Stochastics. Introduction to Probability and Statistics
This is a translation of the third edition of the German textbook “Stochastik”. It presents fundamental ideas and results of both probability theory and statistics. The areas covered from probability are: principles of modelling chance, stochastic standard models, conditional probabilities and independence, expectation and variance, the law of large numbers and the central limit theorem and Markov chains. The book covers the following areas of mathematical statistics: estimation, confidence regions, the normal distribution, hypothesis testing, asymptotic tests and rank tests, regression models and the analysis of variance. The basic notions and theorems are accompanied by interesting illustrative examples. At the end of each chapter there is a collection of problems offering applications, additions and supplements to the text. The book is primarily aimed at students of mathematics but also to scientists with an interest in the mathematical side of stochastics. Knowledge of abstract mathematics including elements of measure theory is assumed. The author gives a recommendation of how to successfully study the book. The book is well-written and mathematically oriented students and researchers will certainly find that it provides a high level introduction to probability theory and mathematical statistics.