This module introduces models to describe patterns of events that occur in time (such as earthquakes) and space (for instance, the occurrence of a plant species). You’ll study situations that occur only at discrete time points, including the gambler’s ruin, and develop probability models for situations where events may occur at any time, such as the spread of an epidemic. The module ends with other situations involving probability, including genetics and changes in stock market prices.
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 frequently used 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 where 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 where 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.
The full content list is on the Open mathematics and statistics website.
Entry requirements
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.
Preparatory work
You should aim to be confident and fluent with the concepts covered in the Are you ready? quiz, 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.
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 forums.
Online tutorials run throughout the module. While they’re not compulsory, we strongly encourage you to participate. Where possible, we’ll make recordings available.
Assessment
Course work includes:
4 Tutor-marked assignments (TMAs)
Examination
For this module, we may use an assessment verification process to meet the requirements of relevant accrediting, professional, statutory or regulatory bodies. As part of this process, you may be asked to attend a short post-assessment video discussion, lasting around 15 minutes. During the discussion, you’ll need to show a photo ID and talk through your answers to a small number of questions with a tutor or a member of the module team. The discussion is not graded and is only used to confirm that you completed the assessment yourself.
We regularly review the assessments in our modules, so we may update the examination method used for this module to an in-person exam or an online invigilated exam. When we are making such a change, we will make it clear on this page. If we need to make a change after you have registered, we will notify you as soon as possible. If you have additional requirements, we will support you to complete your assessments.
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 and submission section
online tutorial access
access to student forums.
We also provide physical:
module books
module handbook.
You will need
a basic calculator.
Computing requirements
Primary device – A desktop or laptop computer with at least 8 GB of RAM and a quad-core processor (2.4 GHz minimum speed). It’s possible to access some materials on a mobile phone, tablet or Chromebook; however, they will not be suitable as your primary device or for taking your online exam.
Peripheral devices – Headphones/earphones with a built-in microphone for online tutorials, plus an external webcam and a microphone.
Operating systems – Windows 11 or the latest supported macOS.
Internet access – A broadband or mobile connection with at least 3 Mbps upload and download speed.
Browser – Google Chrome and Microsoft Edge are recommended. Mozilla Firefox and Safari may be suitable. You may need to use Google Chrome specifically for some activities.
Our OU Study app operates on supported versions of Android and iOS.
Software – Any additional software will be provided or is generally freely available.
If you have a disability
The OU strives to make all aspects of study accessible to everyone, and this Accessibility Statement outlines what studying M343 involves. You should use this information to inform your study preparations and any discussions with us about how we can meet your needs.
To find out more about what kind of support and adjustments might be available, contact us or visit our Disability support website.
Future availability
Applications of probability (M343) starts once a year – in October.
It will next start in October 2027.
We expect it to start for the last time in October 2030.