MA321 Half Unit
Measure Theoretic Probability
This information is for the 2023/24 session.
Teacher responsible
Dr Albina Danilova
Availability
This course is available on the BSc in Financial Mathematics and Statistics, BSc in Mathematics and Economics, BSc in Mathematics with Data Science 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 Autumn 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 spring exam period.
Key facts
Department: Mathematics
Total students 2022/23: 29
Average class size 2022/23: 15
Capped 2022/23: 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