Module Identifier MA26010  
Academic Year 2000/2001  
Co-ordinator Mr D A Jones  
Semester Semester 1  
Other staff Dr J G Basterfield  
Pre-Requisite MA11310  
Mutually Exclusive MX36010  
Course delivery Lecture   19 x 1hour lectures  
  Seminars / Tutorials   3 x 1hour example classes  
Assessment Exam   2 Hours (written examination)   100%  
  Resit assessment   2 Hours (written examination)   100%  

General 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 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 also consolidates the material on estimation introduced in MA11310.

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

1. DISCRETE AND CONTINUOUS BIVARIATE DISTRIBUTIONS: Marginal and conditional distributions. Cumulative distribution functions. Independence. Revision of covariance and correlation.
2. 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.
3. SAMPLING DISTRIBUTIONS AND THE CENTRAL LIMIT THEOREM: The idea of a sample. The chi-squared, t and F distributions and their relationships to the Normal. Sampling distributions for statistics of the Normal sample. The Central Limit Theorem.
4. POINT ESTIMATORS: The concepts of estimator and estimate. Unbiasedness and mean square error as criteria. Maximum likelihood.

Reading Lists
** Recommended Text
W Mendenhall, D D Wackerly & R L Schaeffer. Mathematical Statistics with Applications. PWS-Kent
** Supplementary Text
R V Hogg & A T Craig. Introduction to Mathematical Statistics. Macmillan
B W Lindgren. Statistical Theory. Macmillan
A M Mood, F A Graybill & D C Boes. Introduction to the Theory of Statistics. McGraw-Hill
M G Kendall & A Stuart. The Advanced Theory of Statistics (3 vols. of which vol. 2 (or 2A) is the most relevant). Several editions, the later ones with K Ord. Griffin