t.BA.XX.WAHR.20HS (Probability Calculations)
Module: Probability Calculations
This information was generated on: 27 September 2021
No.
t.BA.XX.WAHR.20HS
Title
Probability Calculations
Organised by
T IDP
Credits
4

### Description

Version: 1.0 start 01 August 2021
•

#### Short description

The module Probability Theory introduces the basics of probability theory. In this module, students learn to describe random events and their properties with probability models and to quantify them with the statistical software R.

#### Module coordinator

Hofer Christoph (hofc)

#### 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
• 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. In addition, simulation experiments are used to  approximate the probability of random events or parameters as well as to illustrate selected concepts of probability theory.

#### Teaching materials

lecture notes, presentation documents, exercises

#### Supplementary literature

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

#### 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.