Das Kapital: Der Produktionsprozeß des Kapitals

Der Produktionsprozeß des Kapitals (1.1928)

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Multivolume work

Identifikator:: 1780159447

Document type:: Multivolume work

Author:: Marx, Karl http://d-nb.info/gnd/118578537

Title:: Das Kapital

Place of publication:: Berlin

Publisher:: J. H. W. Dietz Nachf., G. m. b. H.

Year of publication:: 1926-

Collection:: Economics Books

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Volume

Identifikator:: 1780159595

URN:: urn:nbn:de:zbw-retromon-188277

Document type:: Volume

Author:: Marx, Karl http://d-nb.info/gnd/118578537

Title:: Der Produktionsprozeß des Kapitals

Volume count:: 1.1928

Place of publication:: Berlin

Publisher:: J. H. W. Dietz Nachf., G. m. b. H.

Year of publication:: 1928

Scope:: XLVIII, 768 Seiten

Digitisation:: 2022

Collection:: Economics Books

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Document type:: Multivolume work

Structure type:: Chapter

Title:: Erster Abschnitt. Ware und Geld

Collection:: Economics Books

SUPPLEMENTS—THE LAW OF SMALL CHANCES. 729 The frequent rediscovery of this theorem is due to the fact that its value is felt in the study of problems involving small, inde- pendent probabilities. For instance, if we desired to find the distribution of = things in IV pigeon-holes (all the pigeon-holes being of equal size and equally accessible), I being large, the dis- tribution given by the binomial 1, ¥-1} 7+) FTF would be effectively represented by (8), tables of which for different values of A have been published by v. Bortkewitsch and others. The theorem has also been applied to cases in which, although the actual value of ¢ (or p) is unknown, it may safely be assumed to be very small. It should be noticed that, if (8) is the real law of distribution, certain relations must obtain between the con- stants of the statistics (see par. 12, Chapter XIIL). Using the method of par. 6, Chapter XV., we have for the mean 23 eM A +A+ 2 pF ed 2! 2 : =re A(1+A+ 2+ eta ud 21 =A and for o? 3 eA(A+200 +30 ‘on ) - AZ . AZ A A 222 3A g =e SYRER EL. LY pe (A +2020 ceee)=A 2 =A+e-M(1 Xe 2 piri x 2! =A+A2-A2 = A. Hence any statistics produced by causes conforming to Poisson’s limit should, within the limits of sampling, have the mean equal to the square of the standard deviation. For instance, in the statistics used in par. 12 of Chapter XIII, the mean is ‘61, a="78, ¢2="6079, 2% 24

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