This module introduces models to describe patterns of events that occur in time (such as earthquakes), and in space (for instance, the occurrence of a species of plant). Situations that occur only at discrete time points, including the ruin of a gambler, are studied. Probability models are developed for those situations, such as the spread of an epidemic, in which events may occur at any time. The module ends with other situations involving probability including genetics and changes in stock market prices. You are expected to be reasonably competent in calculus and algebra.
| Course facts | |
|---|---|
| About this course: | |
| Course code | M343 |
| Credits | 30 |
| OU Level | 3 |
| SCQF level | 10 |
| FHEQ level | 6 |
| Course work includes: | |
| 3 Tutor-marked assignments (TMAs) | |
| Examination | |
| No residential school | |
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.
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.
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.
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:
You'll also find it useful to be familiar with the following topics:
An OU level 2 module in mathematics is ideal preparation, and Analysing data (M248) is also useful.
You'll have access to a module website, which includes:
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.
Calculator with the usual mathematical functions (exp, log, sin, cos), but not necessarily with statistical functions.
You'll need broadband internet access and a desktop or laptop computer with an up-to-date version of Windows (10 or 11) or macOS Monterey or higher.
Any additional software will be provided or is generally freely available.
To join in spoken conversations in tutorials, we recommend a wired headset (headphones/earphones with a built-in microphone).
Our module websites comply with web standards, and any modern browser is suitable for most activities.
Our OU Study mobile app will operate on all current, supported versions of Android and iOS. It's not available on Kindle.
It's also possible to access some module materials on a mobile phone, tablet device or Chromebook. However, as you may be asked to install additional software or use certain applications, you'll also require a desktop or laptop, as described above.
Throughout your module studies, you'll get help and support from your assigned module tutor. They'll help you by:
Module tutors also run online tutorials throughout the module. Where possible, recordings of online tutorials will be made available to students. While these tutorials won't be compulsory for you to complete the module, you're strongly encouraged to take part.
The assessment details for this module can be found in the facts box.
Although your scores on the TMAs will not contribute directly to your final grade, you will need to successfully complete at least 2 of the 3 TMAs. You will be given more information when you begin the module.
The OU strives to make all aspects of study accessible to everyone. The Accessibility Statement below outlines what studying this module involves. You should use this information to inform your study preparations and any discussions with us about how we can meet your needs.
Printed materials are provided for the core module text. All of this module's study materials are also online; this includes PDFs of any printed materials, plus some items which are only provided online. Online materials also include links to external resources, online forums and online tutorial rooms.
This module has online tutorials. Although not compulsory, tutorials will help you consolidate your learning.
Mathematical and scientific symbols and expressions are used throughout the module and you will be required to use such notation within assessment.
The study materials contain some graphs. Reading, interpreting and producing examples of these is an important part of the study of this module and is assessed. Figure descriptions are provided for most figures.
In this module you will be working with specialist reading material which includes mathematical notation. This is delivered both online and in printed form.
This module has Tutor-Marked Assignments (TMAs), which can be submitted online via the OU electronic TMA system or by post, and an Exam that you will take remotely.
You will receive feedback from your tutor on your submitted Tutor-Marked Assignments (TMAs). This will help you to reflect on your TMA performance. You should refer to it to help you prepare for your next assignment.
All University modules are structured according to a set timetable and you will need time-management skills to keep your studies on track. You will be supported in developing these skills.
Applications of probability (M343) starts once a year – in October.
This page describes the module that will start in October 2024.
We expect it to start for the last time in October 2026.
This course is expected to start for the last time in October 2026.
This module may help you to gain membership of the Institute of Mathematics and its Applications (IMA). For further information, see the IMA website.
This module may also help you to apply for the professional award of Graduate Statistician conferred by The Royal Statistical Society (RSS).