Modern monetary systems

Kritische Geschichte der Nationalökonomie und des Socialismus

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Monograph

Identifikator:: 1753210836

URN:: urn:nbn:de:zbw-retromon-128414

Document type:: Monograph

Author:: Nogaro, Bertrand http://d-nb.info/gnd/117039713

Title:: Modern monetary systems

Place of publication:: London

Publisher:: King

Year of publication:: 1927

Scope:: XII, 236 S.

Digitisation:: 2021

Collection:: Economics Books

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Document type:: Monograph

Structure type:: Chapter

Title:: Part III. Monetary theory and its application in practice

Collection:: Economics Books

THEORY OF STATISTICS. Tf, as in Chapter XII. §§ 4 et seq. (¢f. especially § 7), a number of variables are involved, the equations for determining the coefficients will be given by differentiating Sabine, pe Tat Dim my 2,2 with respect to each coefficient in turn and equating the result to zero. This gives the equations of the form there stated. If a constant term be introduced, its “least square” value will be found to be zero, as above. III. THE LAW OF SMALL CHANCES. (Supplementary to Chapter XV.) WE have seen that the normal curve is the limit of the binomial (p +g)" when = is large and neither p nor ¢ very small. The student’s attention will now be directed to the limit reached when either p or ¢ becomes very small, but n is so large that either np or ng remains finite. Let us regard the n trials of the event, for which the chance of success at each trial is p, s made up of m +m’ =n trials; then the probability of having at least m successes in the m +m’ trials is evidently the sum of the m'+1 terms of the expansion of (p+¢)® beginning with p™ But this probability, which we may term P,,, can be expressed in another and more convenient form with the help of the following reasoning. The required result might happen in any one of m+ 1 ways. For instance :— (a) Each of the first mm trials might succeed; the chance of this is p™. (3) The first m 41 trials might give m successes and 1 failure, the latter not to happen on the (m + 1)™ trial (a condition already covered by (a)). But the probability of m successes and 1 failure, the latter at a specified trial, is p™. ¢, and, as the failure might occur in any one of m out of m + 1 trials, the complete probability of (0) is mp™. q. (¢) The first m + 2 trials might give m successes and 2 failures, the (m + 2) trial not to be a failure (so as to avoid a repetition of either of the preceding cases); the probability of this is m(m+1) mn aye In a similar way we find for the contribution of m+ 3 trials, giving m successes and 3 failures, m+ 1) +2) ns 366 oF

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Contents: Essays of Benjamin Franklin

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