STU23501 – Probability and Theoretical Statistics I

Module CodeSTU23501
Module Name Probability and Theoretical Statistics 1
ECTS Weighting[1]5 ECTS
Semester taughtSemester 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

Pre-recorded video lectures with accompanying lecture notes and handouts, available through Blackboard.  Question sheets will be handed out and answered in live sessions through Blackboard.

Assessment Details

Assessment ComponentBrief Description Learning Outcomes Addressed% of totalWeek setWeek Due
Online examination To be completed over 24 hoursLO1, LO2, LO3,
LO4, LO5

Reassessment Details

Online examination, to be completed over 24 hours (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 notes33
Laboratory0 hours
Tutorial or seminar24 hours
Other0 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 Hours116 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


Module Website