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

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

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).

15 August 2006

Spring semester

### Assessment Pattern

Unit(s) of Assessment

###### Weighting Towards Module Mark( %)

2 hour unseen examination

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

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).

31 July 2007

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).

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

04.11.08

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).

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

September 10

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.