概率与统计

学分: 3

统计学主要研究数据和不确定性，往往被视为一门独立的科学而非数学的一个分支。统计方法帮助我们根据数据集合得出结论，如居住在高压电线铁塔附近是否非常危险。统计学也用于设计有效的试验，决定应该收集哪些数据。例如，统计方法可能用于确认飞机部件安全测试的频率。这些方法的根本在于假设这些数据是随机变量样本，遵循说明此类行为的概率分布。

本课程将讲述概率与统计；在课堂上简要讨论概率理论，包括贝叶斯定理；讲述关键的离散和连续概率模型（如二项式、泊松分布、正态分布）；讲述期望和方差的属性。在讲述基本统计学概念（如统计推断和假设检验理论）之前，本课程将讲述弱大数定律和中心极限定理。本课程将利用现实世界的数据说明该理论。

在本课程结课时，学生应能够：

• 计算概率和条件概率并在标准情景中应用贝叶斯定理

• 了解和应用合适情景中的标准离散与连续概率模型

• 了解期望和方差的属性，并在标准情景中应用

• 理解弱大数定律和中心极限定理的重要性

• 理解和应用基本统计方法，如推断、点估计、置信区间、假设检验等。

Probability and Statistics 概率与统计

Credits: 3

Statistics, often regarded as distinct science rather than a branch of mathematics, is the study of data and uncertainty. Statistical techniques allow us to make conclusions, such as whether or not living near electricity pylons is dangerous, from sets of data. Statistics is also used in the design of effective experiments and in determining what data should be collected. For example, statistical techniques might be used to determine the frequency with which aircraft components should be tested for safety. Underlying these techniques is the assumption that these data are samples of a random variable that follows a probability distribution describing their behaviour.

This module introduces probability and statistics. Axiomatic probability theory, including Bayes’ Theorem, is discussed briefly. Key discrete and continuous probability modules(such as the binomial, Poisson and normal distributions) are introduced. Properties of expectation and variance are discussed. The Weak Law of Large Numbers and the Central Limit Theorem are covered before basic statistical ideas, such as statistical inference and hypothesis testing are introduced. Real world data are used to illustrate the theory.

By the end of this module, students should be able to:

• Calculate probabilities and conditional probabilities and apply Bayes’ Theorem in standard situations.

• Know and use the standard discrete and continuous probability models in appropriate situations.

• Know the properties of expectation and variance and apply them to in standard situations.

• Appreciate the significance of the Weak Law of Large Numbers and the Central Limit Theorem.

• Understand and apply basic statistical techniques such as inference, point estimation, confidence intervals, hypothesis testing