Voortgezette Kansrekening

The goal of the course is to extend the basic notions of probability with an analytic toolkit.

Rigorous probability is closely related to real and complex analysis. We will explore these connections and learn how concepts from real analysis translate to probability and vice versa.

In particular we will construct a general probability space and perform computations of expectations, and conditional expectation of random variables therein.

We will treat different types of convergences of random variables, Borel-Cantelli Lemmas, Kolmogorov's 0-1 law.

We will learn various analytic methods to prove convergence or random variables: characteristic functions, Fourier inversion, generating function. Laws of Large Numbers and general Central Limit Theorems will be discussed. If time permits, we will learn about stable distributions.

The assessment will consists of one final written exam.

In case of an insufficient final result, repair options may exist in accordance with Article 2 Examinationrequirements, Clause 4, of the Implementation Regulations 2023-2024. The repair option is a resit exam that covers the material of the final exam.

- In case that the resit exam is taken, the final grade is given by 100% of the result on the resit exam; this overwrites the earlier attained result. (That is, it can be both lower or higher than the previously attained grade).

In case of low number of students taking the course the course may be given in a reading seminar form with reduced contact hours and an oral exam that consists of both theory and solving exercises.