| Module Code | STU23501 |
| Module Name | Probability and Theoretical Statistics 1 |
| ECTS Weighting[1] | 5 ECTS |
| Semester taught | Semester 1 |
| Module Coordinator/s | Professor Simon Wilson |
Module Learning Outcomes
On successful completion of this module, students will be able to:
LO1. Derive the probability space for simple experiments, and prove simple
properties of probabilities from its definition;
LO2. Identify when random variables are independent, and derive conditional
distributions and expectations;
LO3. Define the most common discrete and continuous random variables, and
compute their moments and probabilities, moment and characteristic
generating functions where appropriate;
LO4. Define a multivariate distribution and calculate marginal and conditional
distributions from it;
LO5. State and prove the laws of averages and of central limit;
Module Content
This is a rigorous development of probability theory from an axiomatic foundation,
along with some more advanced topics. The topics covered are:
• Events and probabilities
• The laws of probability
• Independence and conditional probability
• Discrete random variables
• Continuous random variables
• Multivariate distributions & independence
• Moment and characteristic generating functions
• The law of averages and the central limit theorem
• Examples and past exam questions
Teaching and learning Methods
Handouts and question sheets, as well as pre-recorded video lectures with accompanying lecture notes are available through Blackboard.
Assessment Details
| Assessment Component | Brief Description | Learning Outcomes Addressed | % of total | Week set | Week Due |
| Examination | In person. To be completed in 2 hours | LO1, LO2, LO3, LO4, LO5 | 100 | n/a | n/a |
Reassessment Details
In person examination (100%)
Contact Hours and Indicative Student Workload
| Contact Hours (scheduled hours per student over full module), broken down by: | 33 hours |
| Video lectures and reading notes | 33 hours |
| Laboratory | 0 hours |
| Tutorial or seminar | 24 hours |
| Other | 0 hours |
| Independent study (outside scheduled contact hours), broken down by: | 72 hours |
| Preparation for classes and review of material (including preparation for examination, if applicable) | 41 hours |
| completion of assessments (including examination, if applicable) | 18 hours |
| Total Hours | 116 hours |
Recommended Reading List
Probability: an Introduction by Grimmett and Welsh, published by Oxford
University Press.
Introduction to Probability Models by Ross, published by Academic Press (10th
edition or later).
Module Pre-requisites
Prerequisite modules: STU12501, STU12502
Other/alternative non-module prerequisites: e.g. programming languages,
specified topics, etc.. This information will be particularly relevant for visiting
students or students taking this module as an approved module (if applicable).
Module Co-requisites
None