t.BA.XX.WAHR.20HS (Probability Calculations) 
Module: Probability Calculations
This information was generated on: 19 April 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

Prerequisites

 ExpD

Teaching language

 (X) German ( ) English

Part of International Profile

 ( ) Yes (X) No

Module structure

 Type 2a
  For more details please click on this link: T_CL_Modulauspraegungen_SM2025

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%

Remarks

  

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.