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Data Science and Artificial Intelligence

# Probability theory and inductive statistics

## Integrated course, 2.50 ECTS

### 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

none

### Assessment methods and criteria

Lecture: final exam, Exercise: examination character