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Given [[Discrete random variable|discrete random variables]] <math>X</math> with image <math>\mathcal X</math> and <math>Y</math> with image <math>\mathcal Y</math>, the conditional entropy of <math>Y</math> given <math>X</math> is defined as the weighted sum of <math>\Eta(Y|X=x)</math> for each possible value of <math>x</math>, using  <math>p(x)</math> as the weights:<ref name=cover1991>{{cite book|isbn=0-471-06259-6|year=1991|authorlink1=Thomas M. Cover|author1=T. Cover|author2=J. Thomas|title=Elements of Information Theory|url=https://archive.org/details/elementsofinform0000cove|url-access=registration}}</ref>{{rp|15}}

Given [[Discrete random variable|discrete random variables]] <math>X</math> with image <math>\mathcal X</math> and <math>Y</math> with image <math>\mathcal Y</math>, the conditional entropy of <math>Y</math> given <math>X</math> is defined as the weighted sum of <math>H(Y|X=x)</math> for each possible value of <math>x</math>, using  <math>p(x)</math> as the weights:<ref name=cover1991>{{cite book|isbn=0-471-06259-6|year=1991|authorlink1=Thomas M. Cover|author1=T. Cover|author2=J. Thomas|title=Elements of Information Theory|url=https://archive.org/details/elementsofinform0000cove|url-access=registration}}</ref>{{rp|15}}

给定具有像<math>\mathcal X</math>的离散随机变量<math>X</math>和具有像<math>\mathcal Y</math>的<math>Y</math>，将给定<math>X</math>的<math>Y</math>的条件熵定义为<mathH(Y|X=x)</math>的权重之和，以<math>x</math>的每个可能值为准，并使用<math>p(x)</math>作为权重：<ref name=cover1991>{{cite book|isbn=0-471-06259-6|year=1991|authorlink1=Thomas M. Cover|author1=T. Cover|author2=J. Thomas|title=Elements of Information Theory|url=https://archive.org/details/elementsofinform0000cove|url-access=registration}}</ref>{{rp|15}}

给定具有像<math>\mathcal X</math>的离散随机变量<math>X</math>和具有像<math>\mathcal Y</math>的<math>Y</math>，将给定<math>X</math>的<math>Y</math>的条件熵定义为<math>H(Y|X=x)</math>的权重之和，以<math>x</math>的每个可能值为准，并使用<math>p(x)</math>作为权重：<ref name=cover1991>{{cite book|isbn=0-471-06259-6|year=1991|authorlink1=Thomas M. Cover|author1=T. Cover|author2=J. Thomas|title=Elements of Information Theory|url=https://archive.org/details/elementsofinform0000cove|url-access=registration}}</ref>{{rp|15}}