Spring semester

Components of Assessment	Method(s)	Percentage Weighting
Coursework	Made up of one mid-term test and two take home assignments.	25%
Examination	Written examination (2 hours, unseen).	75%

MS131 Probability and Statistics.

Realistic modelling of a real system very often requires the inclusion of probabilistic elements. A stochastic (as opposed to a deterministic) model will generally lead to more realistic predictions about the system. In this module we study a large class of stochastic processes, that is, probabilistic models for series of events.

At completion the students should have a thorough understanding of the properties of stochastic processes and be able to apply this knowledge to analyse specific stochastic processes, including biological, financial and engineering processes.

Review of basic probability and distribution theory; concept of stochastic process; random walks; properties of Markov chains: recurrence and transience, periodicity, communicating classes, irreducibility; first step analysis; Basic Limit Theorem, existence proofs for stationary distributions, applications. Markov processes in continuous time: derivation of the Poisson process and generalised birth and death process.

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

3 lectures/tutorials per week for 10 weeks.

Recommended Reading 

Murray R. Spiegel, Schaum's outline of Calculus of Finite Differences and Difference Equations (10th printing), McGraw-Hill Trade, (1994). 

H.M. Taylor and S. Karlin , An Introduction to Stochastic Modelling (rev. ed.), Academic Press, (1994).

Further Reading 

G.P. Beaumont, Introductory Applied Probability, Ellis Horwood, (1983). 

W. Feller, An Introduction to Probability Theory and its Applications: Vol. 1 (3rd ed.), Wiley, (1968). 

H.C. Tuckwell, Elementary Applications of Probability Theory, Chapman and Hall, (1995).

16 January 2008