Aims

To show how probability theory may be used to model a variety of random processes, such as the weather, stock markets and the spread of contagious diseases.

Learning objectives

At the end of the module you should be able to:

• Understand the generating function of a discrete random variable, and know how to interpret and apply it;
• Understand elementary aspects and calculate transition probabilities of Markov chains.

Syllabus

Topics to be discussed are:

• Probability generating functions and applications;
• Markov chains:
  • Markov property
  • Chapman-Kolmogorov equations
  • Recurrence/transience and ergodicity
• Examples: random walks and branching processes.

Recommended texts

• Geoffrey Grimmett & David Stirzaker, Probability and Random Processes, OUP.

Teaching

• Spring Term
• 2 lectures per week
• Weekly seminar

Assessment

One and a half hour closed examination, Week 1 Summer Term (90%)
Coursework (10%).  Note that coursework submitted after the advertised deadlines will be given a mark of zero.

Elective information

This module is an introduction to probability generating functions and stochastic processes.

Please check prerequisites carefully before asking to take this module as an elective.

Prerequisites

• Core Mathematics
• Probability Theory I