Year 13 Edexcel Statistics: Formula & Theorem Quick Reference Handbook | Year 13 Edexcel 统计：公式定理速查手册

📚 Year 13 Edexcel Statistics: Formula & Theorem Quick Reference Handbook | Year 13 Edexcel 统计：公式定理速查手册

This handbook provides a concise summary of key formulas and theorems in Year 13 Edexcel Statistics, covering probability, distributions, estimation and hypothesis testing. Use this quick reference to reinforce your understanding and prepare efficiently for exams.

本手册简要汇总了 Year 13 Edexcel 统计课程的核心公式与定理，涵盖概率、概率分布、估计与假设检验等内容。通过这份速查手册，你可以巩固理解，高效备考。

1. Probability & Bayes’ Theorem | 概率与贝叶斯定理

For any two events A and B, conditional probability: P(A|B) = P(A ∩ B) / P(B), provided P(B) > 0.

对于任意两个事件 A 和 B，条件概率：P(A|B) = P(A ∩ B) / P(B)，其中 P(B) > 0。

Bayes’ Theorem: P(A|B) = [P(B|A) P(A)] / P(B). Often expanded using the law of total probability: P(B) = Σ P(B|A_i) P(A_i).

贝叶斯定理：P(A|B) = [P(B|A) P(A)] / P(B)。通常利用全概率公式展开：P(B) = Σ P(B|A_i) P(A_i)。

Mutual exclusivity: if A ∩ B = ∅ then P(A ∪ B) = P(A) + P(B). Independence: P(A ∩ B) = P(A) P(B).

互斥事件：若 A ∩ B = ∅ 则 P(A ∪ B) = P(A) + P(B)。独立事件：P(A ∩ B) = P(A) P(B)。

2. Discrete Random Variables | 离散随机变量

A discrete random variable X takes countable values x_i with probabilities p(x_i) = P(X = x_i). The total probability is 1: Σ p(x_i) = 1.

离散随机变量 X 取可数个值 x_i，概率为 p(x_i) = P(X = x_i)。概率总和为 1：Σ p(x_i) = 1。

Expected value: E(X) = μ = Σ x_i p(x_i). Variance: Var(X) = E[(X−μ)²] = Σ (x_i−μ)² p(x_i) = E(X²) − [E(X)]².

期望值（均值）：E(X) = μ = Σ x_i p(x_i)。方差：Var(X) = E[(X−μ)²] = Σ (x_i−μ)² p(x_i) = E(X²) − [E(X)]²。

Linear transformations: for constants a, b, E(aX + b) = aE(X) + b, Var(aX + b) = a² Var(X). Standard deviation SD(X) = √Var(X).

线性变换：对于常数 a, b，E(aX + b) = aE(X) + b，Var(aX + b) = a² Var(X)，标准差 SD(X) = √Var(X)。

3. Binomial Distribution | 二项分布

X ~ B(n, p) models the number of successes in n independent trials, each with success probability p.

X ~ B(n, p) 模拟在 n 次独立试验中成功的次数，每次成功概率为 p。

Probability mass function: P(X = r) = ⁿC_r p^r (1−p)^n−r, for r = 0,1,…,n. Here ⁿC_r = n! / [r!(n−r)!].

概率质量函数：P(X = r) = ⁿC_r p^r (1−p)ⁿ⁻

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