Probability Models (L7) (973G1)

15 credits, Level 7 (Masters)

Autumn teaching

This is the first optional Probability module, where we begin to study stochastic (random) processes. In this module our processes are in discrete time, so a stochastic process is a sequence of random variables where we can view it as a (discrete) time evolution of a random experiment. Stochastic processes are used to model several phenomena with uncertain outcomes, such as stock values, the weather, or the profit evolution of a gambler as they evolve through time.

You will develop basic tools for the study of such processes in discrete time (which makes it less technical). The central objects of study are Markov chains and their various models. These include:

  • branching processes
  • finite Markov chains
  • infinite countable Markov chains
  • discrete martingales
  • limits of sequences of independent random variables. 

You will also develop your modelling skills. You will pay particular attention to questions such as:

  • How can we model a certain problem using a discrete process?
  • Can the model be used to estimate probabilities, expected values etc. If so, how?
  • How can we understand what happens to the model when we look far into the future?


100%: Lecture


20%: Coursework (Portfolio, Problem set)
80%: Examination (Unseen examination)

Contact hours and workload

This module is approximately 150 hours of work. This breaks down into about 33 hours of contact time and about 117 hours of independent study. The University may make minor variations to the contact hours for operational reasons, including timetabling requirements.

We regularly review our modules to incorporate student feedback, staff expertise, as well as the latest research and teaching methodology. We’re planning to run these modules in the academic year 2024/25. However, there may be changes to these modules in response to feedback, staff availability, student demand or updates to our curriculum. We’ll make sure to let you know of any material changes to modules at the earliest opportunity.


This module is offered on the following courses: