An Introduction To Probability Theory And Its Applications 2nd Ed Vol 2
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An Introduction to Probability Theory and Its Applications, Volume 1
The nature of probability theory. The sample space. Elements of combinatorial analysis. Fluctuations in coin tossing and random walks. Combination of events. Conditional probability, stochastic independence. The binomial and the Poisson distributions. The Normal approximation to the binomial distribution. Unlimited sequences of Bernoulli trials. Random variables, expectation. Laws of large numbers. Integral valued variables, generating functions. Compound distributions. Branching processes. Recurrent events. Renewal theory. Random walk and ruin problems. Markov chains. Algebraic treatment of finite Markov chains. The simplest time-dependent stochastic processes. Answer to problems. Index.
Probability Theory with Applications
Author: Malempati M. Rao
language: en
Publisher: Springer Science & Business Media
Release Date: 2006-06-03
This book is a revised and expanded edition of a successful graduate and reference text. The material in the book is designed for a standard graduate course on probability theory, including some important applications. This new edition contains a detailed treatment of the core area of probability, and both structural and limit results are presented in full detail. Compared to the first edition, the material and presentation are better highlighted with several (small and large) alterations made to each chapter. Key features of the book include: - Indicating the need for abstract theory even in applications and showing the inadequacy of existing results for certain apparently simple real-world problems - Attempting to deal with the existence problems for various classes of random families that figure in the main results of the subject - Providing a treatment of conditional expectations and of conditional probabilities that is more complete than in other existing textbooks Since this is a textbook, essentially all proofs are given in complete detail (even at the risk of repetition), and some key results are given multiple proofs when each argument has something to contribute.
Introduction to Probability with Statistical Applications
Author: Géza Schay
language: en
Publisher: Springer Science & Business Media
Release Date: 2007-08-15
Introduction to Probability with Statistical Applications targets non-mathematics students, undergraduates and graduates, who do not need an exhaustive treatment of the subject. The presentation is rigorous and contains theorems and proofs, and linear algebra is largely avoided so only a minimal amount of multivariable calculus is needed. The book contains clear definitions, simplified notation and techniques of statistical analysis, which combined with well-chosen examples and exercises, motivate the exposition. Theory and applications are carefully balanced. Throughout the book there are references to more advanced concepts if required.