What you will study
This module in probability and its applications emphasises probability modelling and developing the properties of the models. A considerable amount of mathematics is sometimes required for this development, but we do not always give formal proofs, particularly if the proof does not illuminate the probabilistic ideas.
The module consists of five books.
The first one, which is introductory, revises and develops ideas about probability and introduces some techniques that will be used frequently in the module.
The second book develops models for events occurring in time, including the Poisson process and several extensions of it, and patterns in space, including models for random scatter and clustering of objects.
The third book develops models for processes in which events can occur only at discrete time points, such as a Bernoulli process. This includes practical situations such as the ruin of a gambler and the extinction of a family surname.
In the fourth book, probability models are developed for situations in which events can occur at any time. Examples include queues, the spread of epidemics, and the change in the size of a population due to births and deaths.
In the fifth book, models are developed for various situations, including genetics, the renewal of components, and the change in stock market prices.
You can find the full content list on the Open mathematics and statistics website.
You will learn
Successful study of this module should enhance your skills in understanding mathematical arguments, expressing problems in mathematical language, finding solutions to problems and interpreting mathematical results in real-world terms.
Entry
There is no formal pre-requisite study, but you must have the required mathematical skills.
You can check you’re ready for M343 and see the topics it covers here.
Talk to an advisor if you’re not sure if you’re ready.
Preparatory work
You should aim to be confident and fluent with the concepts covered in the Are you ready? quiz here, and follow the advice in the quiz.
The key topics to revise include:
- calculus
- differential equations
- matrices.
You’ll also find it useful to be familiar with the following topics:
- probability functions
- probability density functions
- the binomial, Poisson, geometric, exponential and normal distributions
- the Poisson process.
An OU level 2 module in mathematics is ideal preparation, and Analysing data (M248) is also useful.
Study materials
What's included
You’ll have access to a module website, which includes:
- a week-by-week study planner
- course-specific module materials
- audio and video content
- assessment details, instructions and guidance
- online tutorial access
- access to student and tutor group forums.
You’ll be provided with printed books covering the content of the module, including explanations, examples and activities to aid your understanding of the concepts and associated skills and techniques. You’ll also receive a printed module handbook.
You will need
Calculator with the usual mathematical functions (exp, log, sin, cos), but not necessarily with statistical functions.
Teaching and assessment
Support from your tutor
You’ll get help and support from an assigned tutor throughout your module.
They’ll help by:
- marking your assignments and offering detailed feedback to help you improve
- providing individual guidance, whether that’s for general study skills or specific module content
- guiding you to additional learning resources
- facilitating online discussions between your fellow students in the dedicated module and tutor group forums.
Online tutorials run throughout the module. Where possible, we’ll make recordings available. While they’re not compulsory, we strongly encourage you to participate.
Assessment
The assessment details for this module can be found in the facts box.
We’re using a new examination verification process for this module. We may ask you to attend a 15-minute post-exam video discussion, where you’ll present a photo ID and discuss your answers to a small number of questions with a tutor or member of the module team. The discussion isn’t graded; it’s only to verify that you completed the exam yourself.