V2EX binomial distribution

Binomial Distribution

定义 Definition

二项分布:一种常见的离散型概率分布,用来描述在固定次数相互独立且每次只有“成功/失败”两种结果的重复试验中,“成功”出现的次数的概率。常用参数为试验次数 n 与成功概率 p。(也存在更广泛的用法与相关分布,但此处为最常见定义。)

发音 Pronunciation (IPA)

/banomil dstrbjun/

例句 Examples

A binomial distribution models the number of heads in ten coin flips.
二项分布可以用来刻画掷十次硬币出现正面的次数。

Assuming each trial is independent with a constant success probability, the binomial distribution lets us compute the probability of observing at least k successes out of n trials.
在每次试验相互独立且成功概率恒定的假设下,二项分布可以用来计算在 n 次试验中至少出现 k 次成功的概率。

词源 Etymology

binomial 来自拉丁语系词根:bi-(“二、双”)+ nomial(与“名称/项”相关,源自拉丁语 nomen “名字”),原意接近由两项组成的”。在数学中先用于“二项式(binomial)”,而二项分布之名与二项式定理密切相关;distribution 源自拉丁语 distribuere,意为“分配、分布”。

相关词 Related Words

文学与经典作品 Literary Works

  • An Introduction to Probability Theory and Its Applications William Feller(经典概率论教材,系统讨论二项分布及其近似)
  • A First Course in Probability Sheldon Ross(入门教材中以大量例题介绍二项分布)
  • Introduction to Mathematical Statistics Hogg, McKean & Craig(统计学教材,二项分布作为基础离散分布重点出现)
  • The Elements of Statistical Learning Hastie, Tibshirani & Friedman(在分类与概率建模背景下涉及二项分布/二项似然)
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