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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
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
Additional available versions:
3.0 start 01 February 2021
,
1.0 start 01 August 2021
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.