📚 A-Level Mathematics: Statistics Exam Essentials | A-Level 数学：统计考点精讲
This article provides a comprehensive revision guide for the Statistics component of A-Level Mathematics, covering all major exam topics including probability, distributions, hypothesis testing, and regression. Master these concepts with clear explanations and key formulas.
本文为A-Level数学的统计部分提供全面的复习指南，涵盖所有主要考点，包括概率、分布、假设检验和回归。通过清晰的解释和关键公式，帮助你掌握这些概念。
1. Probability Basics | 概率基础
(A), satisfies 0 ≤ P(A) ≤ 1. The sum of probabilities of all elementary outcomes equals 1.
样本空间是实验所有可能结果的集合。事件是样本空间的任意子集。事件A的概率记为P(A)，满足0 ≤ P(A) ≤ 1。所有基本结果的概率总和为1。
For any two events A and B, the addition rule states: P(A ∪ B) = P(A) + P(B) − P(A ∩ B). If A and B are mutually exclusive (cannot occur together), P(A ∩ B) = 0, so P(A ∪ B) = P(A) + P(B).
任意两个事件A与B的加法法则为：P(A ∪ B) = P(A) + P(B) − P(A ∩ B)。若A和B互斥（不能同时发生），P(A ∩ B) = 0，则P(A ∪ B) = P(A) + P(B)。
The conditional probability of A given B is P(A|B) = P(A ∩ B)/P(B), provided P(B) > 0. Two events are independent if and only if P(A ∩ B) = P(A)P(B), or equivalently P(A| iagrams are particularly helpful for sequential experiments and conditional probabilities.
给定B发生下A的条件概率为P(A|B) = P(A ∩ B)/P(B)，前提P(B) > 0。两事件独立的充要条件是P(A ∩ B) = P(A)P(B)，或等价地P(A|B) = P(A)。树形图对于序贯实验和条件概率问题尤其方便。
2. Discrete Random Variables | 离散随机变量
probability distribution is often summarised in a table, and must satisfy Σ P(X = x) = 1.
离散随机变量X取可数个不同的值，每个值对应概率P(X = x)。概率分布通常用表格概括，且必须满足Σ P(X = x) = 1。
= P(X ≤ x), obtained by summing probabilities for all values not exceeding x. It is a non‑decreasing function ranging from 0 to 1.
累积分布函数为F(x) = P(X ≤ x)，通过对不超过x的所有值对应的概率求和得到。它是非递减函数，取值从0到1。
The probability mass function can model any discrete scenario, including counts of successes or events. Understanding the difference between probability and cumulative probability is crucial for later topics.
概率质量函数可以模拟任何离散场景，包括成功次数或事件计数。理解概率与累积概率的区别对后续内容至关重要。
3. Expectation and Variance | 期望与方差
The expectation (mean
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