ST202 One Unit
Probability, Distribution Theory and Inference
This information is for the 2025/26 session.
Course Convenor
Dr Milt Mavrakakis
Availability
This course is compulsory on the BSc in Actuarial Science, BSc in Actuarial Science (with a Placement Year), BSc in Financial Mathematics and Statistics and BSc in Mathematics, Statistics and Business. This course is available on the BSc in Data Science, BSc in Econometrics and Mathematical Economics, BSc in Mathematics and Economics, BSc in Mathematics with Data Science, BSc in Mathematics with Economics, Erasmus Reciprocal Programme of Study and Exchange Programme for Students from University of California, Berkeley. This course is freely available as an outside option to students on other programmes where regulations permit. It does not require permission. This course is freely available to General Course students. It does not require permission.
Requisites
Pre-requisites:
Before taking this course, students must have completed: (MA100 and ST102) or (EC1C1 and MA107 and ST109)
Additional requisites:
Students who have not taken these courses should contact Dr Mavrakakis. Equivalent combinations may be accepted at the lecturer's discretion.
Course content
The course covers the probability, distribution theory and statistical inference needed for advanced courses in statistics and econometrics.
Michaelmas term: Probability. Conditional probability and independence. Random variables and their distributions. Moments and generating functions. Transformations. Sequences of random variables and convergence. Multivariate distributions. Joint and marginal distributions. Expectation and joint moments. Independence. Multivariate transformations. Sums of random variables. Conditional distributions. Conditional moments. Hierarchies and mixtures. Random sums.
Lent term: Random samples. Sample mean. Sampling from the Normal distribution. Order statistics. Sample statistics. Sampling distributions. Parameter estimation. Interval estimation. Hypothesis testing. Maximum-likelihood estimation. Likelihood-ratio test. Sufficiency and minimal sufficiency. Rao-Blackwell theorem. Cramér-Rao lower bound. Most powerful tests. Neyman-Pearson lemma. Linear regression. Least-squares estimation. Generalised linear models. Bayesian inference.
Teaching
10 hours of seminars, 10 hours of help sessions and 10 hours of lectures in the Winter Term.
10 hours of seminars, 10 hours of help sessions and 10 hours of lectures in the Autumn Term.
This course has a reading week in Week 6 of Autumn and Winter Term.
Formative assessment
Students will be expected to produce 18 pieces of weekly homework in the AT and WT (8 per term), which will be returned with feedback. If there is sufficient student demand, there will be the option of exam-style class tests in the AT and WT (one per term).
Indicative reading
M C Mavrakakis & J Penzer, Probability and Statistical Inference: From Basic Principles to Advanced Models (primary reading)
G C Casella & R L Berger, Statistical Inference (very useful as a reference)
Assessment
Exam (50%), duration: 120 Minutes in the January exam period
Exam (50%), duration: 120 Minutes in the Spring exam period
Key facts
Department: Statistics
Course Study Period: Autumn and Winter Term
Unit value: One unit
FHEQ Level: Level 5
CEFR Level: Null
Total students 2024/25: 210
Average class size 2024/25: 30
Capped 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 information skills
- Application of numeracy skills
- Specialist skills