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Applied Stochastics

Probability 1

08001300 · Stochastik 1

Lecturer: Prof. Dr. Markus Bibinger

Tutor: Patrick Bossert

  • Date and location: There are  lectures each Wednesday, 10:15-11:45 am, and each Thursday, 12:15-13:45 pm, in Hörsaal 2, Nat.wiss. HS-Bau.
  • Start: 19.10.2022, 10:15 am
  • Exercises (Vst.-Nr.  08001350): Thursday at 10 am and 4 pm in S0.106 and S0.107, BSZ. Tutorials will start in the second lecture week.
  • Exams: Written exam on February 15th, 9am, Turing-Hörsaal.
  • Registration for the exam: Via WueStudy, registration period will be announced.
  • Language: German


Contents of the lecture:

This course gives an introduction to probability theory and its foundations based on measure theory. We consider fundamental concepts of probability including

  • Probability spaces
  • Random variables and measurability
  • Discrete distributions and combinatorics
  • Conditional probability and independence
  • Expectation and integration theory
  • Absolutely continuous distributions, densities and distribution functions
  • First elements of mathematical statistics
  • Asymptotics with laws of large numbers and normal approximation

Requirements: Elementary calculus and algebra


  • Dehling, H. und Haupt, B.: Einführung in die Wahrscheinlichkeitstheorie und
    Statistik. 2. Auflage. Springer, Berlin, 2004.
  • Durrett, R.: Probability Theory and Examples, Wadsworth & Brooks, 1991.
  • Feller, W.: An Introduction to Probability Theory and Its Applications, Volume 1, Wiley, 1968.
  • Georgii, H. O.: Stochastik. 4. Auflage. De Gruyter Verlag, 2009.
  • Henze, N.: Stochastik: Eine Einführung mit Grundzügen der Maßtheorie. Springer Spektrum, 2019.
  • Jacod, J. and P. Protter: Probability Essentials, Springer, 2000.
  • Klenke, A.: Wahrscheinlichkeitstheorie, Springer Spektrum, 3rd edition, 2013.
  • Krengel, U.: Einführung in dieWahrscheinlichkeitstheorie und Statistik . 8. Auflage.
    Vieweg, Wiesbaden, 2005.


(1) Registration (Vst.-Nr. 08001350) in WueStudy is required!

(2) Materials (lecture notes, exercise sheets) via WueCampus (link).