V2EX without replacement

Without Replacement

释义 Definition

without replacement”意为“不放回(抽样);抽取后不再放回原集合”,常用于概率论与统计学中,强调每次抽取会改变后续抽取的可能性(总体成分发生变化)。也可引申为“用过的资源不再补回/重复使用”。

发音 Pronunciation (IPA)

/wat rplesmnt/

例句 Examples

We sampled ten cards without replacement.
我们不放回地抽取了十张牌。

In surveys, selecting households without replacement helps avoid counting the same family twice, but it also means the probability for each remaining household changes after every selection.
在调查中,不放回地抽取住户可以避免同一家庭被重复计入,但这也意味着每次抽取后,剩余住户被抽中的概率都会改变。

词源简述 Etymology

“replacement”来自“replace(替换、放回原位/补回)”,由前缀 **re-**(再次)+ place(放置)构成;“without replacement”字面即“没有补回/放回”。该搭配在统计学语境中固定化,用来对比“with replacement(放回抽样)”。

相关词 Related Words

文学与著作中的用例 Literary Works

  • William Feller, An Introduction to Probability Theory and Its Applications(讨论不放回抽样与超几何分布时常用该表达)
  • Sheldon Ross, A First Course in Probability(在抽样模型对比“with/without replacement”时出现)
  • Morris H. DeGroot & Mark J. Schervish, Probability and Statistics(统计抽样章节常见用语)
  • Richard Courant & Herbert Robbins, *What Is Mathematics?*(在组合与计数问题的讲解中可见相关表述)
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