Topic outline

  • This course is about exploring the mathematical foundations of randomness, which underlies most applications of probabilistic models and statistics. While the applications and use cases of probability theory are in many cases highly concrete, its foundations are rather abstract, and based on measure theory, which in turn builds on analysis and metric topology. In this course, we will simultaneously prove deep and powerful theorems about probability distributions, and discuss why such theorems are needed. In particular, we will unify the rather disparate theories of continuous and discrete random variables, as discussed in the courses Introduction to Probability and Statistics (MS-A050x) and Stochastic Processes (MS-C2111). Doing so will require some previous understanding of the topics from Metric Spaces (MS-C1541).

    The course starts on Mon 10 Jan 2021 at 10:15. It consists of 12 lectures, 12 quizzes, 5 homework sheets, and 1 final exam. The main reference for the course is Kalle Kytölä's lecture notes, found online at this link.

    Lectures: Ragnar Freij-Hollanti (
    Exercises: Kalle Alaluusua (

    There are two ways to pass the course. After completing the final exam, the grade is automatically calculated according to the way that gives you the better final score:
    Path 1: 10% quizzes. 30% homework, 60% final exam.
    Path 2: 100% final exam.