620-302 Modern Probability

Credit Points

Coordinator

Prerequisites

620-201 and one of 620-112, 620-122, 620-200, 620-211.

Semester

Contact

Subject Description

This subject deals with elementary abstract probability theory with its emphasis on probability spaces, random variables and stochastic processes and the basic methods used in probability, particularly involving characteristic functions. The concepts of probabilistic convergence and limit results are introduced. Students learn to handle operations with random variables, distributions and characteristic functions, to derive convergence properties using inequalities and transforms of random variables and to analyse and interpret probabilistic properties in practical situations. The subject demonstrates the importance of probability theory in the study of real life phenomena and shows the importance of probability theory as a basis of the theory of Statistics.

Topics covered: 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; elements of stochastic processes.

Assessment

A 3-hour end of semester written examination; up to 50 pages of assignments may be assessed.