t.BA.XX.WAHR.20HS (Probability Calculations)
Module: Probability Calculations
This information was generated on: 24 July 2024
No.
t.BA.XX.WAHR.20HS
Title
Probability Calculations
Organised by
T IDP
Credits
4

### Description

Version: 4.0 start 01 August 2024
•

#### Short description

The module Probability Theory introduces the basics of probability theory. Students learn to describe random events with probability models and to quantify them using the statistical software R.

#### Module coordinator

Martin Frey (fret)

#### Learning objectives (competencies)

 Objectives Competences Taxonomy levels Students develop an understanding to quantify the uncertainty of  events by probability. F, M K1, K2 Students are able to calculate probabilities, expected values and variances of random events of special discrete and continuous distributions. F, M K2, K3 Students are able to determine the probability distribution of complex random events approximatively with simulation experiments. F, M K3, K4 Students are able to identify random components of everyday processes and formulate them with adequate probability models F, M K3, K4, K5 Students understand the law of large numbers and the central limit theorem. F, M K1, K2

#### Module contents

Students learn to describe random events by probability, to model quantitatively the results of random experiments with random variables, and to determine and interpret their properties such as expected value and variance.

The lessons are divided into the following blocks:
• Random experiment and concept of probability
• Basics of combinatorics
• Conditional probability
• Bayes' theorem
• Independence from events
• Random variables
• Probability function and density
• Distribution function
• Moments
• Special discrete and continuous univariate probability models
• Bivariate Normal distribution
• Law of large numbers
• Central limit theorem
In the lab students learn to implement concepts conveyed in the lecture based on concrete exercises with the statistical software R. This also includes simulation experiments to approximately calcuate the probability of random events or parameters as well as to illustrate selected concepts of probability theory.

#### Teaching materials

Script, lecture notes, worksheets and exercise sheets

#### Supplementary literature

Fahrmeir, L., Künstler, R., Pigeot, I., Tutz, G. (1997). Statistik. Der Weg zur Datenanalyse, Springer.

Meier, L. (2020). Wahrscheinlichtsrechnug und Statistik: Eine Einführung für Verständnis, Intuition und Überblick, Springer

ExpD

#### Teaching language

(X) German ( ) English

( ) Yes (X) No

Type 2a

#### Exams

 Description Type Form Scope Grade Weighting Graded assignments during teaching semester Short presentation Online Quizzes Term paper oral written written 20 min. 3 Quizzes 3-5 pages Grading 5% 5-15% 15% End-of-semester exam exam written 90 min. Grading 65%

#### Legal basis

The module description is part of the legal basis in addition to the general academic regulations. It is binding. During the first week of the semester a written and communicated supplement can specify the module description in more detail.

### Note

Course: Wahrscheinlichkeitsrechnen - Vorlesung
No.
t.BA.XX.WAHR.20HS.V
Title
Wahrscheinlichkeitsrechnen - Vorlesung

### Note

• No module description is available in the system for the cut-off date of 02 August 2099.