cxliv Tables for Statisticians and Biometricians [XXVI XXX 



(6) Symmetrical Limited Range frequency curve 



Range : x = a to + a. 



N 

 2a q z a+m 2 ) 



(c) Symmetrical Unlimited Range frequency curve 



Range : x = oo to + oo . 



N 



Our table will therefore provide for the determination of y Q in cases (b) and 

 (c) of W2 = to 51 '5 and of m 3 = to 53. As raj only ranges from to , or n from 

 1 to 2, the table is by no means adequate for interpolating to find y Q for sym- 

 metrical U -curves, and recourse must be had to tables of the complete F-function as 

 indicated in formula (i) above. The best table for this is Legendre's*. 



Illustration seems hardly needful. For fitting any one of these curves /3i should 

 be zero within the limits of random sampling. The constants of the curves are then 

 obtained from a knowledge of a 2 , the squared standard deviation, and /3 2 . 



For case (a): 



_ 3(3-2771!) 



must lie between 1 and T8. 

 For case (6) : 



must lie between 1'8 and 3'0. 



For case (c): 



2 2/0 ox 5/9 2 -9 



a^^(2m 8 -3), if- 3-^^35, and A _ 



must lie between 30 and + oo . 



TABLES XXVII XXX. 



Small Samples taken from an Infinite Bivariate Normal Population. (R. A. 

 Fisher, Biometrika, Vol. X. pp. 510521 ; K. Pearson, Proc. K S. Vol. 112, A, 

 pp. 1 14; Idem, Biometrika, Vol. xvn. pp. 176 199, Vol. xix. pp. 441 442.) 



1. The exact surfaces and curves of distribution of the constants of samples are 

 now known whatever be the size of the sample for the special case when the 

 parent population is a bivariate normal surface. But little progress has been made 

 when the parent population is not normal, or, being normal, is supposed finite. 

 * Tracts for Computers, No. iv. Cambridge University Press. 



