19200601
Lecture
WiSe 16/17: 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.
close30 Class schedule
Regular appointments
Thu, 2016-10-20 08:00 - 10:00
Thu, 2016-10-27 08:00 - 10:00
Thu, 2016-11-03 08:00 - 10:00
Thu, 2016-11-10 08:00 - 10:00
Thu, 2016-11-17 08:00 - 10:00
Thu, 2016-11-24 08:00 - 10:00
Thu, 2016-12-01 08:00 - 10:00
Thu, 2016-12-08 08:00 - 10:00
Thu, 2016-12-15 08:00 - 10:00
Thu, 2017-01-05 08:00 - 10:00
Thu, 2017-01-12 08:00 - 10:00
Thu, 2017-01-19 08:00 - 10:00
Thu, 2017-01-26 08:00 - 10:00
Thu, 2017-02-02 08:00 - 10:00
Thu, 2017-02-09 08:00 - 10:00
Thu, 2017-02-16 08:00 - 10:00
Mon, 2016-10-24 08:00 - 10:00
Mon, 2016-10-31 08:00 - 10:00
Mon, 2016-11-07 08:00 - 10:00
Mon, 2016-11-14 08:00 - 10:00
Mon, 2016-11-21 08:00 - 10:00
Mon, 2016-11-28 08:00 - 10:00
Mon, 2016-12-05 08:00 - 10:00
Mon, 2016-12-12 08:00 - 10:00
Mon, 2017-01-09 08:00 - 10:00
Mon, 2017-01-16 08:00 - 10:00
Mon, 2017-01-23 08:00 - 10:00
Mon, 2017-01-30 08:00 - 10:00
Mon, 2017-02-06 08:00 - 10:00
Mon, 2017-02-13 08:00 - 10:00