Module Identifier MA10310  
Module Title PROBABILITY  
Academic Year 2003/2004  
Co-ordinator Dr John A Lane  
Semester Semester 1  
Pre-Requisite A-level Mathematics or equivalent.  
Mutually Exclusive May not be taken at the same time as any of MA12410, MA12510 or MA12710.  
Course delivery Seminars / Tutorials   5 x 1 hour tutorials  
  Other   Workshop. 2 x 1 hour workshops (including test)  
  Lecture   20 x 1 hour lectures  
Assessment TypeAssessment Length/DetailsProportion
Semester Exam2 Hours (written examination)  75%
Semester Assessment Continuous Assessment:  25%
Supplementary Assessment2 Hours (written examination)  100%

Learning outcomes

On completion of this module, a student should be able to:

Brief description

This module provides a grounding in probability and is a necessary precursor for any subsequent study of mathematical statistics and operational research. The emphasis is on modelling real situations, including probability calculations motivated by statistical problems. The mathematical techniques required will be introduced or revised as an integral part of the course.


To introduce students to techniques for modelling and understanding randomness and to develop a facility at calculating probabilities and moments of random variables.


1. EVENTS AND PROBABILITY: Elementary set operations; rules for describing events with emphasis on experiments and associated sample spaces; Venn Diagrams; partitions, De Morgan's Laws. The additive rule of probability; probability of the complement.
2. EQUALLY LIKELY OUTCOMES: Defining probabilities on sample spaces with equally likely outcomes: discrete and continuous. Permutations and combinations. Functions of random variables (monotone only).
3. CONDITIONAL PROBABILITY: Definition and simple applications. Tree diagrams; informal applications of the Law of Total Probability and Bayes' Theorem; uses in combinatorial problems; sampling with/without replacement. Independence. Bernoulli trials, infinite games.
4. PROBABILITY DISTRIBUTIONS: Cumulative distribution functions: use in calculating probabilities; medians, percentiles; simple (monotone) transformations.
5. DISCRETE DISTRIBUTIONS: probability mass functions; sketching; examples including Binomial and Geometric.
6. CONTINUOUS DISTRIBUTIONS: Probability density functions; sketching; examples including Pareto, Exponential.
7. MOMENTS: Expected values of X and of functions of X; calculation for simple distributions; mean and variance of aX + b.

Reading Lists

** Recommended Text
J H McColl (1995) Probability Edward Arnold 0340614269
S M Ross (1998) A first course in probability 5th. Prentice Hall 0138965234
** Supplementary Text
D D Wackerley, W Mendenhall & R L Scheaffer (2002) Mathematical Statistics with Applications 6th. Duxbury. 0534377416


This module is at CQFW Level 4