35252 Mathematical Statistics

Warning: The information on this page is indicative. The subject outline for a particular semester, location and mode of offering is the authoritative source of all information about the subject for that offering. Required texts, recommended texts and references in particular are likely to change. Students will be provided with a subject outline once they enrol in the subject.

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, and 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 course aims and graduate attributes

This subject contributes to the development of the following graduate attributes:

1. Disciplinary knowledge and its appropriate application
The lectures, weekly exercises and assignments impart skills necessary in a number of mathematical disciplines and demonstrate how to apply these skills to a variety of problems.

2. An Enquiry-oriented approach
The weekly exercises and assignments present a number of problems where the student has to decide which of the techniques covered in lectures is the most appropriate to deal with the problem. Critical thinking is essential.

3. Professional skills and their appropriate application
This subject helps students learn to manage their own work and to accept responsibility for their own learning. Examples and problems are drawn from typical real life situations.

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

A student must obtain at least 40% of the marks available for the final examination in order to pass the subject. If at least 40% is not achieved, an X (fail) grade will be awarded regardless of the total marks obtained in the subject.

A student should demonstrate competence in all aspects of the assessment in order to pass the subject. To pass the subject, a student must achieve a final result of 50% or more. The final result is simply the sum of the marks gained in each piece of assessment.

Recommended texts

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

Shao, J: Mathematical Statistics. Springer 2003.

Gatt, P.: Probability Theory and Mathematical Statistics for Engineers. Spon Press 2005.

G. Ivchenko Yy. Medvedev A. Chistyakov: Problems in Mathematical Statistics. Mir publishers Moscow