Probability

This subject offers a thorough grounding in the basic concepts of mathematical probability and probabilistic modelling. Topics covered include random experiments and sample spaces, probability axioms and theorems, discrete and continuous random variables/distributions (including measures of location, spread and shape), expectations and generating functions, independence of random variables and measures of dependence (covariance and correlation), methods for deriving the distributions of transformations of random variables or approximations for them (including the central limit theorem). The probability distributions and models discussed in the subject arise frequently in real world applications. These include a number of widely used one- and two-dimensional (particularly the bivariate normal) distributions and also fundamental probability models such as Poisson processes and Markov chains.

本课程提供数学概率和概率建模基本概念的全面基础。涵盖的主题包括随机实验和样本空间、概率公理和定理、离散和连续随机变量/分布（包括位置、散布和形状的度量）、期望和生成函数、随机变量的独立性和依赖性度量（协方差和相关性）、推导随机变量变换分布或其近似值的方法（包括中心极限定理）。本课程讨论的概率分布和模型在现实世界应用中频繁出现。

• 1have a systematic understanding of the basic concepts of probability space, probability distribution, random variable (including the bivariate case) and expectation
• 2be able to use conditional expectations, generating functions and other basic techniques taught in the subject;
• 3be able to interpret a number of important probabilistic models, including simple random processes such as the Poisson process and finite discrete time Markov chains, and appreciate their relevance to real world problems;
• 4be able to formalize simple real-life situations involving uncertainty in the form of standard probabilistic models and to analyse the latter;
• 5develop understanding of the relevance of the probabilistic models from the subject to the important areas of applications such as statistics and actuarial studies.