Module Identifier MX36010  
Academic Year 2003/2004  
Co-ordinator Mr Alan Jones  
Semester Semester 1  
Other staff Dr J G Basterfield  
Pre-Requisite MA11310  
Mutually Exclusive MA26010  
Course delivery Lecture   19 x 1 hour lectures  
  Seminars / Tutorials   3 x 1 hour example classes  
Assessment TypeAssessment Length/DetailsProportion
Semester Exam2 Hours (written examination)  100%
Supplementary Assessment2 Hours (written examination)  100%

Learning outcomes

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

Brief description

In many situations in statistics and probability it is necessary to handle more than one random variable at the same time. This module covers techniques needed to do this, and also to deal with functions of random variables. Particular attention will be paid to the case of random variables arising from a Normal random sample. The module concludes with some material on the theory of estimation.


This module will provide a thorough grounding in distribution theory for several random variables, and will also consolidate the material on estimation introduced in MA11310.


1. DISCRETE AND CONTINUOUS BIVARIATE DISTRIBUTIONS: Marginal and conditional distributions. Cumulative distribution functions. Independence.
2. GAMMA DISTRIBUTION: Gamma function. Gamma distribution.
3. FUNCTIONS OF RANDOM VARIABLES: Calculation of the pdf of a function of one or more random variables by (a) distribution functions, (b) transformation using the Jacobian, (c) moment generating functions.
4. SAMPLING DISTRIBUTIONS FOR NORMAL SAMPLES: The chi-squared, t and F distributions and their relationships to the Normal. The idea of a sample. Sampling distributions for statistics of the Normal sample.
5. POINT ESTIMATORS: The concepts of estimator and estimate. Maximum likelihood. Unbiasedness as a criterion.

Reading Lists

** Supplementary Text
D D Wackerley, W Mendenhall & R L Scheaffer (2002) Mathematical Statistics with Applications 6th. Duxbury. 0534377416


This module is at CQFW Level 6