Georgii H.-O. Stochastics. Introduction To Probability And Statistics

2nd edition. — Berlin: de Gruyter, 2013. — 420 p.This textbook, now in its second revised and extended edition, presents the fundamental ideas and results of both probability theory and statistics. It comprises the material of a one-year course, which is addressed to students of mathematics and to scientists with an interest in the mathematical side of stochastics.
The stochastic concepts, models and methods are motivated by examples and then developed and analysed systematically. Some measure theory is included, but this is done at an elementary level that is in accordance with the introductory character of the book. A large number of problems, now in part with solutions, offer applications and supplements to the text.Principles of Modelling Chance
Stochastic Standard Models
Conditional Probabilities and Independence
Expectation and Variance
The Law of Large Numbers and the Central Limit Theorem
Markov Chains
Estimation
Confidence Regions
Around the Normal Distributions
Hypothesis Testing
Asymptotic Tests and Rank Tests
Regression Models and Analysis of Variance
Solutions TablesList of Notation Index