619-310 Further Probability

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Objectives:

Students completing this subject should:

Comprehend:

• elementary abstract probability theory with its emphasis on probability spaces, random variables and stochastic processes;

• the basic methods used in Probability particularly involving characteristic functions;

• the concepts of probabilistic convergence and limit results.

• Have developed the skills:

• to handle operations with random variables, distributions and characteristic functions;

• to derive convergence properties using inequalities and transforms of random variables;

• to analyse and interpret probabilistic properties in practical situations.

Appreciate:

• the importance of probability theory in the study of real life phenomena;

• the importance of probability theory as a basis of the theory of Statistics.

Content:

Basic methods in probability and distribution theory for discrete and continuous sample spaces; some convergence and limit theorems; distribution functions, generating functions, characteristic functions; random sums and their applications; Brownian motion; introduction to diffusion processes.

Assessment: