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.

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

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 six 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.

Computer simulations are used to illustrate some of the phenomena studied, and associated activities are included in a separate book.

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.

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
  • relevant computer software and associated guidance
  • 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.

Computing requirements

A computing device with a browser and broadband internet access is required for this module. Any modern browser will be suitable for most computer activities. Functionality may be limited on mobile devices.

Any additional software will be provided, or is generally freely available. However, some activities may have more specific requirements. For this reason, you will need to be able to install and run additional software on a device that meets the requirements below.

A desktop or laptop computer with either an up-to-date version of Windows or macOS.

The screen of the device must have a resolution of at least 1024 pixels horizontally and 768 pixels vertically.

To join in the spoken conversation in our online rooms we recommend a headset (headphones or earphones with an integrated microphone).

Our Skills for OU study website has further information including computing skills for study, computer security, acquiring a computer and Microsoft software offers for students.

Teaching and assessment

Support from your tutor

You'll have a tutor who will help you with the study material and mark and comment on your written work, and who you can ask for advice and guidance. Your tutor can also provide additional assistance with your study skills, especially if you're new to OU study.

Tutorials are designed to aid student success by providing help and guidance with your studies, including hints and tips to improve your understanding. You are encouraged to attend as many as you can – whether face-to-face or online they are an informal way to ask questions and to feel part of a student community.

We aim to provide face-to-face tutorials in a range of locations students can travel to, though we cannot guarantee availability close to where you live. An online alternative, covering similar content, is usually provided, typically with a recording of at least one such online tutorial being made available.

Student numbers on the module, and where tutors are based, will affect which tutor may lead a particular tutorial, the locations of face-to-face tutorials, and what online alternatives are offered.

Contact us if you want to know more about study with The Open University before you register.

Assessment

The assessment details for this module can be found in the facts box above. Although your scores on the TMAs and iCMAs 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.

You can choose whether to submit your tutor-marked assignments (TMAs) on paper or online through the eTMA system. You may want to use the eTMA system for some of your assignments but submit on paper for others. This is entirely your choice.

If you have a disability

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.

Mode of study

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.

Tuition strategy

This module provides a range of learning events: e.g. face-to-face tutorials, day schools/workshops. Each face-to-face learning event offers an online (or other) alternative. Although not compulsory, attendance at tutorials will help you consolidate your learning.

Mathematical and scientific expressions and notations

Mathematical and scientific symbols and expressions are used throughout the module and you will be required to use such notation within assessment.

Diagrams and other visual content

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.

Specialist reading material

In this module you will be working with specialist reading material which includes mathematical notation. This is delivered both online and in printed form.

Assessment

This module has Tutor-Marked Assignments (TMAs), which can be submitted online via the OU electronic TMA system or by post, Interactive Computer-Marked Assignments (iCMAs) completed online, and an Exam that must be taken at an exam centre.

Feedback

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. Solutions and some explanations will also be provided for the interactive Computer-Marked Assignments (iCMAs).

Schedule

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.

Future availability

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

This page describes the module that will start in October 2020.

We expect it to start for the last time in October 2022.

This course is expected to start for the last time in October 2022.

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.

This module may also help you to apply for the professional award of Graduate Statistician conferred by The Royal Statistical Society (RSS).