MDE-MET-02: Probability for Graduate Students
This site will be the primary source of information for this course.
Lectures
Lectures will take place in autumn 2025.
An office hour can be arranged by appointment.
Course notes can be found here.
Recommendations for Preparation
There are no recommendations beyond reading the syllabus and the outline of the course.
Content and Educational Aims
This module offers a highly structured introduction to the fundamentals of combinatorics and probabilities as they are used for statistical modeling and estimation. It is a gateway for graduate students who have not been exposed to the topics so far, or who were exposed long ago and needs to be refreshed.
The module starts with the concept of probabilities, including joint, conditional and total probabilities with a focus on independence, which leads us to a discussion of Bayes’s theorem. We shall then proceed to factorials, and binomial coefficients, with many applications to be followed by the binomial law, and its Poisson and Normal approximations.
A second block covers random variables with their distributions and density functions. Here we are going to discuss continuous random variables in detail.
Block three continues with the essential ideas of expected values, moments, and estimation.
Intended Learning Outcomes
Upon completion of this module, students will be able to:
- understand the fundamental concepts of probabilities and combinatorics and to apply them in structured situations,
- apply important probability laws (Binomial, Poisson, Normal),
- understand and apply probability distributions and densities,
- understand and apply means, variances, and covariances – also in the context of simple estimation contexts.
Indicative Literature
The course loosely follows:
- “Probability and Random Processes: With Applications to Signal Processing” - H. Stark & J. W. Woods (2001) Person Press, 3rd edition ISBN: 0-13-178457-9.
Usability and Relationship to other Modules
Familiarity with probability-related concepts is the basis to understand the foundations of stochastic modelling and the data analytics and machine learning techniques which form a central part of data engineering.
There is a placement test offered in the orientation week before the start of the first semester to help all students to find out if they need to take this remedial course.
Course Outline
The following topics will be covered:
- Probability
Itinerary
An outline will be produced shortly.
Structure
The course content has the following structure:
Assessment
Examination Type
| Examination Type: | Module examination |
| Assessment Type: | Written examination |
| Scope: | All intended learning outcomes of this module |
| Duration: | 120 min |
| Weight: | 100% |
You have three attempts to pass the module. Once you pass the module, no further retakes of the exam are possible. (See Academic Policies for more details.) The exams in this course are offered twice per year: in December and January.
No supplementary material can be brought to the exam. A calculator is necessary. Graphical and scientific calculators are permitted.
The pass mark is 45%.
Assignments
By submitting homework assignments, via Teams as a single pdf, you can improve this grade by up to 0.66 points, as bonus achievements.
Homework submission is voluntary although highly recommended. It is possible to get a 100% final grade without submitting homework or participating in quizzes.
Homework will be assigned every two weeks. Homework assignments are posted on here and on Teams approximately ten days before the due date.
You are encouraged to discuss homework between each other. However, the submitted assignments should be written individually. No copying is allowed!
The two lowest homework scores will be discarded before the final homework score is calculated. This rule covers short illness, excursions, late joining of the course, and similar situations.
Note that each homework assignment carries equal marks.
The problems on the final exam will be similar to the ones from homework. So, by doing homework you prepare for the final exam - maths is not a spectator sport.
Academic Integrity
All involved parties (lecturers, instructors and students) are expected to abide by the word and spirit of the “Code of Academic Integrity”. Violations of the Code should be brought to the attention of the Academic Integrity Committee.
Artifical Intelligence Use Policy
This policy covers any generative AI tool, such as ChatGPT, Elicit, etc. This includes text, slides, artwork/graphics/video/audio and other products.
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You are discouraged from using AI tools unless under direct instruction from your instructor to do so. Please contact your instructor if you are unsure or have questions before using AI for any assignment.
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Note that the material generated by these programs may be inaccurate, incomplete, or otherwise problematic. Their use may also stifle your own independent thinking and creativity. Accordingly, reduction in the grade is likely when using AI.
If any part of this AI policy is confusing or uncertain, please reach out before submitting your work.