Kai Lai Chung (1917–2009)

I usually find books on probability boring and irritating, but I was very happy with this one.
It does a fine job of covering measure theory in a useful fashion, and is an acceptable first pass at covering stochastic processes.

Indeholder "Preface to the Third Edition", "Preface to the Second Edition", "Preface to the First Edition", "Chapter 1: Set", "1.1 Sample sets", "1.2 Operations with sets", "1.3 Various relations", "1.4 Indicator", "Exercises", "Chapter 2: Probability", "2.1 Example of probability", "2.2 Definition and illustrations", "2.3 Deductions from the axioms", "2.4 Independent events", "2.5 Arithmetical density", "Exercises", "Chapter 3: Counting", "3.1 Fundamental rule", "3.2 Diverse ways of show more sampling", "3.3 Allocation models; binomial coefficients", "3.4 How to solve it", "Exercises", "Chapter 4: Random Variables", "4.1 What is a random variable?", "4.2 How do random variables come about?", "4.3 Distribution and expectation", "4.4 Integer-valued random variables", "4.5 Random variables with densities", "4.6 General case", "Exercises", "Appendix 1: Borel Fields and General Random Variables", "Chapter 5: Conditioning and Independence", "5.1 Examples of conditioning", "5.2 Basic formulas", "5.3 Sequential Sampling", "5.4 Pólya's urn scheme", "5.5 Independence and relevance", "5.6 Genetic models", "Exercises", "Chapter 6: Mean, Variance and Transforms", "6.1 Basic properties of expectation", "6.2 The density case", "6.3 Multiplication theorem; variance and covariance", "6.4 Multinomial distribution", "6.5 Generating function and the like", "Exercises", "Chapter 7: Poisson and Normal Distributions", "7.1 Models for Poisson Distribution", "7.2 Poisson proces", "7.3 From binomial to normal", "7.4 Normal distribution", "7.5 Central limit theorem", "7.6 Law of large numbers", "Exercises", "Appendix 2: Stirling's Formula and DeMoivre-Laplace's Theorem", "Chapter 8: From Random Walks to Markov Chains", "8.1 Problems of the wanderer or gambler", "8.2 Limiting schemes", "8.3 Transition probabilities", "8.4 Basic structure of Markov chains", "8.5 Further developments", "8.6 Steady state", "8.7 Winding up (or down?)", "Exercises", "Appendix 3: Martingale", "General References", "Answers to Problems", "Index".

Udmærket introduktion, men måske lidt rigeligt snakkende.
Lærebog i sandsynlighedsregning på statistik 1 i Århus, 1979/1980. show less