V2EX random variable

Random Variable

Definition / 定义

随机变量:在概率论中,把随机试验的每个结果映射为一个数值的函数(通常记为 \(X, Y\))。它的取值不确定,但可以用概率分布来描述其规律。(也常泛指“离散随机变量/连续随机变量”等类型。)

Pronunciation / 发音

/rndm vribl/

Examples / 例句

A random variable can take different values each time you repeat the experiment.
随机变量在你每次重复实验时都可能取不同的值。

Let \(X\) be a random variable representing daily demand; if \(X\) follows a normal distribution, we can compute the probability that demand exceeds a certain threshold.
设 \(X\) 表示每日需求的随机变量;如果 \(X\) 服从正态分布,我们就能计算需求超过某个阈值的概率。

Etymology / 词源

random 源自中古法语 randon(意为“冲动、随意、偶然”一类的含义),后来在英语里发展为“随机的、非确定的”。variable 来自拉丁语 variabilis(“可变化的”)。合在一起的 random variable 是概率论中的专门术语,强调“其数值会随随机结果而变化”。

Related Words / 相关词汇

Literary Works / 文学作品举例

  • William Feller, An Introduction to Probability Theory and Its Applications(系统使用并阐释“random variable/随机变量”概念)
  • Sheldon M. Ross, A First Course in Probability(入门教材中大量出现该术语与例题)
  • Grimmett & Stirzaker, Probability and Random Processes(在随机过程语境下频繁出现)
  • A. N. Kolmogorov, Foundations of the Theory of Probability(现代概率论公理化框架下的核心概念之一)
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