MAS8601 : Graduate Foundations of Probability and Mathematical Statistics
- Offered for Year: 2025/26
- Module Leader(s): Dr Tom Nye
- Lecturer: Mr Axel Finke
- Owning School: Mathematics, Statistics and Physics
- Teaching Location: Newcastle City Campus
Semesters
Your programme is made up of credits, the total differs on programme to programme.
| Semester 1 Credit Value: | 30 |
| ECTS Credits: | 15.0 |
| European Credit Transfer System | |
Aims
The aim of this module is to provide students with a comprehensive and rigorous foundation in the principles and techniques of probability and mathematical statistics. This module is designed to equip students with both the theoretical understanding and practical skills necessary for advanced study of application areas.
Outline Of Syllabus
Introduction to the topic by means of sets, outcomes and events. Detailed study of probability and measures. Overview of random variables, transformations of random variables, expectations, moments, moment generating functions, conditional probability and independence. Coverage of key analytical techniques, such as Chebyshev’s inequality, and common distributions. Overview of both point estimation and interval estimation, as well as associated key notions of convergence, maximum likelihood estimation and efficiency. Coverage of both discrete-time and continuous-time stochastic processes (to include Markov chains and Poisson processes), in both theory and application.
Teaching Methods
Teaching Activities
| Category | Activity | Number | Length | Student Hours | Comment |
|---|---|---|---|---|---|
| Guided Independent Study | Assessment preparation and completion | 2 | 12:00 | 24:00 | Completion of in course assessments |
| Guided Independent Study | Assessment preparation and completion | 1 | 3:00 | 3:00 | Unseen Exam |
| Scheduled Learning And Teaching Activities | Lecture | 20 | 1:00 | 20:00 | Problem Classes |
| Scheduled Learning And Teaching Activities | Lecture | 5 | 1:00 | 5:00 | Revision Lectures |
| Scheduled Learning And Teaching Activities | Lecture | 30 | 2:00 | 60:00 | Formal Lectures |
| Guided Independent Study | Independent study | 30 | 1:00 | 30:00 | Background reading on lectured content |
| Guided Independent Study | Independent study | 2 | 3:00 | 6:00 | Review of Coursework |
| Guided Independent Study | Independent study | 40 | 1:00 | 40:00 | Revision for unseen exam |
| Guided Independent Study | Independent study | 56 | 2:00 | 112:00 | Preparation time for lectures and consolidation of material afterwards |
| Total | 300:00 |
Teaching Rationale And Relationship
Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem classes are used to help develop the students’ abilities at applying the theory to solving problems.
The teaching methods are appropriate to allow students to develop a wide range of skills. From understanding basic concepts and facts to higher-order thinking.
Assessment Methods
The format of resits will be determined by the Board of Examiners
Exams
| Description | Length | Semester | When Set | Percentage | Comment |
|---|---|---|---|---|---|
| Written Examination | 180 | 1 | A | 80 | 3 hour written exam, comprising a Section A and a Section B. |
Other Assessment
| Description | Semester | When Set | Percentage | Comment |
|---|---|---|---|---|
| Prob solv exercises | 1 | M | 20 | Coursework 2. 40 minute class test, conducted during one of the timetabled one hour lecture slots. |
Zero Weighted Pass/Fail Assessments
| Description | When Set | Comment |
|---|---|---|
| Practical/lab report | M | PRACTICAL/LAB REPORT 1& 2: MUST achieve a passing mark (40%) in at least one of the two reports to pass module. |
Formative Assessments
Formative Assessment is an assessment which develops your skills in being assessed, allows for you to receive feedback, and prepares you for being assessed. However, it does not count to your final mark.
| Description | Semester | When Set | Comment |
|---|---|---|---|
| Prob solv exercises | 1 | M | Coursework 1. 40 minute class test, conducted during one of the timetabled one hour lecture slots. |
Assessment Rationale And Relationship
A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes.
Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one way for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.
The coursework assignments allow the students to develop their problem-solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; the summative assessment has a secondary formative purpose as well as its primary summative purpose.
Reading Lists
Timetable
- Timetable Website: www.ncl.ac.uk/timetable/
- MAS8601's Timetable