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. Subject, Origin Mathematics, 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.

• 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