Der österreichische Exporteur

Bibliographic data

Monograph

Identifikator:: 1758074884

URN:: urn:nbn:de:zbw-retromon-135614

Document type:: Monograph

Title:: Der österreichische Exporteur

Edition:: [2. Aufl]

Place of publication:: Wien

Publisher:: [Kammer für Handel, Gewerbe und Industrie]

Year of publication:: 1927

Scope:: 240 S.

Digitisation:: 2021

Collection:: Economics Books

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

Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: Abkürzungen - Abbreviations - Abréviations - Abreviaturas

Collection:: Economics Books

SUPPLEMENTS—THE LAW OF SMALL CHANCES. Ultimately we reach 2, =| 1 +mg +741 Dee. arti... tn ypu'=1) = Gus 02 z ed 247) This expression is of course equivalent to the first m'+ 1 terms of the binomial expansion beginning with p™, as the student can verify. For instance, if m =n — 2, so that m' = 2, we have 7d #la-2g +2221 0s - ge] = pn-2 2 n-2 n(n—1) n-2,2 =p" (1=q)* + np (1-9) + =r 7. 2 =p" + nph-lq %s 2: L) Let us now suppose that ¢ is very small, so that > = ratio of n failures to total trials is also very small. Let us also suppose that n is so large that ng =A is finite. Writing ¢ — A and putting n m=mn—m', (T) becomes A\ A= \2 3 Am (1-2) (1-3) erat oy . 2 since Z* and smaller fractions can be neglected. n But ( 1- Ay is shown in books on algebra to be equal to e-A, n where e is the base of the natural logarithms, when = is infinite and, under similar conditions, (1-2-1 n Hence, if n be large and ¢ small, we have x2 ing Am =e=N Pp=e (tere 342+ a =) J Ss If we put m'=0, we have the chance that the event succeeds every time, and (8) reduces to e-A. Put m'=1, and we get the chance that the event shall not fail more than once, e=A(1 + A), 80 that e-*,X is the chance of exactly one failure, and the terms 367

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