Current 2011/12 Module Catalogue

Module Details

Module Code:
MAT2013
Module Provider:
Mathematics
Level:
HE2
Number of Credits:
15
Module Title:
MATHEMATICAL STATISTICS
Module Co-ordinator:
YOUNG KD Dr (Maths)
ECTS Credits
7.5

Module Availability

Spring semester

Assessment Pattern

Components of Assessment 
Method(s) 
Percentage weighting 
Coursework 
Assignments and tests  
25%
Examination  
Written Examination (2 hours, unseen) 
75%

Prerequisites/Co-requisites

MS131 Probability and Statistics

Module Aims

This module provides theoretical background for many of the topics introduced in MS131 and for some of the topics that will appear in subsequent statistics modules.

Learning Outcomes

At the end of the module, a student should:
(1) be familiar with the main results of intermediate distribution theory;
(2) be able to apply this knowledge to suitable problems in statistics.

Module Content

  • Review of probability and basic univariate distributions.
  • Bivariate and multivariate distributions.
  • Transformations.
  • Moments, generating functions and inequalities.
  • Further discrete and continuous distributions: negative binomial, hypergeometric, multinomial, gamma, beta.
  • Univariate, bivariate and multivariate normal distributions.
  • Proof of the central limit theorem.
  • Distributions associated with the normal distribution: Chi-square, t and F. Application to normal linear models.
  • Theory of minimum variance unbiased estimation.

Methods of Teaching/Learning

Teaching is by lectures and tutorials. Learning takes place through lectures, tutorials, exercises and background reading.

3 lecture/tutorial hours per week for 10 weeks

Selected Texts/Journals

Recommended Reading
R.V. Hogg and E.A. Tanis, Probability and Statistical Inference, Prentice-Hall, (1997).

Further Reading
A.M. Mood, F.G. Graybill and D.C. Boes, Introduction to the Theory of Statistics, McGraw-Hill, (1974).

Last Updated

15 August 2006

Module Availability

Spring semester

Assessment Pattern

Unit(s) of Assessment

 

Weighting Towards Module Mark( %)

 

2 hour unseen examination

 

75%

 

corsework

 

25%

 

Qualifying Condition(s) 

 

A weighted aggregate mark of 40% is required to pass the module.

 

Prerequisites/Co-requisites

MS131 Probability and Statistics

Module Aims

This module provides theoretical background for many of the topics introduced in MS131 and for some of the topics that will appear in subsequent statistics modules.

Learning Outcomes

At the end of the module, a student should:
(1) be familiar with the main results of intermediate distribution theory;
(2) be able to apply this knowledge to suitable problems in statistics.

Module Content

  • Review of probability and basic univariate distributions.
  • Bivariate and multivariate distributions.
  • Transformations.
  • Moments, generating functions and inequalities.
  • Further discrete and continuous distributions: negative binomial, hypergeometric, multinomial, gamma, beta.
  • Univariate, bivariate and multivariate normal distributions.
  • Proof of the central limit theorem.
  • Distributions associated with the normal distribution: Chi-square, t and F. Application to normal linear models.
  • Theory of minimum variance unbiased estimation.

Methods of Teaching/Learning

Teaching is by lectures and tutorials. Learning takes place through lectures, tutorials, exercises and background reading.

3 lecture/tutorial hours per week for 10 weeks

Selected Texts/Journals

Recommended Reading
R.V. Hogg and E.A. Tanis, Probability and Statistical Inference, Prentice-Hall, (1997).

Further Reading
A.M. Mood, F.G. Graybill and D.C. Boes, Introduction to the Theory of Statistics, McGraw-Hill, (1974).

Last Updated

31 July 2007

Module Availability

Spring Semester

Assessment Pattern

Unit(s) of Assessment
Weighting Towards Module Mark( %)
2 hour unseen examination
75%
Test
10%
Coursework
15%
Qualifying Condition(s) 
A weighted aggregate mark of 40% is required to pass the module.

Module Overview

The module gives a presentation of some fundamental mathematical theory underlying statistics.

Prerequisites/Co-requisites

The probability component of MAT1017 is pre-requisite.

Module Aims

This module provides theoretical background for many of the topics introduced in the probability component of MS125 and for some of the topics that will appear in subsequent statistics modules.

Learning Outcomes

At the end of the module, a student should: 
(1) be familiar with the main results of intermediate distribution theory; 
(2) be able to apply this knowledge to suitable problems in statistics.

Module Content

Review of probability and basic univariate distributions.
 
Bivariate and multivariate distributions.
 
Transformations.
 
Moments, generating functions and inequalities.
 
Further discrete and continuous distributions: negative binomial, hypergeometric, multinomial, gamma, beta.
 
Univariate, bivariate and multivariate normal distributions.
 
Proof of the central limit theorem.
 
Distributions associated with the normal distribution: Chi-square, t and F.
 
Application to normal linear models.
 
Theory of minimum variance unbiased estimation.

Methods of Teaching/Learning

Teaching is by lectures and example classes. Learning takes place through lectures, exercises (example sheets) and background reading.

Selected Texts/Journals

Recommended
J.E. Freund, Mathematical Statistics with Applications, Pearson, (2004).
R.V. Hogg and E.A. Tanis, Probability and Statistical Inference, Prentice-Hall, (1997).
 
Further Reading
A.M. Mood, F.G. Graybill and D.C. Boes, Introduction to the Theory of Statistics, McGraw-Hill, (1974).

Last Updated

04.11.08

Module Availability

Semester 2

Assessment Pattern

Unit(s) of Assessment

 

Weighting Towards Module Mark( %)

 

2 hour unseen examination

 

75

 

Test

 

10

 

Coursework

 

15

 

Qualifying Condition(s) 

 

A weighted aggregate mark of 40% is required to pass the module.

 

 

Module Overview

The module gives a presentation of some fundamental mathematical theory underlying statistics.

Prerequisites/Co-requisites

The probability component of MAT1025 is a pre-requisite.

Module Aims

This module provides theoretical background for many of the topics introduced in the probability component of MS1025 and for some of the topics that will appear in subsequent statistics modules.

Learning Outcomes

At the end of the module, a student should: 
(1) be familiar with the main results of intermediate distribution theory; 
(2) be able to apply this knowledge to suitable problems in statistics.

Module Content

Review of probability and basic univariate distributions.

 

 

 

Bivariate and multivariate distributions.

 

 

 

Transformations.

 

 

 

Moments, generating functions and inequalities.

 

 

 

Further discrete and continuous distributions: negative binomial, hypergeometric, multinomial, gamma, beta.

 

 

 

Univariate, bivariate and multivariate normal distributions.

 

 

 

Proof of the central limit theorem.

 

 

 

Distributions associated with the normal distribution: Chi-square, t and F.

 

 

 

Application to normal linear models.

 

 

 

Theory of minimum variance unbiased estimation.

Methods of Teaching/Learning

Teaching is by lectures and example classes. Learning takes place through lectures, exercises (example sheets) and background reading.

Selected Texts/Journals

Recommended

 

J.E. Freund, Mathematical Statistics with Applications, Pearson, (2004).

 

R.V. Hogg and E.A. Tanis, Probability and Statistical Inference, Prentice-Hall, (1997).

 

 

 

Further Reading

 

A.M. Mood, F.G. Graybill and D.C. Boes, Introduction to the Theory of Statistics, McGraw-Hill, (1974).

Last Updated

September 10

Module Availability

Semester 1

Assessment Pattern

Unit(s) of Assessment
Weighting Towards Module Mark( %)
2 hour unseen examination
75
2 class tests
25
 
 
Qualifying Condition(s) 
A weighted aggregate mark of 40% is required to pass the module.
 

Module Overview

The module gives a presentation of some fundamental mathematical theory underlying statistics.

Prerequisites/Co-requisites

MAT1028 Probability

Module Aims

This module provides theoretical background for many of the topics introduced in the probability component of MS1025 and for some of the topics that will appear in subsequent statistics modules.

Learning Outcomes

At the end of the module, a student should:
(1) be familiar with the main results of intermediate distribution theory;
(2) be able to apply this knowledge to suitable problems in statistics.

Module Content

Review of probability and basic univariate distributions.
Bivariate and multivariate distributions.
Transformations.
Moments, generating functions and inequalities.

Further discrete and continuous distributions: negative binomial, hypergeometric, multinomial, gamma, beta.
Univariate, bivariate and multivariate normal distributions.
Proof of the central limit theorem.
Distributions associated with the normal distribution: Chi-square, t and F.
Application to normal linear models.
Theory of minimum variance unbiased estimation.

Methods of Teaching/Learning

Teaching is by lectures and example classes. Learning takes place through lectures, exercises (example sheets) and background reading.

Selected Texts/Journals

Background Reading
J.E. Freund, Mathematical Statistics with Applications, Pearson, (2004).
R.V. Hogg and E.A. Tanis, Probability and Statistical Inference, Prentice-Hall, (1997).
A.M. Mood, F.G. Graybill and D.C. Boes, Introduction to the Theory of Statistics, McGraw-Hill, (1974).

Last Updated

8 June 2011