Aims

The aim of the module is to give students an heuristic introduction to elementary probability theory, in preparation for courses on statistical analysis and advanced courses on probability and stochastic processes.

Learning objectives

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

• Model simple experiments using probability theory;
• Perform standard probability calculations;
• Understand the concepts of random variables and distributions;
• Compute moments of random variables;
• Perform simple transformations of random variables.

Syllabus

Topics to be discussed are:

• Experiments and sample spaces;
• Basic laws of probability;
• Counting arguments (permutations and combinations);
• Conditional probability and Bayes' theorem;
• Random variables;
• Some discrete and continuous distributions, and their moments;
• Transformations of random variables (time permitting).

Recommended texts

• ** S M Ross. A First Course in Probability, Prentice Hall (S 9 ROS) (5 copies in reserve collection)
• * A M Arthurs, Probability theory. London: Routledge & Kegan Paul. (S 9 ART).
• * M Dwass, Probability and Statistics: An Undergraduate Course. W.A. Benjamin, Inc. (S 9 DWA).
• * S M Ross, Introduction to Probability models. London: Academic Press (S 9.2 ROS).

In addition, students may find it useful to obtain a copy of the following tables:

• H R Neave, Statistics tables for mathematicians, engineers, economists and the behavioural and management sciences (SF 0.83 NEA and REF SF 0.83 NEA).

Teaching

• Summer Term
• 3 lectures per week
• Weekly seminar

Assessment

One and a half hour closed examination, late Week 8 or Week 9 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 theory. The approach is heuristic and non-rigorous and it is expected that students develop problem solving skills that require simple probabilistic modeling.
Please check prerequisites carefully before asking to take this module as an elective. You will need to be confident with the notions of sets, functions, limits, differentiation and integration, and the Fundamental Theorum of Calculus.

Prerequisites

• Core Mathematics

Postrequisites

The following modules use material from this module

• Statistical Theory I requires: all
• Probability Theory II requires: all
• Mathematical Finance I requires: all