MA321 Half Unit
Measure Theoretic Probability
This information is for the 2019/20 session.
Teacher responsible
Dr Pavel Gapeev COL 4.10
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
20 hours of lectures and 10 hours of classes in the MT.
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 2018/19: Unavailable
Average class size 2018/19: Unavailable
Capped 2018/19: No
Value: Half Unit
Personal development skills
- Self-management
- Problem solving
- Communication
- Application of numeracy skills
- Specialist skills
