ST452 Half Unit
Probability and Mathematical Statistics I
This information is for the 2025/26 session.
Course Convenor
Prof Umut Cetin
Giulia Livieri
Availability
This course is available on the MRes in Management (Employment Relations and Human Resources), MRes in Management (Organisational Behaviour) and MSc in Quantitative Methods for Risk Management. This course is available with permission as an outside option to students on other programmes where regulations permit.
The availability as an outside option requires a demonstration of sufficient background in mathematics and statistics. Prior training on basic concepts of real analysis providing experience with formal proofs, sequences, continuity of functions, and calculus and is at the discretion of the instructor.
Course content
This course provides theoretical and axiomatic foundations of probability and mathematical statistics. In particular, the following topics will be covered:
1. Measure spaces; Caratheodory extension theorem; Borel-Cantelli lemmas.
2. Random variables; monotone-class theorem; different kinds of convergence.
3. Kolmogorov’s 0-1 law; construction of Lebesgue integral.
4. Monotone convergence theorem; Fatou's lemmas; dominated convergence theorem.
5. Expectation; L^p spaces; uniform integrability.
6. Characteristic functions; Levy inversion formula; Levy convergence theorem; CLT.
7. Principle and basis for statistical inference: populations and samples, decision theory, basic
measures for estimators.
8. Estimation: U and V statistics, unbiased estimators, MVUE, MLE.
9. Hypothesis testing: Neyman-Pearson lemma, UMP, confidence sets.
10. Product measures; conditional expectation.
Teaching
10 hours of seminars and 20 hours of lectures in the Autumn Term.
This course has a reading week in Week 6 of Autumn Term.
Formative assessment
Students will be expected to produce 9 problem sets in the AT.
Weekly problem sets that are discussed in subsequent seminars. The coursework that will be used for summative assessment will be chosen from a subset of these problems.
Indicative reading
- Williams, D. (1991). Probability with Martingales. Cambridge University Press.
- Durrett, R. (2019). Probability: Theory and Examples. Cambridge Series in Statistical and Probabilistic Mathematics.
- Shao, J. (2007). Mathematical Statistics. Springer Texts in Statistics.
- Keener, R. (2010). Theoretical Statistics. Springer Texts in Statistics.
Assessment
Exam (70%), duration: 120 Minutes, reading time: 10 minutes in the Spring exam period
Problem sets (30%)
Three of the homework problem sets will be submitted and marked as assessed coursework.
Key facts
Department: Statistics
Course Study Period: Autumn Term
Unit value: Half unit
FHEQ Level: Level 7
CEFR Level: Null
Total students 2024/25: 1
Average class size 2024/25: 1
Controlled access 2024/25: NoCourse 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
- Problem solving
- Application of numeracy skills
- Specialist skills