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→Example: Exponential distribution
Here, <math>h_e(X)</math> was used rather than <math>h(X)</math> to make it explicit that the logarithm was taken to base ''e'', to simplify the calculation.
Here, <math>h_e(X)</math> was used rather than <math>h(X)</math> to make it explicit that the logarithm was taken to base ''e'', to simplify the calculation.
--[[用户:CecileLi|CecileLi]]([[用户讨论:CecileLi|讨论]]) 【审校】补充翻译：
设<math>X</math>为[[指数分布|指数分布]]随机变量，参数为<math>\lambda</math>，即概率密度函数
：<math>f（x）=\lambda e^{-\lambda x}\mbox{for}x\geq 0.</math>
它的微分熵是
{|
|-
|<math>h\u e（X）\，</math>
|<math>=-\int\u 0^\infty\lambda e^{-\lambda x}\log（\lambda e^{-\lambda x}）\，dx</math>
|-
|
|<math>=-\left（\int\u 0^\infty（\log\lambda）\lambda e^{-\lambda x}\，dx+\int\u 0^\infty（-\lambda x）\lambda e^{-\lambda x}\，dx\right）</math>
|-
|
|<math>=-\log\lambda\int\u 0^\infty f（x）\，dx+\lambda E[x]</math>
|-
|
|<math>=-\log\lambda+1\，.</math>
|}
这里，使用<math>h（X）</math>而不是<math>h（X）</math>来明确对数取基数“e”，以简化计算。
==Relation to estimator error==
==Relation to estimator error==