Kommentar zum Gesetz über eine Kriegsabgabe von Vermögenszuwachs und zum Gesetz über eine außerordentliche Kriegsabgabe für das Rechnungsjahr 1919 vom 10. September 1919

An Introduction to the theory of statistics

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Monograph

Identifikator:: 1016238525

URN:: urn:nbn:de:zbw-retromon-55274

Document type:: Monograph

Title:: Kommentar zum Gesetz über eine Kriegsabgabe von Vermögenszuwachs und zum Gesetz über eine außerordentliche Kriegsabgabe für das Rechnungsjahr 1919 vom 10. September 1919

Place of publication:: Berlin

Publisher:: Verlag von Otto Liebmann

Year of publication:: 1920

Scope:: 1 Online-Ressource (XXIII, 548 Seiten)

Collection:: Economics Books

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20° THEORY OF STATISTICS. binomial distributions. It will have been noted that any one term—say the 7th—in one series is obtained by taking ¢ times the rth term together with p times the (r—1)th term of the preceding series. Now if AP, CR (figure 46) be two verticals, and a third, BQ), be erected between them, cutting PR in , so that AB :BC :q:p, then BQ=p.AP + q.CR. (This follows at once on joining AR and considering the two segments into which BQ is divided.) Consider then some binomial, say for the case p=1, g=2. Draw a series of verticals (the heavy verticals of fig. 47) at any convenient distance apart on Bpc Fre. 46. on a horizontal base line, and erect other verticals (the lighter verticals) dividing the distance between them in the ratio of q:p, viz. 3:1. Next, choosing a vertical scale, draw the binomial polygon for the simplest case n=1; in the diagram XN has been taken = 4096, and the polygon is abed, 0b = 3072, 1lc=1024, The polygons for higher values of » may now be constructed graphi- cally. Mark the points where ab, bc, cd respectively cut the intermediate verticals and project them horizontally to the right on to the thick verticals. This gives the polygon ad'c’d’e for n=2. Forob =gq.0b, 1c'=p.0b+q.1c, and so on. Similarly, if the points where a®’, b'c, etc.,, cut the intermediate verticals are projected horizontally on to the thick verticals, we have the polygon ab”¢"d"¢"f” for n=38. The process may be continued 96

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