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MA321 Half Unit

Measure Theoretic Probability

**This information is for the 2022/23 session.**

**Teacher responsible**

Dr Albina Danilova

**Availability**

This course is available on the BSc in Financial Mathematics and Statistics, BSc in Mathematics and Economics and BSc in Mathematics with Economics. This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.

**Pre-requisites**

Students must have completed Real Analysis (MA203).

**Course content**

This is a first course in measure-theoretic probability. It covers the following topics. Abstract probability spaces: sample spaces, sigma-algebras, probability measures, examples. Borel sigma-algebra, Lebesgue measure. Random variables: distribution functions, discrete and absolutely continuous distributions, examples. Expectation and the Lebesgue integral: convergence theorems and properties. Different modes of convergence of random variables. Conditional expectation: definition, properties, examples. Changes of probability measure, Bayes' theorem.

**Teaching**

This course is delivered through a combination of classes and lectures totalling a minimum of 30 hours across Michaelmas Term.

**Formative coursework**

Written answers to set problems will be expected on a weekly basis.

**Indicative reading**

Comprehensive lecture notes will be provided.

The following books may prove useful:

D Williams, Probability with Martingales.

J. Jacod & P. Protter, Probability Essentials; A. Klenke Probability Theory. A Comprehensive Course

**Assessment**

Exam (100%, duration: 2 hours) in the summer exam period.

** Key facts **

Department: Mathematics

Total students 2021/22: 33

Average class size 2021/22: 16

Capped 2021/22: No

Value: Half Unit

**Course selection videos**

Some departments have produced short videos to introduce their courses. Please refer to the course selection videos index page for further information.

**Personal development skills**

- Self-management
- Problem solving
- Communication
- Application of numeracy skills
- Specialist skills