Stochastik

Due to the extremely positive reception of this textbook, it is now being published in its 5th edition. The book provides an introduction to the key ideas and elements of probability theory and statistics. Stochastic concepts, models, and methods are highlighted through typical application examples, then analyzed theoretically and systematically explored.

Autorentext

Hans-Otto Georgii, LMU München.

Zusammenfassung

Review for the 3rd edition by Vladimir P. Kurenok (MathSciNet)

"The 3rd edition of the book has been further extended and improved. The textbook is based on a series of lectures taught by the author for many years at the Mathematical Institute of the University of Munich. The material of the book covers two one-semester courses in probability and mathematical statistics, respectively. All chapters are equipped with exercises of varying degrees of difficulty that help to clarify the concepts.

The first part of the book is an introduction to probability theory. The material is presented using little of the measure-theoretical background but rather application-oriented examples that preserve its introductory character. Topics range from classical probability distributions to conditional distributions and limit theorems. A short introduction to Markov chains is also given. The second part of the book gives an introduction to mathematical statistics and describes main statistical procedures: parameter and interval estimation, hypothesis testing, linear regression and basics of the analysis of variance approach.

The book can be used by undergraduate mathematics majors but also by science and engineering students who wish not only to apply probability and statistics but also to understand how the methods work."

Inhalt

Wahrscheinlichkeitstheorie

• Mathematische Beschreibung von Zufallssituationen
• Stochastische Standardmodelle
• Bedingte Wahrscheinlichkeiten und Unabhängigkeit
• Erwartungswert und Varianz
• Gesetz der großen Zahl und zentraler Grenzwertsatz

• Markov-Ketten Statistik

• Parameterschätzung
• Konfidenzbereiche
• Rund um die Normalverteilung
• Testen von Hypothesen
• Asymptotische Tests und Rangtests
• Regressions- und Varianzanalyse