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Notice, as per property of the [[Kullback–Leibler divergence]], that <math>I(X;Y)</math> is equal to zero precisely when the joint distribution coincides with the product of the marginals, i.e. when <math>X</math> and <math>Y</math> are independent (and hence observing <math>Y</math> tells you nothing about <math>X</math>). In general <math>I(X;Y)</math> is non-negative, it is a measure of the price for encoding <math>(X,Y)</math> as a pair of independent random variables, when in reality they are not.

Notice, as per property of the [[Kullback–Leibler divergence]], that <math>I(X;Y)</math> is equal to zero precisely when the joint distribution coincides with the product of the marginals, i.e. when <math>X</math> and <math>Y</math> are independent (and hence observing <math>Y</math> tells you nothing about <math>X</math>). In general <math>I(X;Y)</math> is non-negative, it is a measure of the price for encoding <math>(X,Y)</math> as a pair of independent random variables, when in reality they are not.

注意，根据 Kullback-Leibler 散度的性质，当联合分布与边际乘积重合时，<math>I(X;Y)</math> 恰好等于零，即。当数学 x / 数学和数学 y / 数学是独立的(因此观察数学 y / 数学并不能告诉你数学 x / 数学)。在一般的数学 i (x; y) / math 是非负的，它是一种测量方法，用于将 math (x，y) / math 作为一对独立的随机变量进行编码，而实际上它们并不是。

需要注意的是，根据Kullback–Leibler散度的性质，当联合分布与边缘的乘积重合时，即当<math>X</math>和<math>Y</math>是独立的时，<math>I(X;Y)</math>等于零（因此已知𝑌的信息并不能得到任何关于𝑋的信息）。一般来说，<math>I(X;Y)</math>是非负的，因为它是编码<math>(X,Y)</math>作为一对独立随机变量的价格度量，但实际上它们并不是非负的。

== 关于离散分布的PMF In terms of PMFs for discrete distributions ==

== 关于离散分布的PMF In terms of PMFs for discrete distributions ==