19200601
Lecture
WiSe 17/18: 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.
close31 Class schedule
Additional appointments
Wed, 2018-04-25 16:00 - 18:00Nachklausur
Regular appointments
Thu, 2017-10-19 08:00 - 10:00
Thu, 2017-10-26 08:00 - 10:00
Thu, 2017-11-02 08:00 - 10:00
Thu, 2017-11-09 08:00 - 10:00
Thu, 2017-11-16 08:00 - 10:00
Thu, 2017-11-23 08:00 - 10:00
Thu, 2017-11-30 08:00 - 10:00
Thu, 2017-12-07 08:00 - 10:00
Thu, 2017-12-14 08:00 - 10:00
Thu, 2017-12-21 08:00 - 10:00
Thu, 2018-01-11 08:00 - 10:00
Thu, 2018-01-18 08:00 - 10:00
Thu, 2018-01-25 08:00 - 10:00
Thu, 2018-02-01 08:00 - 10:00
Thu, 2018-02-08 08:00 - 10:00
Thu, 2018-02-15 08:00 - 10:00
Mon, 2017-10-23 08:00 - 10:00
Mon, 2017-10-30 08:00 - 10:00
Mon, 2017-11-06 08:00 - 10:00
Mon, 2017-11-13 08:00 - 10:00
Mon, 2017-11-20 08:00 - 10:00
Mon, 2017-11-27 08:00 - 10:00
Mon, 2017-12-04 08:00 - 10:00
Mon, 2017-12-11 08:00 - 10:00
Mon, 2017-12-18 08:00 - 10:00
Mon, 2018-01-08 08:00 - 10:00
Mon, 2018-01-15 08:00 - 10:00
Mon, 2018-01-22 08:00 - 10:00
Mon, 2018-01-29 08:00 - 10:00
Mon, 2018-02-05 08:00 - 10:00
Mon, 2018-02-12 08:00 - 10:00