Statistics
ST415: Probability Theory and Applications (5 ECTS)
This module develops probability theory that is useful in a myriad of applications. The theory is implemented in the development of statistical theory and methods, and a variety of applications will be given in IT and Communications Systems, and in other areas. The module is quite advanced and requires knowledge of probability to the level of at least ST235 or equivalent, and preferably also some mathematical statistics.
Taught in Semester(s) I. Examined in Semester(s) I.
Workload: 36 hours (24 Lecture hours, 12 Tutorial hours).
Module Learning Outcomes.
On successful completion of this module the learner should be able to:
- Understand probability and random variables at a measure-theoretic level.
- Understand joint, marginal and conditional distributions and their moments.
- Derive and compare various modes of convergence of random variables.
- Develop properties of characteristic functions and be able to use them to establish various properties including limiting distributions.
- Understand discrete-time Martingales.
- Be able to apply the theory to various problems in statistical theory, Information Technology and Communications Systems, in Game Theory and in Finance.
Indicative Content
This module provides a fairly rigorous approach to probability theory but there is a heavy emphasis also on applications. Topics covered include:
- Probability spaces.
- Measurable functions and random variables.
- Expectations and conditional expectations.
- Probability, moment generating and characteristic functions.
- Convergence of sequences of random variables, laws of large numbers, rates of convergence and and limiting distributions.
- Applications to various fields, including statistics, commmunication systems and IT, game theory and finance.
Module Resources
- Richard Durrett. Probability: theory and examples, 1996. Wadsworth & Brooks/Cole Statistics/Probability Series.
- Ingemar Kaj. Stochastic modeling in broadband communications systems, 2002. Siam.
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