Universität Wien

250068 VO Wahrscheinlichkeitstheorie und Statistik (2020S)

7.00 ECTS (4.00 SWS), SPL 25 - Mathematik
Moodle

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).
Register/Deregister for this course

Details

Language: German

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

For information on home-learning, please refer to the Moodle-page of this course

  • Tuesday 03.03. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 05.03. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 10.03. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 17.03. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 19.03. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 24.03. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 26.03. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 31.03. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 02.04. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 21.04. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 23.04. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 28.04. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 30.04. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 05.05. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 07.05. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 12.05. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 14.05. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 19.05. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 26.05. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 28.05. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 04.06. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 09.06. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 16.06. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 18.06. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 23.06. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 25.06. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 30.06. 13:15 - 14:45 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

This lecture provides an introduction into elementary probability theory and statistics.

The following topics will be discussed:

1. Basic notions of probability theory
σ−algebra, probability measures, discrete and continuous probability spaces

2. Conditional probability and independence of events:
Conditional probability, Bayes' formula, independence, product measures.

3. Random variables:
Random variable, distribution, density, discrete distributions ( Bernoulli, binomial, geometric, Poisson), Poisson limit theorem, independent random variables, expected value, variance, covariance, correlation.

4. Limit theorems:
Chebychev's inequality, convergence in probability, weak law of large numbers, Hoeffding's inequality, convergence almost surely, strong law of large numbers, convergence in distribution, central limit theorem.

5. Elementary statistics:
statistical models, maximum likelihood method, unbiased estimators, consistency of estimators.

6. Tests:
Neyman–Pearson framework, Neyman-Pearson lemma.

7. Confidence intervals

8. Statistical learning theory:
linear regression and outlook to basic statistical learning theory.

Assessment and permitted materials

Written exam

Minimum requirements and assessment criteria

Examination topics

Everything presented in the lecture

Reading list

J. Gärtner, Wahrscheinlichkeitstheorie 1, 2007, lecture notes, TU Berlin.

A. Klenke, Wahrscheinlichkeitstheorie, Springer, Berlin, 2006

H.-O. Georgii, Stochastik: Einführung in die Wahrscheinlichkeitstheorie und Statistik, Walter de Gruyter GmbH & Co KG, 2015.

J. T. H. Föllmer, H. Künsch, Wahrscheinlichkeitsrechnung und Statistik, lecture notes, ETHZ, 2013

S. Shalev-Shwartz and S. Ben-David, Understanding machine learning: From theory to algorithms. Cambridge university press, 2014.

Association in the course directory

PTS

Last modified: Fr 12.05.2023 00:21