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第128行：
第128行： − 上面的定义是针对离散随机变量的，不过对于连续随机变量同样有效。离散联合熵的连续形式称为联合微分（或连续）熵。令<math>X</math>和<math>Y</math>为具有'''<font color="#ff8000"> 联合概率密度函数Joint probability density function</font>''' <math>f(x,y)</math>的连续随机变量，那么微分联合熵<math>h(X,Y)</math>定义为：+ 第157行：
第157行： − + − −
→Definition 定义
The above definition is for discrete random variables and just as valid in the case of continuous random variables. The continuous version of discrete joint entropy is called ''joint differential (or continuous) entropy''. Let <math>X</math> and <math>Y</math> be a continuous random variables with a [[joint probability density function]] <math>f(x,y)</math>. The differential joint entropy <math>h(X,Y)</math> is defined as<ref name=cover1991 />{{rp|249}}
The above definition is for discrete random variables and just as valid in the case of continuous random variables. The continuous version of discrete joint entropy is called ''joint differential (or continuous) entropy''. Let <math>X</math> and <math>Y</math> be a continuous random variables with a [[joint probability density function]] <math>f(x,y)</math>. The differential joint entropy <math>h(X,Y)</math> is defined as<ref name=cover1991 />{{rp|249}}
上文中的定义是针对离散随机变量的，而其实对于连续随机变量，联合熵同样成立。离散联合熵的连续形式称为联合微分（或连续）熵。令<math>X</math>和<math>Y</math>分别为具有'''<font color="#ff8000"> 联合概率密度函数Joint probability density function</font>''' <math>f(x,y)</math>的连续随机变量，那么微分联合熵<math>h(X,Y)</math>定义为：
The [[integral]] is taken over the support of <math>f</math>. It is possible that the integral does not exist in which case we say that the differential entropy is not defined.
The [[integral]] is taken over the support of <math>f</math>. It is possible that the integral does not exist in which case we say that the differential entropy is not defined.
这里可以用积分处理表达<math>f</math>。当然如果微分熵没有定义，积分也可能不存在。
这里可以用积分处理表达<math>f</math>。当然，如果微分熵没有定义，那么积分也可能不存在。
=== Properties 属性 ===
=== Properties 属性 ===