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.
References
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.
Additional information
Audience:
Students from the 3rd semester
Requirements:
Basics of Analysis and Linear Algebra
Additional appointments
Klausur
HFB/B Hörsaal
Timothy JohnSullivan
15.02.2019 12:30 - 15:30
Appointment series
A6/SR 031 Seminarraum
Timothy JohnSullivan
wöchentlich, ab 18.10.2018, 08:00 - 10:00 (16 Termine)
A6/SR 031 Seminarraum
Timothy JohnSullivan
wöchentlich, ab 15.10.2018, 08:00 - 10:00 (16 Termine)