We are glad to welcome you to the course SF2940 Probability Theory. All information will be available on this page -- most of it on this Home page and eventually some (e.g., lecture notes) will be found in Modules. This page will be updated continuously throughout the course.

News: preliminary solutions to the re-exam can be found below.

Organisation:

The course will be taught on KTH campus and exercise sessions will be offered (on campus as well). There will be some time-limited assignments/quizzes which will be done by distance. Exams will be on campus.

IF YOU HAVE QUESTIONS: SEE THE FAQ BELOW FIRST.

Course content

Probability spaces, random variables and their distributions, functions of random
variables, expectation
Independence, conditional probabilities, conditional expectation
Probability and moment generating functions, characteristic function, sums of random variables
Convergence of random variables, law of large numbers, central limit theorem
Multivariate normal distribution and applications

Lecture plan (updated every week -- newest version 13/10 2025): Lecture_plan.pdf

Course literature and resources

Main course book:
Allan Gut, An Intermediate Course in Probability, Springer Texts in Statistics, 2nd edition, ISBN 978-1-4419-0161-3.

Secondary reading and exercises:
Timo Koski, Lecture Notes: Probability and Random Processes at KTH. PDF

Exercises (updated 6/10): Exercises.pdf

Grades

You can find your grades on submitted assignments and quizzes under Grades.

Quizzes

The quizzes will be done online, on a computer at home (or wherever else one might be) and will consist of multiple choice questions. They will be open for one hour and 15 minutes. Each quiz contains five questions, worth one point each, and each quiz will be worth 5% of the points which are on the exam.

Quiz 1: Wednesday 10 September, 17.30-18.45. Will cover the material of the first two weeks (multivariate random variables and conditioning).
Answers and solutions to Quiz 1: SolutionsQuiz1.pdf

Quiz 2: Wednesday 1 October, 17.30-19.15. Will cover generating functions and convergence.
Answers and solutions to Quiz 2: Quiz2_solutions.pdf

Exam

Information about the exam: Exam_Information.pdf

Table of probability distributions for exam: TableDistributions.pdf

Preliminary solutions, Exam 2025 (there may be typos and problems can be solved in other ways): Exam_solutions.pdf

Grading scale for the October exam can be found here.

Preliminary solutions, re-exam 2025: solutions_re-exam_2025.pdf

AI Policy

No use of generative AI tools is allowed, see here.

Contact information

Lecturer:
Lukas Schoug, lschoug@kth.se

Teaching assistants:
Zacharias Ljungström, zlj@kth.se
TA session style: Blackboard teaching.
Office hours: Wednesdays 14-16.

Babak Majidzadeh Garjani, babakmg@kth.se
TA session style: Blackboard teaching.

Karl Malterling Ruderfors, karlru@kth.se
TA session style: Blackboard teaching. Office hours: Mondays 15–16. Email for appointment.

Remark: The TAs will be in the classroom whose order on the list in the schedule corresponds to their order in the list above (first: Zacharias, second: Babak, third: Karl).

FAQ:

Q: Will you hand out solutions to the exercises? What about the recommended ones which will not be prioritised during the exercise sessions?
A: No solutions will be given out. In order to get solutions, attend exercise sessions or copy a fellow student's notes. You can also attend office hours to discuss problems.

Q: Why is the Modules section mostly empty? Where is the content?
A: The lecture plan and exercises can be found in pdf:s on the Home page, above. They will be updated.

Q: Where can I find old exams?
A: Don't worry about old exams for now. Learn the content. I will provide old exams when we get closer to the end of the course, in the Resources module. Old exams will be available in the Resources module Thursday 2/10.

Q: What about the partial exam/kontrollskrivning?
A: There is none -- it was apparently scheduled because they used to have one a few years ago. Instead there will be a few online quizzes.

Q: Will solutions to problems be provided?
A: Solutions to problems will be presented by TAs during the exercise sessions. No further solutions will be provided by the teachers (lecturer and TAs), but a good idea is to attend office hours to ask questions -- this will certainly help you in solving problems. Solutions may be freely shared between students (except for during the online quizzes). The examples of Gut's book are a great resource for understanding how to use the theory and results to compute different quantities.

Q: Will branching processes, random walks, and the Wiener process/Brownian motion be on the exam?
A: No.

Administrative matters

For administrative queries (registration for course, exams, re-exams, access to Canvas, etc) see the student office.