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One thousand exercises in probability /

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Bibliographic Details
Main Authors: Grimmett, Geoffrey (Author), Stirzaker, David (Author)
Corporate Author: ProQuest (Firm)
Format: eBook
Language:English
Published: Oxford, United Kingdom ; New York, NY : Oxford University Press, 2020.
Edition:Third edition.
Subjects:
Probabilities > Problems, exercises, etc.
Stochastic processes > Problems, exercises, etc.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • 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