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Graduate Certificate in Theoretical Statistics and Probability

This certificate teaches the theory that underpins statistical inference and probability. Equipping you to understand the assumptions and limitations of a range of statistical models. You’ll gain a thorough understanding of the theory you need to underpin your work as a professional statistician. Learn to develop probability models for practical situations and investigate the model’s properties. Study the mathematical theory underlying methods and concepts used in practical statistical analyses.

Key features of the course

  • Cover key analytical approaches, classical and Bayesian statistics and the underpinning mathematical theory.
  • Learn about distribution theory and a range of probabilistic models.
  • Understand the theory behind statistical inference.
  • Gain the skills to critically comment on analyses and model choices.

Course Summary



  • An OU level 3 qualification.
  • Designed for graduates.
  • Provides knowledge to work at a professional level.
  • Only qualification of its type offered by the OU.
Course code


  • Credits measure the student workload required for the successful completion of a module or qualification.
  • One credit represents about 10 hours of study over the duration of the course.
  • You are awarded credits after you have successfully completed a module.
  • For example, if you study a 60-credit module and successfully pass it, you will be awarded 60 credits.
How long it takes
Part time – 1 year
Time limit – 4 years
Study method
Distance learning

Course details

This certificate has one stage, comprising 60 credits.

  • You’ll start Stage 1 with either 30-credit module or take both together.

Stage 1 (60 credits)

You’ll learn how to develop probability models for practical situations, including random processes, and investigate the properties of the model. You’ll also study the mathematical theory underlying the methods and concepts used in practical statistical analyses.
You'll study both of the following:
Applications of probability (M343)30
Mathematical statistics (M347)30

We regularly review our curriculum; therefore, the qualification described on this page – including its availability, its structure, and available modules – may change over time. If we make changes to this qualification, we’ll update this page as soon as possible. Once you’ve registered or are studying this qualification, where practicable, we’ll inform you in good time of any upcoming changes. If you’d like to know more about the circumstances in which the University might make changes to the curriculum, see our Academic Regulations or contact us. This description was last updated on 17 March 2021.


We make all our qualifications as accessible as possible and have a comprehensive range of services to support all our students. The Graduate Certificate in Theoretic Statistics and Probability uses a variety of study materials and has the following elements:

  • studying a mixture of printed and online material – online learning resources may include websites, audio/video media clips, and interactive activities such as online quizzes
  • using mathematical and scientific expressions, notations and associated techniques
  • using and producing diagrams and screenshots
  • undertaking practical work
  • using specialist software
  • face-to-face tutorials/day schools and/or online tutorials
  • continuous and end-of-module assessment in the form of short and long answer questions, and an examination
  • using feedback: continuous assessment involves receiving detailed feedback on your work from your tutor and using this feedback to improve your performance
  • engagement with learning and assessment within a pre-determined schedule or timetable – time management will be needed during your studies.

For more detailed information, see the Accessibility Statements on individual module descriptions. If you feel you may need additional support, visit Disability support to find more about what we offer.

Learning outcomes, teaching and assessment

This qualification develops your learning in four main areas:

  • Knowledge and understanding
  • Cognitive skills
  • Practical and professional skills
  • Key skills

The level and depth of your learning gradually increases as you work through the qualification. You’ll be supported throughout by the OU’s unique style of teaching and assessment – which includes a personal tutor to guide and comment on your work; top quality course texts; elearning resources like podcasts, interactive media and online materials; tutorial groups and community forums.

Read the detailed learning outcomes here

On completion

On successfully completing this course, we’ll award you our Graduate Certificate in Theoretical Statistics and Probability.

International recognition

If you intend to use your Open University qualifications to seek work or undertake further study outside the UK, we recommend checking whether your intended qualification will meet local requirements for your chosen career. Find out more about international recognition of Open University qualifications.


As a student of The Open University, you should be aware of the content of the qualification-specific regulations below and the academic regulations that are available on our Student Policies and Regulations website. 

Entry requirements

You must have an undergraduate degree with a substantial amount of mathematical and/or statistical content.

You need a high degree of mathematical competence in the following areas:

  • logarithmic and exponential functions
  • calculus (including Taylor series)
  • algebra (including manipulation of inequalities)
  • matrices.

In addition, you’ll need a working knowledge of the following statistical topics:

  • histograms and scatterplots
  • Normal, Poisson and binomial distributions
  • the central limit theorem
  • point estimation
  • maximum likelihood estimation
  • confidence intervals
  • hypothesis testing
  • simple linear regression
  • correlation.

If you meet these entry requirements and wish to study this qualification, download the application form.

You can also check you’re ready to study, and see the topics each module covers, here.

How much time do I need?

  • Most of our students study part time, completing 60 credits a year.
  • This will usually mean studying for 16–18 hours a week.

Find out if you have enough time to study with our time planner

How much will it cost in England?

We believe cost shouldn’t be a barrier to achieving your potential. That’s why we work hard to keep the cost of study as low as possible and have a wide range of flexible ways to pay to help spread, or even reduce, the cost.

  • Fees are paid on a module-by-module basis – you won't have to pay for the whole of your qualification up front.
  • A qualification comprises a series of modules, each with an individual fee. Added together, they give you the total cost.
  • Most OU students study part time at a rate of 60 credits a year.
  • Our current fee for 60 credits is £3,168*.
  • Our current fee for 120 credits, which is equivalent to a year's full-time study, is £6,336*.
  • At current prices, the total cost of your qualification would be £3,168*.
  • .

*The fee information provided here is valid for modules starting before 31 July 2022. Fees normally increase annually in line with inflation and the University's strategic approach to fees.

Additional costs

Study costs

There may be extra costs on top of the tuition fee, such as set books, a computer and internet access.

If your income is not more than £25,000 or you are in receipt of a qualifying benefit, you might be eligible for help with some of these costs after you start studying.

Skills for career development

Statistics is important for everyday problem solving and decision making. This certificate will equip you with the important mathematical underpinning for statistical methods, so you’ll have the theoretical knowledge to prepare you for work as a statistician. Applications of probability theory include patterns of events that occur in both time, such as earthquakes; and space, for example the occurrence of a species of plant; together with areas such as genetics and changes in stock market prices.

Career relevance

Qualified statisticians are in great demand in the workplace – in particular, those with the theoretical underpinning to ensure the correct analysis is undertaken are in short supply in all areas, including the sciences, economics, education, engineering, environmental studies, finance, government statistics, logistics, medicine and pharmaceuticals.

Exploring your options

Once you register with us (and for up to three years after you finish your studies), you’ll have full access to our careers service for a wide range of information and advice, including: online forums, website, interview simulation and vacancy service, as well as the option to email or speak to a careers adviser. Some areas of the careers service website are available for you to see now, including help with looking for and applying for jobs. You can also read more general information about how OU study enhances your career.

In the meantime, if you want to do some research around where this qualification might take you, we’ve put together a list of relevant job titles as a starting point (note that some careers may require further study, training and/or work experience beyond your qualification):

  • actuary
  • business analyst
  • business manager
  • climate scientist
  • data scientist
  • environmental scientist
  • financial consultant
  • health professional
  • marketing professional
  • meteorologist
  • policy maker
  • research analyst
  • sport scientist
  • teacher

Register for this course

To register for this course, please refer to our entry requirements and registration information. Online registration is not available. 

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