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Probability Theory and Statistics
Wahrscheinlichkeitstheorie und Statistik
Last Updated: 2026-02-05 16:22:13
Abstract
Probability models and applications, introduction to statistical estimation and statistical tests.
Objective
Ability to understand the covered methods and models from probability theory and to apply them in other contexts. Ability to perform basic statistical tests and to interpret the results.
Content
The concept of probability space and some classical models: the axioms of Kolmogorov, easy consequences, discrete models, densities, product spaces, relations between various models, distribution functions, transformations of probability distributions. Conditional probabilities, definition and examples, calculation of absolute probabilities from conditional probabilities, Bayes' formula, conditional distribution. Expectation of a random variable,application to coding, variance, covariance and correlation, linear estimator, law of large numbers, central limit theorem. Introduction to statistics: estimation of parameters and tests
Resources
Lecture Notes
yes
Literature
Textbuch: P. Brémaud: 'An Introduction to Probabilistic Modeling', Springer, 1988.
Learning Materials (Links)
- Main link
- Information
General Information
- Language
- English (lecture), German (exercise)
- Levels
- BSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- written 90 minutes
- Aids
- 5 beidseitig von Hand beschriebene A4-Blätter, keine Taschenrechner.
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Wahrscheinlichkeitstheorie und Statistik (Probability Theory and Statistics) |
|
2 h weekly |
| exercise |
Wahrscheinlichkeitstheorie und Statistik
Groups are selected in myStudies.
|
|
1 h weekly |