Probability Models (L6) (G1100)
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Probability Models (L6)
Module G1100
Module details for 2025/26.
15 credits
FHEQ Level 6
Module Outline
Probability Models is the first module concerned with the notion of a random (stochastic) process. 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 the evolve through time.
In this module we 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 and limits of sequences of independent random variables.
The module will also help you to develop your modelling skills. Through this material we 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?
Module learning outcomes
Setting up probability spaces, events and random variables to solve real-life probability problems.
Manipulating distributions, densities, sums of random variables, basic random processes and Markov chains with applications.
Understanding and using the Laws of Large Numbers and the Central Limit Theorem, with an eye to statistics and probability modelling.
Acquire and rediscover set-theoretical and calculus skills in the context of probabilistic manipulations.
| Type | Timing | Weighting |
|---|---|---|
| Unseen Examination | Semester 1 Assessment | 80.00% |
| Coursework | 20.00% | |
| Coursework components. Weighted as shown below. | ||
| Portfolio | T1 Week 11 | 40.00% |
| Problem Set | T1 Week 5 | 15.00% |
| Problem Set | T1 Week 10 | 15.00% |
| Problem Set | T1 Week 8 | 15.00% |
| Problem Set | T1 Week 3 | 15.00% |
Timing
Submission deadlines may vary for different types of assignment/groups of students.
Weighting
Coursework components (if listed) total 100% of the overall coursework weighting value.
| Term | Method | Duration | Week pattern |
|---|---|---|---|
| Autumn Semester | Lecture | 2 hours | 11111111111 |
| Autumn Semester | Lecture | 1 hour | 11111111111 |
How to read the week pattern
The numbers indicate the weeks of the term and how many events take place each week.
Dr Vladislav Vysotskiy
Assess convenor
/profiles/406081
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