An Introduction to the theory of statistics

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Monograph

Identifikator:: 84539584X

URN:: urn:nbn:de:zbw-retromon-36509

Document type:: Monograph

Author:: Koechlin, Armand

Title:: L' Industrie cotonnière en Allemagne

Place of publication:: Paris

Publisher:: Pelletier

Year of publication:: 1906

Scope:: 1 Online-Ressource (387 S)

Collection:: Economics Books

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Document type:: Monograph

Structure type:: Chapter

Title:: Assurances gouvernementales

Collection:: Economics Books

XVIL.—NORMAL CORRELATION. 219 tribution of each of the deviations singly be normal, we must have for the frequency-distribution of pairs of deviations of x; and z,., Vig =Y10 gy 93) A IER xf | 3, a; x; o Ty St = Frag my ni or 031 oi(l—-1}) oy(1 —1},) oyoa(1 — 77) 2 2 Ba 2. PR Rk Ojot-05y 912021 Evidently we would also have arrived at precisely the same expression if we had taken the distribution of frequency for z, and z, ,, and reduced the exponent Oz: Oi» We have, therefore, the general expression for the normal correlation surface for two variables 2 2 x x 2s SC NE. (6) ’ a go, 2 : Yi2= Yat 1.2 21 1.2 21 Further, since #, and ,.,, z, and 7.9, are independent, we must have ie YW h . Y= 27.0100; 27.0000, 2mo, op(1 — ri) - (7) 4. Tf we assign to x, some fixed value, say h, we have the distribution of the array of x,’s of type A, ( = Le op i ) hy ols oh; of 2721 Y12=Yr-e : a1 z ‘2 (= lt) = Vine 3 207 This is a normal distribution of standard-deviation 01.0 With a —r o Tp mean deviating by r,, hy from the mean of the whole distribu- 2 tion of z’s. As A, represents any value whatever of z,, we see (1) that the standard-deviations of all arrays of x, are the same, aki : (v Buu ’ i

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