Régime des chambres de commerce

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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

Usage license:: Get license information via the feedback formular.

THEORY OF STATISTICS. within the bracket give us the proportional frequencies of 0, 1, 2, etc. failures. In other words, (8) is the limit of the binomial (p+ ¢)* when ¢ is very small but ng finite. The investigation contained in the preceding paragraphs was published in 1837 by Poisson, so that (8) may be termed Poisson’s limit to the binomial ; but the result has been reached indepen- dently by several writers since Poisson’s time, and we shall give one of the methods of proof adopted by modern statisticians, which the student may perhaps find easier to follow than that of Poisson (see ref. 19, p. 273). x 2 (par =(-g+oy=Q-gp(1+ 2). © The first bracket on the right is equal to e=* when ¢ is inde- finitely small. Expanding the second bracket, we have A/A Ag oe E 1) 7 \ 143.00 00 JSF. HET ar (Z x The ratio of the (r+ 1)™ to the 7 term is 2 Rl gt + (9a) 1-9 2 which reduces to 2 when ¢ is very small. The convergence of gq the series is seen from the fact that » cannot exceed > and the substitution of this value in (9a) reduces it to g? (1-g\ which vanishes with gq. Hence the second bracket on the right of (9) may be written X23 y (1 + A+ Tit Tide and (9) is ; AZ As e (T+d4g ++ o (was identical with (8). 268

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