Kai Lai Chung. Elementary Probability Theory with Stochastic Processes

New York: Springer, 2012. — 338 p.A new feature of this edition consists of photographs of eight masters in the contemporary development of probability theory. All of them appear in the body of the book, though the few references there merely serve to give a glimpse of their manifold contributions. It is hoped that these vivid pictures will inspire in the reader a feeling that our science is a live endeavor created and pursued by real personalities. I have had the privilege of meeting and knowing most of them after studying their works and now take pleasure in introducing them to a younger generation. In collecting the photographs I had the kind assistance of Drs Marie-Helene Schwartz, Joanne Elliot, Milo Keynes and Yu. A. Rozanov, to whom warm thanks are due. A German edition of the book has just been published. I am most grateful to Dr. Herbert Vogt for his careful translation which resulted also in a consid­erable number of improvements on the text of this edition.Preface
Set
Sample sets
Operations with sets
Various relations
Indicator
Exercises
Probability
Examples of probability
Definition and illustrations
Deductions from the axioms
Independent events
Arithmetical density
Exercises
Counting
Fundamental rule
Diverse ways of sampling
Allocation models; binomial coefficients
How to solve it
Exercises
Random Variables
What is a random variable?
How do random variables come about?
Distribution and expectation
Integer-valued random variables
Random variables with densities
General case
Exercises
Borel Fields and General Random Variables
Conditioning and Independence
Examples of conditioning
Basic formulas
Sequential sampling
Pólya's urn scheme
Independence and relevance
Genetical models
Exercises
Mean, Variance and Transforms
Basic properties of expectation
The density case
Multiplication theorem; variance and covariance
Multinomial distribution
Generating function and the like
Exercises
Poisson and Normal Distributions
Models for Poisson distribution
Poisson process
From binomial to normal
Normal distribution
Central limit theorem
Law of large numbers
Exercises
Stirling's Formula and De Moivre-Laplace's Theorem
From Random Walks to Markov Chains
Problems of the wanderer or gambler
Limiting schemes
Transition probabilities
Basic structure of Markov chains
Further developments
Steady state
Winding up (or down?)
Exercises
Martingale
General References
Answers to Problems
Table Values of the standard normal distribution function
Index