England.

# Applications of probability

Qualification dates
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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 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.

### Professional recognition

This module may help you to gain membership of the Institute of Mathematics and its Applications (IMA). For further information, see the IMA website.

## Entry requirements

There is no formal pre-requisite study, but you must have the required mathematical skills.

## 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.

## What's included

• a week-by-week study planner
• course-specific module materials
• audio and video content
• assessment details, instructions and guidance
• online tutorial access

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.

### Computing requirements

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 Ventura 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.

## Teaching and assessment

• Marking your assignments (TMAs) and providing detailed feedback for you to improve.
• Guiding you to additional learning resources.
• Providing individual guidance, whether that’s for general study skills or specific module content.
• Facilitating online discussions between your fellow students, in the dedicated module and tutor group forums.

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.

### Assessment

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.

## 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.

## Future availability

Applications of probability (M343) starts once a year – in October.