Introductory description

This module introduces core concepts in Probability and Statistics that are needed for further modules in both Probability and Statistics.

Pre-requisites: ST118 Probability 1, ST119 Probability 2, and ST117 Introduction to Statistical Modelling, or equivalents.

This module is core for students with their home department in Statistics. It is not available to other students, for whom ST232/ST233 (Introduction to Mathematical Statistics) is provided as an alternative.

This module is a pre-requisite for ST230 Mathematical Statistics and a number of ST3 and ST4 modules.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

This module introduces the systematic study of the theory of mathematical statistics.

1. Statistical motivation for studying sample averages and joint distributions.
2. Definitions of joint, marginal and conditional distributions (discrete and continuous cases). Independent random variables. Conditional expectation and properties. Conditional variance and properties.
3. Multivariate Normal/Gaussian distribution, its properties and distributions related to it. Simulating Gaussian distributions.
4. Properties of finite sums and averages of random variables, expectation and variance of sample means, focusing on the Normal/ Gaussian distribution case.
5. Weak law of large numbers and the central limit theorem.

Learning outcomes

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

• Derive properties of finite and infinite sums and averages of random variables, including the central limit theorem. Describe its significance in statistics.
• Demonstrate knowledge of joint and conditional probability distributions, conditional expectation and conditional variance.
• State/derive and use the properties of multivariate Normal/Gaussian distribution and distributions related to Normal/Gaussian distribution.
• Communicate solutions to problems accurately with structured and coherent arguments.

Indicative reading list

Jim Pitman, Probability. 1999. Springer-Verlag New York Inc. ISBN: 9780387979748. (Available online and in print in the Main Campus Library.)

Allan Gut. An intermediate course in probability. 2009. Springer. ISBN: 9781441901620. Available online and in print in the Main Campus Library.)

View reading list on Talis Aspire

Subject specific skills

Demonstrate knowledge of key mathematical and statistical concepts, both explicitly and by applying them to the solution of mathematical problems.

Select and apply appropriate mathematical and/or statistical techniques

Create structured and coherent arguments communicating them in written form.

Transferable skills

Problem-solving skills: The module requires students to solve problems presenting their conclusions as logical and coherent arguments.

Written communication skills: Students complete written assessments that require precise and unambiguous communication in the manner and style expected in mathematical sciences.

Verbal communication skills: Students are encouraged to discuss and debate formative assessment and lecture material within small-group tutorials sessions. Students can continually discuss specific aspects of the module with the module leader. This is facilitated by staff office hours.

Professionalism: Students work autonomously by developing and sustaining effective approaches to learning, including time-management, organisation, flexibility, creativity, collaboration and intellectual integrity.