Applications of probability
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.
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.
Read the full content list here.
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.
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).
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:
- differential equations
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.
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.
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 (10.15 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.