Probability Theory Autumn 2021

Wendelin Werner
Daniel Contreras and Matthis Lehmkühler


Measure theory formalism and probability theory, Dynkin's lemma and independence, convergence of series of independent random variables, law of large numbers, conditional expectation, martingale convergence theorems, uniform integrability, optional stopping theorem for martingales, the Galton-Watson process and its R-number, convergence in law and the central limit theorem, a bit of Markov chains and large deviations.


Lectures will take place in-person and will be livestreamed.
Time Room Livestream
Tuesdays 10:15-11:55 HG D 1.2 Livestream HG D 1.2
Thursdays 10:15-11:55 HG E 3 Livestream HG E 3
A recording will be available shortly after the lecture here.

Important: The link to access the final two (recorded) lectures has been e-mailed to the students.

According to ETH Guidelines, a COVID certificate together with an ID card or Legi should be presented to enter the room for in-person teaching.

Lecture Notes


The new exercises will be posted here on Mondays. Please hand in your solutions by the following Monday at 17:00 using the links in the table below. Your solutions will corrected and returned by email.

Exercise sheet Due by Solutions
Exercise sheet 1 September 27 Solution 1
Exercise sheet 2 October 4 Solution 2
Exercise sheet 3 October 11 Solution 3
Exercise sheet 4 October 18 Solution 4
Exercise sheet 5 October 25 Solution 5
Exercise sheet 6 November 1 Solution 6
Exercise sheet 7 November 8 Solution 7
Exercise sheet 8 November 15 Solution 8
Exercise sheet 9 November 22 Solution 9
Exercise sheet 10 November 29 Solution 10
Exercise sheet 11 December 6 Solution 11
Exercise sheet 12 December 13 Solution 12
Exercise sheet 13 December 20 Solution 13

Exercise classes

Students are distributed in 4 groups according to family name. Assitants will correct the exercises of their corresponding group. Nonetheless, you can enroll in any of the classes below in myStudies. Exercises classes start the second week of the semester.
Time Room Distribution Assistant
Tu 14:15-15:00 HG F 26.5 A-Ge Matthis Lehmkühler
Tu 14:15-15:00 ML H 41.1 Gi-Li Luca Pelizzari
Tu 15:15-16:00 Zoom Lo-Re Daniel Contreras
Tu 15:15-16:00 ML H 41.1 Ri-Z Genc Kqiku

Online Class

A recording of the Zoom exercise class will be available soon after below.

Office hours

Office hours are offered by group 3 on Mondays and Thursdays from 12:00 to 13:00 in HG G 32.6 starting the fourth week of the semster.