## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Module MAT-14-14LBBS-M-3

## Module Identification

Module Number Module Name CP (Effort)
MAT-14-14LBBS-M-3 Mathematics as Solution Potential B: Introduction to Stochastics (BBS) 6.0 CP (180 h)

## Basedata

CP, Effort 6.0 CP = 180 h 1 Sem. in WiSe [3] Bachelor (Core) [DE] German Lossen, Christoph, Dr. habil. (WMA | DEPT: MAT) Korn, Ralf, Prof. Dr. (PROF | DEPT: MAT) Redenbach, Claudia, Prof. Dr. (PROF | DEPT: MAT) Ritter, Klaus, Prof. Dr. (PROF | DEPT: MAT) Sass, Jörn, Prof. Dr. (PROF | DEPT: MAT) [MAT-EDU] Mathematics (B.Ed./M.Ed.) [MAT-47.105-SG] B.Ed. LaBBS Mathematics [NORM] Active

## Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
4V MAT-14-14-K-3
Stochastic Methods
P 56 h 124 h - - PL1 6.0 WiSe
• About [MAT-14-14-K-3]: Title: "Stochastic Methods"; Presence-Time: 56 h; Self-Study: 124 h

## Examination achievement PL1

• Form of examination: oral examination (20-30 Min.)
• Examination Frequency: each semester

## Contents

Introduction to Stochastics.

Fundamentals of probability theory:

• basic concepts of probability theory (probability space, random variable, distribution);
• distribution of real-valued random variables (binomial, Poisson, exponential and normal distribution, etc.);
• expected value, variance, covariance;
• distribution of random vectors, multivariate normal distribution as an example;
• conditional probability, independence;
• law of large numbers;
• Monte Carlo simulation;
• central limit value theorem.

Fundamental of statistics:

• parameter estimator;
• interval estimator;
• tests.

## Competencies / intended learning achievements

The students
• are familiar with stochastic concepts, the fundamental concepts of probability theory and statistics;
• can apply stochastic methods to simple practical problems.

## Literature

• D. Williams: Weighing the Odds - A Course in Probability and Statistics,
• H.O. Georgii: Stochastik - Einführung in die Wahrscheinlichkeitstheorie und Statistik,
• U. Krengel: Einführung in die Wahrscheinlichkeitstheorie und Statistik,
• K.L. Chung: Elementare Wahrscheinlichkeitsrechnung und stochastische Prozesse.

## Materials

Further literature will be announced in the lecture; Exercise material is provided.

None

## References to Module / Module Number [MAT-14-14LBBS-M-3]

Course of Study Section Choice/Obligation
[MAT-47.105-SG] B.Ed. LaBBS Mathematics [Section (non-specific)] Compulsory Modules [P] Compulsory