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.

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.

Audience:
Students from the 3rd semester

Requirements:
Basics of Analysis and Linear Algebra