The students learn to understand and apply basic notions of stochastics and stochastic processes.

2/3 of the VC's time consists of a lecture, the content of which is developed live on a tablet. This content will be made available to the students. In addition, we provide short videos revising parts of this lecture in English as well as videos of the lecture Stochastik 1 in German.1/3 of the VC's time consists of exercises that shall deepen the students' knowledge and ability to apply the content from the lecture. The exercises take place biweekly for 90 minutes. Exercises will be presented in smaller groups; two of these are held online via BBB.In the first exercise class, students will train how to solve exercises by solving an exercise sheet in small break-out groups. In the following weeks, an exercise sheet will be provided in advance and students are expected to solve these exercise sheets alone or in small groups. In the exercise classes, students will present the solutions to the solved exercises. In advance, every student selects the exercises which they would like to present in front of the class; one of these will be chosen for the exercise. Every student is expected to present at least one exercise per semester. If no student volunteers for an exercise, the lecturer will either give a hint, conduct a break-out session on this exercise, or solve the exercise themselves.

Finite probability spacesCountable probability spacesConditional probability and independenceRandom variables, expectation, variance, covariance, correlation, momentsProbability distributions with densitiesParameter estimationSimulation of random variablesLimit theoremsMonte Carlo simulationBrownian motion and Poisson processPath generation

Basic math courses in Linear Algebra and Analysis

Lecture notes

There will be two written exams: a mid term exam on November 23, 2023 and a final exam on January 25, 2024.Also there will be the possibility to write a third exam (in February or March) either in order to replace the mid term or the final exam.  The number of points of the third exam replaces the number of points of the exam that is repeated.The mid term exam counts 35 points, the final exam counts 60 points, the first presentation counts up to 5 points. Any further presentation counts up to 2 bonus points, so that in total more than 100 points can be reached.It is expected that the students work on all the exercises, but they are not mandatory and will not be graded any further than mentioned above.The marks are calculated as follows:[87.5 , 200] P. -> 1[75 , 87.5) P. -> 2[62.5 , 75) P. -> 3[50 , 62.5) P. -> 4[0 , 50) P. -> 5

The whole content of the VC is relevant for the exam. Should additional content be relevant, it will be announced explicitly in the lecture.

The mark is determined by the points.Cancellation of participation without grading is possibly until November 22, 2023.