V2EX expected value

Expected Value

释义 Definition

expected value期望值/数学期望。在概率与统计中,表示一个随机变量在长期重复试验中“平均”会得到的数值(按各结果发生的概率加权平均)。常记作 **E(X)**。在更广义的语境里也可指“预期值/预期收益”。

发音 Pronunciation (IPA)

/kspktd vlju/

例句 Examples

The expected value of a fair die roll is 3.5.
公平六面骰子掷一次的期望值是 3.5。

Even if you sometimes lose money, a strategy with positive expected value can be profitable in the long run.
即使你有时会亏钱,从长期看,期望值为正的策略仍可能带来收益。

词源 Etymology

expected 来自拉丁语 expectare,意为“等待、期待”;value 来自拉丁语 valere,意为“有价值、强健”。在数学语境中,“expected value”并非“你希望发生的值”,而是指按概率加权后的“理论平均值”,这一用法在概率论形成与发展过程中逐渐固定下来。

相关词 Related Words

文学与著作中的用例 Literary Works

  • An Introduction to Probability Theory and Its Applications William Feller(概率论经典教材,系统使用“expected value/expectation”)
  • A First Course in Probability Sheldon Ross(入门教材中频繁出现该术语)
  • Probability and Random Processes Geoffrey Grimmett & David Stirzaker(在随机过程与期望的章节中反复使用)
  • The Black Swan Nassim Nicholas Taleb(讨论风险与决策时涉及“expected value/expectation”的概念与批评)
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