# Elementary Probability and Statistics (dt. Elementare Stochastik)

 Level, degree of commitment Advanced module, required module Forms of teaching and learning,workload Lecture (4 SWS), recitation class (2 SWS) or lecture using videos (4 SWS), Repetitorium (2 SWS), recitation class (2 SWS), 270 hours (90 h attendance, 180 h private study or 60 h attendance and 210 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 (individual 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. Duration,frequency One semester, each winter semester Person in charge of the module's outline Prof. Dr. Hajo Holzmann

## Contents

Basic concepts of probability theory

• Result 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
• Stochastic convergence and laws of large numbers
• Convergence in distribution and the central limit theorem
• Basic concepts of statistics
• descriptive statistics and data types
• Elements of inferential statistics: statistical models, estimation, confidence intervals, hypothesis testing

## Qualification Goals

Students will

• know the basic concepts of stochastics,
• have practiced the basics of modeling random quantities using probabilistic models,
• know basic principles of descriptive and inferential statistics,
• have practiced mathematical working methods (development of mathematical intuition and its formal justification, abstraction, proof),
• have improved their oral communication skills in exercises by practicing free speech in front of an audience and in 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

Module imported from B.Sc. Business Mathematics.

It can be attended at FB12 in study program(s)

• B.Sc. Data Science
• B.Sc. Mathematics
• M.Sc. Computer Science
• BA Minor Mathematics

When studying B.Sc. Mathematics, this module must be completed in the study area Continuing Modules in Mathematics (Core Subjects).

• Henze, N. „Stochastik für Einsteiger“, 13. Auflage, Springer Spektrum , 2021
• Krengel, U. "Einführung in die Wahrscheinlichkeitstheorie und Statistik", 8. Auflage, Vieweg Studium, 2008
• Georgii, H. O. „Stochastik: Einführung in die Wahrscheinlichkeitstheorie und Statistik“, 4. Auflage. De Gruyter, 2009