Spring semester

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.

MS131 Probability and Statistics

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.

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.

• 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.

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

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).

31 July 2007