Stochastics Introduction To Probability And Statistics

Description

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. 1- Principles of Modelling Chance 2- Stochastic Standard Models 3- Conditional Probabilities and Independence 4- Expectation and Variance 5- The Law of Large Numbers and the Central Limit Theorem 6- Markov Chains 7- Estimation 8- Confidence Regions 9- Around the Normal Distributions 10- Hypothesis Testing 11- Asymptotic Tests and Rank Tests 12- Regression Models and Analysis of Variance Solutions Tables References List of Notation Index