -\sum_{y\in\mathcal Y} {p_Y(y) \log_2{p_Y(y)}},</math>
= -\sum_{y\in\mathcal Y} {p_Y(y) \log_2{p_Y(y)}},</math>
where <math>\operatorname{I}(y_i)</math> is the [[information content]] of the [[Outcome (probability)|outcome]] of <math>Y</math> taking the value <math>y_i</math>. The entropy of <math>Y</math> conditioned on <math>X</math> taking the value <math>x</math> is defined analogously by [[conditional expectation]]:
where <math>\operatorname{I}(y_i)</math> is the [[information content]] of the [[Outcome (probability)|outcome]] of <math>Y</math> taking the value <math>y_i</math>. The entropy of <math>Y</math> conditioned on <math>X</math> taking the value <math>x</math> is defined analogously by [[conditional expectation]]:
这里当取值<math>y_i</math>时，<math>\operatorname{I}(y_i)</math>是结果<math>Y</math>的信息内容。类似地以<math>X</math>为条件的<math>Y</math>的熵，当值为<math>x</math>时，可以通过条件期望来定义：
:<math>\Eta(Y|X=x)
:<math>\Eta(Y|X=x)