An Elementary Introduction to the Theory of Probability

by Boris V. Gnedenko, Aleksandr Yakovlevich Khinchin, Oscar Sheynin (Translator)

This compact volume equips the reader with all the facts and principles essential to a fundamental understanding of the theory of probability. It is an introduction, no more: throughout the book the authors discuss the theory of probability for situations having only a finite number of possibilities, and the mathematics employed is held to the elementary level. But within its purposely restricted range it is extremely thorough, well organized, and absolutely authoritative.

After explaining in simple terms the meaning of the concept of probability and the means by which an event is declared to be in practice, impossible, the authors take up the processes involved in the calculation of probabilities. They survey the rules for addition and multiplication of probabilities, the concept of conditional probability, the formula for total probability, Bayes's formula, Bernoulli's scheme and theorem, the concepts of random variables, insufficiency of the mean value for the characterization of a random variable, methods of measuring the variance of a random variable, theorems on the standard deviation, the Chebyshev inequality, normal laws of distribution, distribution curves, properties of normal distribution curves, and related topics.

The book is unique in that, while there are several high school and college textbooks available on this subject, there is no other popular treatment for the layman that contains quite the same material presented with the same degree of clarity and authenticity. Anyone who desires a fundamental grasp of this increasingly important subject cannot do better than to start with this book.

Genres: Mathematics, Textbooks

96 pages, ebook

First published January 1, 1976

Reviews

[Hibiscus · Rating 3 out of 5]

Премилая книжка, давно валялась в пыли, без шансов на прочтение. Но тут появился я и P выстрелила!

Книга напичкана примерами разных практических применений, хотя все они так или иначе связаны с военным делом или народным хозяйством (выражаясь в духе автора). Понял три четверти, включая Байеса, Бернулли и Чебышёва. С нормальными законами стало труднее, много матжонглирования, под конец Хинчин включил свои собственные наработки по теории случайных процессов, и тут меня вконец заклинило.

Да, и каждый раз улыбало, что перед своими учеными (и только своими) стояли шикарные эпитеты типа великий русский математик Чебышёв, в другом месте он же гениальный математик Чебышёв, выдающийся русский математик А.А. Марков и т.д. Впрочем список действительно впечатляет, гордиться есть чем.

[ilya murychev · Rating 4 out of 5]

Изложение немного сложноватое, но интересные мысли подчерпнуть можно