Probability theory and inductive statistics

Course content

Area 1: Probability Theory
- Basic concepts of probability theory
- Limit theorems
- Conditional probabilities and Bayes theorem
- Basic concepts of combinatorics
- Important discrete and continuous univariate distributions
Area 2: Inductive statistics
- Samples and confidence intervals
- Data reduction and sampling theorem
- Hypothesis tests for parametric and nonparametric distributions
- Resampling (bootstrapping, cross-validation, ...) and Monte Carlo method
- Maximum likelihood method

Learning outcomes

Students have a profound knowledge of probability theory and univariate inductive statistics. In particular, they are able to perform hypothesis tests based on parametric and nonparametric distributions.

Recommended or required reading and other learning resources / tools

Recommended Literature and Books: - Arens, T., Hettlich, F. (2018). Mathematik. Springer Spektrum, 4. Auflage.
- Bronstein, I. N., Mühlig, H. (2016). Taschenbuch der Mathematik. Europa-Lehrmittel, 10. Auflage.
- Büning, H., Trenkler, G. (1994). Nichtparametrische statistische Methoden (De Gruyter Lehrbuch). De Gruyter, 2. Auflage.
- Field, A., Miles, H. (2012). Discovering Statistics Using R. Sage Publications Ltd., 1. Auflage.
- Hedderich, J., Sachs, L. (2018). Angewandte Statistik: Methodensammlung mit R. Springer Spektrum, 16. Auflage.
- Ugarte M. D., Miltino A. F. (2015). Probability and Statistics with R. CRC-Press, 2. Auflage.
Recommended journals and selected articles: All relevant journals and articles will be given in the class. Typical software for this module: R/RStudio etc.

Mode of delivery

1,25 ECTS Lecture, 1,25 ECTS Exercise

Prerequisites and co-requisites

none

Assessment methods and criteria

Lecture: final exam, Exercise: examination character