Module Identifier MA10310  
Module Title PROBABILITY  
Academic Year 2000/2001  
Co-ordinator Dr J A Lane  
Semester Semester 1  
Other staff Mr D A Jones  
Pre-Requisite A-level Mathematics or equivalent.  
Mutually Exclusive May not be taken at the same time as any of MA12410 or MA12510.  
Course delivery Lecture   20 x 1 hour lectures  
  Seminars / Tutorials   6 x 1 hour tutorials  
  Workshop   2 x 1 hour workshops (including test)  
Assessment Exam   2 Hours (written examination)   75%  
  Continuous assessment     25%  
  Resit assessment   2 Hours (written examination)   100%  

General 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.

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

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 [MWS 2.3]. The additive rule of probability; probability of the complement. Defining probablties on sample spaces with equally likely outcomes: discrete and continuous. Permutations and combinations. Functions of random variables (monotone only). Conditional probability: definition; simple applications [MWS 2.4, 2.5, 2.8, 2.9]. 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 [MWS 2.7-2.10].
2. PROBABILITY DISTRIBUTIONS: Cumulative distribution functions: use in calculating probabilities; medians, percentiles; simple (monotone) transformations. Discrete distributions: probability mass functions; sketching; examples including Geometric [MWS 3.1, 3.2]. Continuous distributions: probability density function; sketching; examples including Pareto, Exponential [MWS 4.2]. Expected values of X and of functions of X; calculation for simple distributions; mean and variance of aX + b [MWS 3.3, 4.3].

Reading Lists
** Recommended Text
J H McColl. (1995) Probability. Edward Arnold
W Mendenhall, D D Wackerly, R L Scheaffer, [MWS]. Mathematical Statistics with Applications. 4th. PWS - Kent.
S M Ross. A First Course in Probability. Prentice Hall