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Mr. Fisher has requested that an introduction be written to this, the second edition of his work on probabilities, which shall indicate some of the practical applications of the mathematical theory with which his treatise deals. The writer has only a limited knowledge of mathematical technique yet it has so happened that in twenty-five years of active work as engineer, statistician and executive he has had frequent occasion to call upon the skill of trained mathematicians for the solution of practical problems involving frequency curves and probabilities. A mong such mathematicians none has been more helpful, or quicker to perceive the possibility of making valuable applications of higher mathematics to business problems ,than Mr. Fisher himself. For this reason it is a duty as well as a privilege to outline, at his request, certain actual practical experiences with mathematical applications and to indicate such possible applications for the future. The writers initial experience with frequency curves and probabilities was in the years 1902 and 1903, when it became evident, in analyzing various problems in telephone traffic, that certainpeak loads, which were superimposed upon the normal seasonal, weekly, and daily fluctuations, could be accounted for only by the laws of chance. Recourse was, therefore, had to the formulae then available for approximate summations of the terms of the binomial expansion, and from these a series of curves was drawn which indicated for any given normal hourly traffic (as indicated by studies of seasonal, weekly, and daily variations) the probability that any given short period load would be equalled or exceeded.. Practical experience with these curves soon showed that, in spite of minor errors, they were close enough to the real facts to make them of primary importance in traffic studies of all kinds, and particularly in the de
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