Essays of Benjamin Franklin

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Monograph

Identifikator:: 1752429486

URN:: urn:nbn:de:zbw-retromon-127700

Document type:: Monograph

Author:: Franklin, Benjamin http://d-nb.info/gnd/118534912

Title:: Essays of Benjamin Franklin

Place of publication:: New York

Publisher:: G. P. Putnam's Sons

Year of publication:: 1927

Scope:: xi, 273 Seiten

Digitisation:: 2021

Collection:: Economics Books

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Document type:: Monograph

Structure type:: Chapter

Title:: XIX. Sketch of proposition for a peace

Collection:: Economics Books

XV.—BINOMIAL DISTRIBUTION AND NORMAL CURVE. 301 unnecessary detail: as a matter of practice, we would not have comp ‘ed a frequency-distribution by single male births, but would certainly have grouped our observations, taking probably 10 births as the class-interval. We want, therefore, to replace the binomial series by some continuous curve, having approximately the same ordinates, the curve being such that the area between any two ordinates 7, and y, will give the frequency of observations between the corresponding values of the variable x, and z,. 9. It is possible to find such a continuous limit to the binomial series for any values of p and ¢, but in the present work we will confine ourselves to the simplest case in which p = q¢=05, and the binomial is symmetrical. The terms of the series are od n(n-1) n(n-1)(n-2) NE) 1 1b 5 Ag + —t i +....% The frequency of m successes is £2 N(3) [m|n—m and the frequency of m+ 1 successes is derived from this by multiplying it by (n-m)/(m+1). The latter frequency is therefore greater than the former so long as n—m>m+1 n-1 mM THT Suppose, for simplicity, that = is even, say equal to 2%; then the frequency of % successes is the greatest, and its value is 12 2 %=N@) kk (1) The polygon tails off symmetrically on either side of this greatest ordinate. Consider the frequency of + x successes ; the value is =NG 2k. | 24 9 = eh 123) and therefore veo BDE-DE=2) .... (i=2+1) Yo (k + 1)(% + 2)(k + 3) EN CE) 1 2 3 xz-1 Joi. 300). ufr-%0 . = +3) 2) 3 ry EY ! (143 1+72\1+7) . (1+ (143) or od

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