Chung Elementary Probability Theory with Stochastic Processes

Erscheinungsjahr 2013
ISBN: 978-1-4757-3973-2
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 325 Seiten, eBook

Reihe: Undergraduate Texts in Mathematics

In the past half-century the theory of probability has grown from a minor isolated theme into a broad and intensive discipline interacting with many other branches of mathematics. At the same time it is playing a centrat role in the mathematization of various applied sciences such as statistics, Opera tions research, biology, economics and psychology-to name a few to which the prefix "mathematical" has so far been firmly attached. The coming-of-age of probability has been reflected in the change of contents of textbooks on the subject. In the old days most of these books showed a visible split personality torn between the combinatorial games of chance and the so-called "theory of errors" centering in the normal distribution. This period ended with the appearance of Feller's dassie treatise (see [Feiler I]t) in 1950, from the manuscript of which I gave my first substantial course in probability. With the passage of time probability theory and its applications have won a place in the college curriculum as a mathematical discipline essential to many fields of study. The elements of the theory are now given at different Ievels, sometimes even before calculus. The present textbook is intended for a course at about the sophomore Ievel. It presupposes no prior acquaintance with the subject and the first three chapters can be read largely without the benefit of calculus.

Zielgruppe

Research

Autoren/Hrsg.

Chung, K. L.

Inhaltsverzeichnis

1: Set.- 2: Probability.- 3: Counting.- 4: Random Variables.- 5: Conditioning and Independence.- 6: Mean, Variance and Transforms.- 7: Poisson and Normal Distributions.- 8: From Random Walks to Markov Chains.- General References.- Answers to Problems.