📚 Pre-U CAIE Statistics: Unit Test Mock Paper Analysis | Pre-U CAIE 统计:单元测试模拟卷解析
This mock unit test analysis is designed to reinforce key topics in the Pre-U CAIE Statistics syllabus. The paper contains eight structured questions that span discrete random variables, Poisson approximation, normal distribution, sampling distributions, confidence intervals, hypothesis testing, chi-squared goodness-of-fit, and linear regression. Every question is fully worked through, with detailed steps and commentary in both English and Chinese. Use these solutions to identify common pitfalls and strengthen your exam technique.
本模拟单元测试解析旨在巩固 Pre-U CAIE 统计课程的核心考点。试卷包含八道结构化题目,涵盖离散随机变量、泊松近似、正态分布、抽样分布、置信区间、假设检验、卡方拟合优度以及线性回归。每道题均提供完整演算步骤和中英双语解析,帮助你发现易错点,提升应试技巧。
1. Exam Overview | 考试概览
This mock paper simulates the style of Pre-U Statistics unit tests, blending straightforward calculations with interpretative questions. The eight questions progress from probability foundations to inference and modelling. Candidates should pay close attention to the phrasing of hypotheses, the choice of distributional approximations, and the proper use of statistical tables. Marks are awarded not only for correct numerical answers but also for clear reasoning and accurate notation.
本模拟卷贴近 Pre-U 统计单元测试风格,将基础计算与分析性问题相结合。八道题目由概率基础逐步推进到推断与建模。考生应特别注意假设的表述方式、分布近似的适用条件以及统计表格的规范使用。得分不仅依赖数值正确,更看重清晰的推理过程和准确的符号表达。
2. Q1: Discrete Random Variables | 离散随机变量
Question: The probability distribution of a discrete random variable X is given by P(X = 1) = 0.2, P(X = 2) = 0.5 and P(X = 3) = 0.3. (a) Find E(X) and Var(X). (b) Given Y =
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