A complete guide to the theory and practical applications of probability theory
An Introduction to Probability Theory and Its Applications uniquely blends a comprehensive overview of probability theory with the real-world application of that theory. Beginning with the background and very nature of probability theory, the book then proceeds through sample spaces, combinatorial analysis, fluctuations in coin tossing and random walks, the combination of events, types of distributions, Markov chains, stochastic processes, and more. The book's comprehensive approach provides a complete view of theory along with enlightening examples along the way.
This is the book we called Feller Volume II in graduate school. We used it to sharpen our intuition about probability. Feller was a master at explaining difficult things in simple ways. This includes the waiting time paradox and Benford's laws. For structure and rigor we looked elsewhere, Chung and/or Neveu. But Feller's books brought a joy and love for the subject. No statistician or probabilist should be without a copy on...
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I used volume I in my class in probability at CALTECH in 1980/81. While never sacrificing rigor, Prof. Feller had the rare gift of explaining difficult things is such away, that they would become not only mathematically clear, but also intuitively obvious. I consider this book one of the best math books available!
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This book is one of the tomes of probability theory. The material covered is not for the faint of heart though. The text explains things as do most graduate level math texts, in proofs and theory.
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