全部书籍

1 Primary & Middle School Mathematics1–9 年级在线 2 High School Mathematics10–12 年级在线 3 University Mathematics — Year 1本科一年级在线 4 University Mathematics — Year 2本科二年级在线 5 University Mathematics — Year 3本科三年级在线

1 Primary & Middle School Physics1–9 年级在线 2 High School Physics10–12 年级在线 3 University Physics — Year 1本科一年级在线 4 University Physics — Year 2本科二年级在线 5 University Physics — Year 3本科三年级在线

1 School Chemistry — Grades 1 to 121–12 年级在线 2 University Chemistry — Year 1本科一年级在线 3 University Chemistry — Year 2本科二年级在线 4 University Chemistry — Year 3本科三年级在线

1 Primary & Middle School Biology1–9 年级在线 2 High School Biology10–12 年级在线 3 University Biology — Year 1本科一年级在线 4 University Biology — Year 2本科二年级在线 5 University Biology — Year 3本科三年级在线

1 Primary & Middle School Earth and Space Sciences1–9 年级在线 2 High School Earth and Space Sciences10–12 年级在线 3 University Earth and Space Sciences — Year 1本科一年级在线 4 University Earth and Space Sciences — Year 2本科二年级在线 5 University Earth and Space Sciences — Year 3本科三年级在线

1 Markets I: The Ecosystem and Exchange-Traded Markets市场在线 2 Markets II: Rates, FX and Credit市场在线 3 Markets III: Commodities, Energy and Crypto市场在线 4 Quantitative Methods方法在线 5 Derivatives and Volatility衍生品在线 6 Rates, Credit, XVA and Risk利率、信用与风险在线 7 Research Craft: Predictors, Backtests, Measurement, Portfolios研究在线 8 Strategies I: Equities and Futures策略在线 9 Strategies II: Volatility, Relative Value, Macro and the Bank Desks策略在线 10 Microstructure and Execution交易执行在线 11 Market Making and High-Frequency Trading做市在线 12 Machine Learning for Markets机器学习在线 13 Low-Latency Software技术在线 14 Networks, Hardware and Trading Infrastructure技术在线 15 Research, Data and Risk Platforms技术在线 16 The Desk and the Firm公司运营在线 17 The Industry: Firms, Roles and Careers职业发展在线 18 Interviews I: Maths, Probability and Speed职业发展在线 19 Interviews II: Markets, Trading Games and the Final Round职业发展在线 20 Interviews III: Code职业发展在线

全部游戏 Math Fuse Word Reactor Atlas Dash

应用关于

Coach

English Français Español Nederlands Português हिन्दी العربية Bahasa Indonesia 简体中文 বাংলা

登录开始阅读

书籍暂未推出简体中文版——当前显示英文版。

Mathematics · 术语表

什么是 Independent random variables？

又称： random variable independent

Definition 34.2 High School Mathematics · 第 34 章 — Sums of Random Variables and the Law of Large Numbers

$X$ and $Y$ are independent if for all values $x, y$ :

\P(X = x \text{ and } Y = y) = \P(X = x)\,\P(Y = y).

Several variables $X_1, \dots, X_n$ are independent if this product rule holds for every choice of values of every subfamily.

示例

Example 34.5 (Binomial revisited)

A binomial variable $X \sim \mathcal B(n, p)$ is a sum $X = X_1 + \dots + X_n$ of $n$ independent Bernoulli variables. Hence, structurally:

\E(X) = np, \qquad \V(X) = np(1-p),

recovering Theorem 33.8 without any computation.

在原文中阅读 →