Aims

This module builds on the foundations of probability from MAS1616 in order for students to acquire the mathematical and probabilistic skills necessary for the further study of probability and statistics.

Module Summary
Probability is the branch of mathematics which helps us to describe, analyse and understand chance phenomena. While the development of competence in probability is an essential preparation for the study of modern statistics, probability is also an important object of study for pure mathematicians and plays a key role in many areas of applied mathematics. Perhaps the most remarkable thing we discover is that even random objects demonstrate regular patterns of behaviour which can helpfully be thought of as laws of probability.

Frequently we need to examine two or more variables at a time. Although we could study each random variable of interest separately, it may be more useful to study them jointly in order to discover relationships between them.

Outline Of Syllabus

Review of probability; Multivariate distributions; Marginal and conditional distributions; Covariance and recap of independence; Multivariate transformations; Modes of convergence of random variables; Markov & Chebyshev inequalities recap; Generating functions; Central limit theorem and Law of Large Numbers; Asymptotic confidence intervals for sample means.

Teaching Rationale And Relationship

The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking. Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems. Module drop-in sessions allow students to receive learning support in areas where they may need additional guidance.

Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of the programme accreditation.

Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one ways for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.

The coursework assignments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.