Introduction to Probability Theory

by Paul Gerhard Hoel, Sidney C. Port, Charles J. Stone

Brand New. Will be shipped from US.

Genres: Mathematics, Textbooks

258 pages, Hardcover

First published June 30, 1971

Reviews

[Mark Mitchell · Rating 4 out of 5]

I needed a firmer mathematical foundation for some work on financial models, so I went back to Introduction to Probability Theory, which I bought for a long-ago college course. I worked through the text and accompanying problems and now have a much better understanding of the topics covered than I did as a college student.

The book covers both discrete and continuous random variables. The authors describe specific distributions (binomial distributions, Poisson distributions, normal distributions, gamma distributions, etc.) and provide examples illustrating situations where these distributions can arise. Of course, the book also covers the general theory of probability spaces, independence, expectation, higher-order moments, densities, conditional probability, and characteristic functions. The main body of the book builds to proofs of the Weak Law of Large Numbers and the Central Limit Theorem. The final chapter introduces random walks and Poisson processes.

The back of the book has the answers to those problems that require calculations. The answers provided are only the final result, not complete step-by-step solutions. There are no solutions to those problems that require proof. The answers made it easy for me to check my work, or, in some cases, obtain a hint. Without the answers, I would have had much less confidence that my solutions were correct.

A prospective reader should have familiarity with both differential and integral calculus and related concepts such as Taylor series. The reader needs a grasp of basic set theory, basic trigonometry, and sums of power series. Although there are certainly newer textbooks, the theorems in the book are as true now as they were when the book was first published in 1971, and the book will serve a current student of probability as well as it did its first readers nearly 50 years ago.

[Vaidas Juknevičius · Rating 5 out of 5]

First of the three volumes. A compact and accessible introduction to probability. This volume, and the other two (statistics and stochastic processes), together provide a strong undergrad level basis and everything a practitioner in an applied field needs to use at work or to be able to profitably read the more specialized literature.
Plenty exercises and problems after each chapter. Solving them pays off!!!

[Santaraksita · Rating 4 out of 5]

An introductory, non-measure theoretic probability textbook more succint than War & Peace and written for adults.