# Elementary Stochastics (for teacher students) (dt. Elementare Stochastik (Lehramt))

 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 (attendance in den Lehrveranstaltungen 90 h, 150 h preparation and follow-up inklusive Studienleistungen, 30 h Vorbereitung and Ablegen von Prüfungsleistungen) Credit points,formal requirements 9 CP Course requirement(s): Successful completion of at least 50% of the weekly exercises. The coursework is a prerequisite for admission to the module examination. Examination type: Written examination (90-120 min.) Language,Grading German,The grading is done with 0 to 15 points according to the examination regulations for the degree program LAaG Mathematics. In the event of failure, a total of 4 attempts are available for the examination. Origin LAaG Mathematics Duration,frequency One semester, Jedes zweite Semester Person in charge of the module's outline Prof. Dr. Hajo Holzmann

## Contents

Scientific contents:

• 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
• law of large numbers and central limit theorem,
• descriptive statistics and data types
• elements of inferential statistics: estimates, confidence sets,
• hypothesis testing

Didactic contents:

Tasks and short lectures in the exercises on teaching related topics of elementary stochastics as well as projects on selected topics of school mathematics in connection with the current lecture material. Basic terms and topics are given special consideration, e.g.

• from the intuitive concept of probability to axiomatics
• historical aspects of probability theory
• statistical (mis)interpretations of everyday examples

## Qualification Goals

The students are familiar with the basic concepts of stochastics, can apply them to concrete tasks and assess their possible applications in class.

## Prerequisites

None. The competences taught in the following modules are recommended: Analysis I, Analysis II, Linear Algebra incl. Foundations of Mathematics.

## Applicability

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

• LAaG Mathematics

When studying LAaG Mathematics, this module must be completed in the study area Advanced Modules.