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This entry is from Winter semester 2019/20 and might be obsolete. You can find a current equivalent here.

Elementary Stochastics
(dt. Elementare Stochastik)

Level, degree of commitment Advanced module, depends on importing study program
Forms of teaching and learning,
workload		 Lecture (4 SWS), recitation class (2 SWS),
270 hours (90 h attendance, 180 h private study)
Credit points,
formal requirements		 9 CP
Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination
Language,
Grading		 German,
The grading is done with 0 to 15 points according to the examination regulations for the degree program B.Sc. Business Mathematics.
Origin B.Sc. Business Mathematics
Duration,
frequency		 One semester,
each winter semester
Person in charge of the module's outline Prof. Dr. Markus Bibinger, Prof. Dr. Hajo Holzmann

Contents

Basic concepts of probability theory

  • probability space, events, discrete probability distributions, combinatorics
  • conditional probability, independence, random variables, expected value, conditional expected value, variance, covariance, correlation, moments
  • general probability spaces and random variables
  • laws of large numbers and central limit theorem, basic concepts of statistics
  • descriptive statistics and data types
  • elements of inferential statistics: estimation, confidence sets, hypothesis testing

Qualification Goals

The students shall

  • learn the basics of stochastics,
  • practice to model random quantities using theoretical probabilistic models,
  • get to know the basic principles of descriptive and conclusive statistics,
  • practice mathematical working methods (development of mathematical intuition and its formal justification, training of the ability to abstract, proof techniques),
  • improve their oral communication skills in the exercises by practicing free speech in front of an audience and during discussion.

Prerequisites

None. The competences taught in the following modules are recommended: either Foundations of Mathematics and Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis.


Applicability

The module can be attended at FB12 in study program(s)

  • B.Sc. Data Science
  • B.Sc. Computer Science
  • B.Sc. Mathematics
  • B.Sc. Business Mathematics
  • M.Sc. Computer Science
  • M.Sc. Mathematics
  • M.Sc. Business Informatics
  • M.Sc. Business Mathematics

When studying B.Sc. Business Mathematics, this module must be completed in the study area Basics of Mathematics.

The module can also be used in other study programs (export module).


Recommended Reading

  • Dehling, H., Haupt, B., „Einführung in die Wahrscheinlichkeitstheorie und Statistik“, Springer 2003.
  • Georgii, H. O. „Stochastik: Einführung in die Wahrscheinlichkeitstheorie und Statistik“, 4. Auflage. De Gruyter, 2009
  • Henze, N. „Stochastik für Einsteiger“, 7. Auflage, Vieweg, 2008



Please note:

This page describes a module according to the latest valid module guide in Winter semester 2019/20. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.