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→Other properties 其他性质
=== Other properties 其他性质 ===
=== Other properties 其他性质 ===
For any <math>X</math> and <math>Y</math>:
For any <math>X</math> and <math>Y</math>:
对于任何<math>X</math>和<math>Y</math>：
:<math display="block">\begin{align}
:<math display="block">\begin{align}
H(Y|X) &\le H(Y) \, \\
H(Y|X) &\le H(Y) \, \\
where <math>\operatorname{I}(X;Y)</math> is the [[mutual information]] between <math>X</math> and <math>Y</math>.
where <math>\operatorname{I}(X;Y)</math> is the [[mutual information]] between <math>X</math> and <math>Y</math>.
其中<math>\operatorname{I}(X;Y)</math>是<math>X</math>和<math>Y</math>之间的相互信息。
For independent <math>X</math> and <math>Y</math>:
For independent <math>X</math> and <math>Y</math>:
对于独立的X和Y：
:<math>H(Y|X) = H(Y) </math> and <math>H(X|Y) = H(X) \, </math>
:<math>H(Y|X) = H(Y) </math> and <math>H(X|Y) = H(X) \, </math>
Although the specific-conditional entropy <math>H(X|Y=y)</math> can be either less or greater than <math>H(X)</math> for a given [[random variate]] <math>y</math> of <math>Y</math>, <math>H(X|Y)</math> can never exceed <math>H(X)</math>.
Although the specific-conditional entropy <math>H(X|Y=y)</math> can be either less or greater than <math>H(X)</math> for a given [[random variate]] <math>y</math> of <math>Y</math>, <math>H(X|Y)</math> can never exceed <math>H(X)</math>.
尽管对于给定的<math>Y</math>随机变量<math>y</math>，特定条件熵<math>H(X|Y=y)</math>可以小于或大于<math>H(X)</math>，但<math>H(X|Y)</math>永远不会超过<math>H(X)</math>。
== Conditional differential entropy 条件微分熵 ==
== Conditional differential entropy 条件微分熵 ==