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Probability Theory and Statistics
Wahrscheinlichkeitstheorie und Statistik
Last Updated: 2026-02-05 15:10:17
Abstract
The course introduces the fundamental concepts of probability theory and illustrates them with numerous examples. In particular, notions such as sigma algebra, probability measure, independence, expectation value, variance, and so on in discrete and continuous models are treated. The course ends with an introduction to statistics.
Objective
Probability models and applications, introduction to statistical estimation and statistical tests.
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, conditional expectation, law of large numbers, central limit theorem. Introduction to statistics: estimation of parameters and tests
Resources
Lecture Notes
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Literature
Textbuch: P. Brémaud: 'An Introduction to Probabilistic Modeling', Springer, 1988.
General Information
- Language
- German
- 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 |
|
2 h weekly |
| exercise | Wahrscheinlichkeitstheorie und Statistik |
|
1 h weekly |