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This subject introduces a measured-theoretic approach to probability theory and presents its fundamentals concepts and results.
Topics covered include: probability spaces and random variables, expectation, conditional expectation and distributions, elements of multivariate distribution theory, modes of convergence in probabilty theory, characteristics functions and their application in key limit theorems.
Intended learning outcomes
On completion of this subject students should:
- Have a systematic understanding of the fundamentals of modern probability theory;
- Know and be able to work with the most important univariate and multivariate probability distributions;
- Have a good knowledge of general conditional expectations, integral transforms and key ideas of different modes of convergence of random variables and distributions.
In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:
- problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
- analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
- collaborative skills: the ability to work in a team;
- time-management skills: the ability to meet regular deadlines while balancing competing commitments.
Last updated: 8 November 2019