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2014 Reprint of 1963 Second Edition. Full facsimile of the original edition. Not reproduced with Optical Recognition Software. Gnedenko was a Soviet mathematician and a student of Kolmogorov. He is perhaps best known for his work with Kolmogorov, and his contributions to the study of probability theory, such as the Fisher-Tippett-Gnedenko theorem. He was a leading member of the Russian school of probability theory and statistics. He also worked on applications of statistics to reliability and quality control in manufacturing. This is perhaps Gnedenko's most famous book and first appeared in Russian in 1950. Written in a clear and concise manner, the book was very successful in providing a first introduction to probability and statistics.