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| Module Availability |
| Semester 2 |
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| Assessment Pattern |
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Unit(s) of Assessment
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Weighting Towards Module Mark( %)
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2 hour unseen examination
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75
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Test
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10
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Coursework
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15
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Qualifying Condition(s)
A weighted aggregate mark of 40% is required to pass the module.
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| Module Overview |
| The module gives a presentation of some fundamental mathematical theory underlying statistics. |
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| Prerequisites/Co-requisites |
| The probability component of MAT1025 is a pre-requisite. |
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| 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. |
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| 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. |
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| 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. |
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| Methods of Teaching/Learning |
| Teaching is by lectures and example classes. Learning takes place through lectures, exercises (example sheets) and background reading. |
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| 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). |
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| Last Updated |
| September 10 |
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