Stochastics: Introduction to Probability and StatisticsWalter de Gruyter, 2008 - 370 Seiten This book is a translation of the third edition of the well accepted German textbook 'Stochastik', which presents the fundamental ideas and results of both probability theory and statistics, and comprises the material of a one-year course. The stochastic concepts, models and methods are motivated by examples and problems and then developed and analysed systematically. |
Inhalt
Preface | 1 |
1 | 7 |
3 | 19 |
Stochastic Standard Models | 26 |
Conditional Probabilities and Independence | 50 |
Expectation and Variance | 90 |
The Law of Large Numbers and the Central Limit Theorem | 117 |
Markov Chains | 149 |
Confidence Regions | 222 |
Around the Normal Distributions | 241 |
Hypothesis Testing | 255 |
Asymptotic Tests and Rank Tests | 283 |
Regression Models and Analysis of Variance | 318 |
Tables | 349 |
References | 355 |
| 363 | |
Häufige Begriffe und Wortgruppen
alternative apply approximation arbitrary assume assumption average balls binomial calculate called choose claim condition consider construction contains continuous convergence Corollary corresponding defined Definition density depend described determine discrete equal equation error estimator event Example exists expectation exponential fact Figure finite function given Hence holds identity implies increasing independent inequality infinite interval likelihood limit linear Markov chain matrix means namely normal distribution null hypothesis observations obtain outcomes parameter particular Poisson positive possible probability measure Problem product model Proof properties question random variables region rejection Remark replacement respect result sample satisfies sequence Show situation specific standard statement statistical step stochastic Suppose Table Theorem unbiased uniform distribution unique unknown variance vector write