http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Cover -- One Thousand Exercises in Probability -- Copyright -- Epigraph -- Preface to the Third Edition -- Contents -- Questions -- 1 Events and their probabilities -- 1.2 Exercises. Events as sets -- 1.3 Exercises. Probability -- 1.4 Exercises. Conditional probability -- 1.5 Exercises. Independence -- 1.7 Exercises. Worked examples -- 1.8 Problems -- 2 Random variables and their distributions -- 2.1 Exercises. Random variables -- 2.2 Exercises. The law of averages -- 2.3 Exercises. Discrete and continuous variables -- 2.4 Exercises. Worked examples -- 2.5 Exercises. Random vectors
2.7 Problems -- 3 Discrete random variables -- 3.1 Exercises. Probability mass functions -- 3.2 Exercises. Independence -- 3.3 Exercises. Expectation -- 3.4 Exercises. Indicators and matching -- 3.5 Exercises. Examples of discrete variables -- 3.6 Exercises. Dependence -- 3.7 Exercises. Conditional distributions and conditional expectation -- 3.8 Exercises. Sums of random variables -- 3.9 Exercises. Simple random walk -- 3.10 Exercises. Random walk: counting sample paths -- 3.11 Problems -- 4 Continuous random variables -- 4.1 Exercises. Probability density functions
4.2 Exercises. Independence -- 4.3 Exercises. Expectation -- 4.4 Exercises. Examples of continuous variables -- 4.5 Exercises. Dependence -- 4.6 Exercises. Conditional distributions and conditional expectation -- 4.7 Exercises. Functions of random variables -- 4.8 Exercises. Sums of random variables -- 4.9 Exercises. Multivariate normal distribution -- 4.10 Exercises. Distributions arising from the normal distribution -- 4.11 Exercises. Sampling from a distribution -- 4.12 Exercises. Coupling and Poisson approximation -- 4.13 Exercises. Geometrical probability -- 4.14 Problems
5 Generating functions and their applications -- 5.1 Exercises. Generating functions -- 5.2 Exercises. Some applications -- 5.3 Exercises. Random walk -- 5.4 Exercises. Branching processes -- 5.5 Exercises. Age-dependent branching processes -- 5.6 Exercises. Expectation revisited -- 5.7 Exercises. Characteristic functions -- 5.8 Exercises. Examples of characteristic functions -- 5.9 Exercises. Inversion and continuity theorems -- 5.10 Exercises. Two limit theorems -- 5.11 Exercises. Large deviations -- 5.12 Problems -- 6 Markov chains -- 6.1 Exercises. Markov processes
6.2 Exercises. Classification of states -- 6.3 Exercises. Classification of chains -- 6.4 Exercises. Stationary distributions and the limit theorem -- 6.5 Exercises. Reversibility -- 6.6 Exercises. Chains with finitely many states -- 6.7 Exercises. Branching processes revisited -- 6.8 Exercises. Birth processes and the Poisson process -- 6.9 Exercises. Continuous-time Markov chains -- 6.10 Exercises. Kolmogorov equations and the limit theorem -- 6.11 Exercises. Birth-death processes and imbedding -- 6.12 Exercises. Special processes -- 6.13 Exercises. Spatial Poisson processes
6.14 Exercises. Markov chain Monte Carlo
Geoffrey R. Grimmett and David R. Stirzaker.
Includes bibliographical references and index.
One Thousand Exercises in Probability : Third Edition
Oxford : Oxford University Press, Incorporated,c2020