An Elementary Introduction to the Theory of Probability

Front Cover

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. It is the only English translation of the latest revised Russian edition; and it is the only current translation on the market that has been checked and approved by Gnedenko himself.
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. New preface for Dover edition by B. V. Gnedenko.

 

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Contents

THE PROBABILITY OF AN Event
3
RULE FOR THE ADDITION OF PROBABILITIES
11
CONDITIONAL PROBABILITIES AND THE MULTIPLICA
18
CONSEQUENCES OF THE ADDITION AND MULTIPLICA
27
BERNOULLIs schEME
38
BERNOULLIs THEOREM
49
RANDOM variaBLES AND DISTRIBUTION LAws
59
MEAN VALUES
65
MEAN VALUE OF A SUM AND OF A PRODUCT
74
DISPERSION AND MEAN DEVIATIONS
80
LAW OF LARGE NUMBERS
93
NoRMAL LAws
100
CONCLUSION
118
BIBLIOGRAPHY
125
Copyright

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