19200601
Lecture
WiSe 18/19: Stochastik I
Timothy John Sullivan
Additional information / Pre-requisites
Audience:
Students from the 3rd semester
Requirements:
Basics of Analysis and Linear Algebra
Comments
Content:
- Models for situations involving chance: probability spaces, probability measures; frequentist and Bayesian interpretations of probability.
- Conditional probabilities and expectations.
- Random variables and their distributions; Characteristic values of the distributions: the expectation and variance
- Discrete distributions: e.g. the uniform, binomial, geometric, and Poisson distributions.
- Distributions with densities: e.g. the uniform, normal, and exponential distributions.
- Joint distributions of several random variables: independence of random variables; conditional distributions; sums of independent random variables and their distributions.
- Features of common distributions: expectation, covariance and correlation; characteristic and generating functions.
- Approximation of the binomial distribution by the Poisson and normal distributions.
- Limit theorems: the weak and strong laws of large numbers; the central limit theorem.
- Data analysis and descriptive statistics: histograms; empirical distribution; features of sample distributions; examples of misleading descriptive statistics; linear regression.
- Basic concepts and techniques of testing and estimation: maximum likelihood principle; confidence intervals; hypothesis testing; type I and type II errors.
Suggested reading
literature
- E. Behrends: Elementary Stochastics, Springer, 2013
- H.-O. Georgii: Stochastics: Introduction to Probability Theory and Statistics, De Gruyter, 2007
- U. Krengel: introduction to Probability Theory and Statistics, Vieweg, 2005
- D. Meintrup, S. Schäffler, Stochastics: Theory and Applications, Springer, 2005 .
Most of the books listed are available online via the UB.
close32 Class schedule
Additional appointments
Fri, 2019-02-15 12:30 - 15:30Klausur
Regular appointments
Mon, 2018-10-15 08:00 - 10:00
Mon, 2018-10-22 08:00 - 10:00
Mon, 2018-10-29 08:00 - 10:00
Mon, 2018-11-05 08:00 - 10:00
Mon, 2018-11-12 08:00 - 10:00
Mon, 2018-11-19 08:00 - 10:00
Mon, 2018-11-26 08:00 - 10:00
Mon, 2018-12-03 08:00 - 10:00
Mon, 2018-12-10 08:00 - 10:00
Mon, 2018-12-17 08:00 - 10:00
Mon, 2019-01-07 08:00 - 10:00
Mon, 2019-01-14 08:00 - 10:00
Mon, 2019-01-21 08:00 - 10:00
Mon, 2019-01-28 08:00 - 10:00
Mon, 2019-02-04 08:00 - 10:00
Mon, 2019-02-11 08:00 - 10:00
Thu, 2018-10-18 08:00 - 10:00
Thu, 2018-10-25 08:00 - 10:00
Thu, 2018-11-01 08:00 - 10:00
Thu, 2018-11-08 08:00 - 10:00
Thu, 2018-11-15 08:00 - 10:00
Thu, 2018-11-22 08:00 - 10:00
Thu, 2018-11-29 08:00 - 10:00
Thu, 2018-12-06 08:00 - 10:00
Thu, 2018-12-13 08:00 - 10:00
Thu, 2018-12-20 08:00 - 10:00
Thu, 2019-01-10 08:00 - 10:00
Thu, 2019-01-17 08:00 - 10:00
Thu, 2019-01-24 08:00 - 10:00
Thu, 2019-01-31 08:00 - 10:00
Thu, 2019-02-07 08:00 - 10:00
Thu, 2019-02-14 08:00 - 10:00