133 Advanced statistics: distribution theory (half unit)

Prerequisite

If taken as part of a BSc Degree, 04A Statistics 1 and 04B Statistics 2 as a
prerequisite. A high level of competence in mathematics is also assumed.

Aims and objectives

The aim of this unit is to provide a thorough theoretical grounding in probability
distributions. The unit teaches fundamental material that is required for specialised
courses in statistics, actuarial science and econometrics.
Learning outcomes
After successfully completing this half unit students will:
? Be familiar with a large number of distributions and be competent working with
their mass/density, distribution functions and moment generating function.
? Understand relationships between variables, conditioning, independence and
correlation.
?
Be able to put together the theory and method taught in the unit to solve practical
problems. Syllabus
Probability; Probability measure. Conditional probability. Bayes’ theorem.
Distribution Theory; Distribution function. Mass and density. Expectation
operator. Moments, moment generating functions, cumulant generating functions.
Convergence concepts
Multivariate Distributions; Joint distributions. Conditional distributions,
conditional moments. Functions of random variables.
Essential reading
Grimmett, G. and D. Stirzaker Probability and Random Processes. (OUP, 2001)
third edition [ISBN 0198572220]
Casella, G. and R.L. Berger Statistical Inference. (Duxbury, 2002) second edition
[ISBN 0534243126]
Assessment
This half unit is assessed by a two hour unseen written examination.

All information in this document is subject to confirmation in the Programme Regulations for
degrees and diplomas in Economics, Management, Finance and the Social Sciences that are
reviewed annually. Notice is also given in the Regulations of any units which are being phased
out and students are advised to check unit availability.