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Unit information: Further Topics In Probability 3 in 2016/17

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Unit name Further Topics In Probability 3 MATH30006 20 H/6 Teaching Block 2 (weeks 13 - 24) Dr. Balazs Not open Applied Probability 2 (MATH21400). Measure Theory and Integration (MATH34000) would be useful but is not essential. None. School of Mathematics Faculty of Science

Description

Unit aims

To outline, discuss, and prove with full mathematical rigour some of the key results in classical probability theory; with special emphasis on applications.

General Description of the Unit

This course deals with various analytic tools used and exploited in probability theory. Various modes of convergence of random variables (almost surely, weak, in probability, in Lp and in distribution) and the connections between them are presented. The key theorems are the Weak and Strong Laws of Large Numbers and the Central Limit Theorem. The analytic tools are: generating functions, Laplace- and Fourier transforms and fine analysis thereof.

Additional unit information can be found at http://www.maths.bristol.ac.uk/study/undergrad/current_units/index.html

Intended learning outcomes

Learning Objectives

To gain profound understanding of the basic notions and techniques of analytic methods in probability theory. In particular: generating functions, Laplace- and Fourier-transforms. To gain insight and familiarity with the various notions of convergence in the theory of random variables (in probability, almost sure, L^p, in distribution). Special emphasis will be on various “down-to-earth” applications of the mathematical theory.

Teaching details

Lectures supported by problem sheets and solution sheets.

Assessment Details

80% Examination and 20% Coursework

Reading and References

Reading and references are available at http://www.maths.bristol.ac.uk/study/undergrad/current_units/index.html