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MA321 Half Unit

Measure Theoretic Probability

**This information is for the 2020/21 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 seminars totalling a minimum of 30 hours across Michaelmas Term. This year, some or all of this teaching will be delivered through a combination of virtual seminars and classes delivered as online videos.

**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.

**Important information in response to COVID-19**

Please note that during 2020/21 academic year some variation to teaching and learning activities may be required to respond to changes in public health advice and/or to account for the situation of students in attendance on campus and those studying online during the early part of the academic year. For assessment, this may involve changes to mode of delivery and/or the format or weighting of assessments. Changes will only be made if required and students will be notified about any changes to teaching or assessment plans at the earliest opportunity.

** Key facts **

Department: Mathematics

Total students 2019/20: 24

Average class size 2019/20: 8

Capped 2019/20: No

Value: Half Unit

**Personal development skills**

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