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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

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Mathematics · 术语表

什么是 Random variable, distribution？

又称： random variable · distribution

Definition 18.5 High School Mathematics · 第 18 章 — Probability and Random Variables

A random variable on $\Omega$ is a function $X$ assigning a number to each outcome. Its distribution is the table of its possible values $x_1, \dots, x_k$ together with their probabilities

\P(X = x_i) = \P\bigl(\{\omega : X(\omega) = x_i\}\bigr), \qquad \sum_{i=1}^k \P(X = x_i) = 1 .

示例

Example 18.6

A game: pay $2$ euros, roll one fair die, receive the value shown if it is at least $5$ , nothing otherwise. Let $G$ be the gain (received minus paid). The outcomes $1, 2, 3, 4$ give $G = -2$ ; the outcome $5$ gives $G = 3$ ; the outcome $6$ gives $G = 4$ . The distribution of $G$ :

$g$	$-2$	$3$	$4$
$\P(G = g)$	$\dfrac46$	$\dfrac16$	$\dfrac16$

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Definition 33.1 High School Mathematics · 第 33 章 — Random Variables and the Binomial Distribution

A random variable on a finite sample space $\Omega$ is a function $X \colon \Omega \to \R$ . Its distribution (or law) is the data of its possible values $x_1, \dots, x_k$ and of the probabilities

p_i = \P(X = x_i), \qquad \sum_{i=1}^{k} p_i = 1 .

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