35252 Mathematical Statistics

Subject coordinator

Name: Narelle Smith

Phone: 9514 2239

Room: CB01.15.39

Email: narelle.smith@uts.edu.au

Handbook description

Advanced statistical analysis in areas such as marketing, survey design and financial modelling requires insight into the mathematical foundations of statistics. This subject aims to develop such insight and introduces students to the concepts and terminology required in more advanced applications. Topics include: probability; random variables and their probability distributions; limiting distributions; multivariate probability distributions; functions of random variables; estimators and their properties; hypotheses and their tests; order statistics.

Subject objectives/outcomes

After successfully completing this subject you should be able to:

1.  Define relevant terminology, notation, theorems and concepts in mathematical terms and in your own words.
2.  Formulate and solve applied and theoretical problems in probability and statistics.
3. Represent and use probability distributions and random variables.
4.  Determine moments and generating functions for discrete and continuous random variables.
5.  Use the standard univariate distributions to solve theoretical and applied problems.
6.  Use a variety of methods for transformation and change of variables in one and two dimensions.
7.  Discuss and derive standard sampling distributions based on the normal distribution and order statistics.
8.  Discuss and explain the concepts of point estimation and be able to determine moment and maximum likelihood estimators and examine their properties.
9.  Understand different types of tests and determine the most appropriate type of test in a given situation.

Contribution to graduate profile

This subject provides students with the skills and understanding to apply appropriate statistical techniques and methods in solving problems in a variety of professional fields. It also helps students appreciate the need for critical and independent evaluation of statistical problems and the effective communication of the results of the statistical analysis.

Teaching and learning strategies

The presentation of this subject will consist of three hours of lectures and a one hour tutorial session each week.

Face-to-face classes will incorporate a range of teaching and learning strategies including presentation of theoretical material, discussion of readings and practical applications and both student groupwork and individual problem solving. It is expected that students will supplement this with individual study and problem solving.

Content

This subject will cover topics selected from: probability spaces; density and generating functions for discrete and continuous random variables; marginal, conditional and joint density functions of multivariate distributions; methods of finding distributions of functions of random variables; limiting distributions; properties and methods of finding estimators of parameters; different forms of hypothesis tests and the distribution and use of order statistics.

Assessment

Assessment item 1: Assignment 1

Assessment item 2: Assignment 2

Assessment item 3: Final examination

Minimum requirements

If you score less than 40% on the final examination, your final assessment mark will be the minimum of a mark of 44% and the mark obtained by using the standard assessment procedure. If you score less than 55% on the final examination, your final assessment mark will be the minimum of a mark of 64% and the mark obtained by using the standard assessment procedure.

Recommended text(s)

Wackerly, D., Mendenhall, W. and Scheaffer, Mathematical Statistics with Applications 7th ed. Duxbury 2002.