394 Mr. L. Isserlis : : Application of Solid Hyper geometrical 



§11. Numerical Example 1. 



As a first numerical example we will take the following 

 table : — 









4 



3 







18 



36 



9 





12 



54 



36 



3 



1 



12 



18 



4 





This table is the theoretical frequency distribution of black 

 balls in a draw of 4 balls followed by one of 3 out of a bag 

 containing 4 white and 6 black balls, the draw being repeated 

 210 times. 



Taking moments about (0, 0) we find 



p' i0 = 56-1143, 

 A = 21-8, 



y i0 = 2-4, p' 20 =6-4, ^30 = 18-4, 

 /oi = l'8, //o2=3-8, p' 03 = S-8, 



*'ii=4 p' 2 i=io, y 12 =s. 



Transferring to the mean at 2'4, 1*8 we find 



i> 20 ='64, i > 30 =--032, ^ 4 o=l-1254857 ? 



^ 02 = *56, ^ 03= _.()56, p 04 =-8192, 



^ n =--32, ^ 21 =-016, j9 12 =-032. 

 Whence we obtain 

 . ^=--5345, ft = -00390625, #/ = -01785714, 



/3 2 = 2'747768, &/ = 2-6122449. 

 The formulae of §10 give 



\ = 2-138, ? = 1'5, ^ = 2-3333, y=J; 

 so that, if we use 



n = 6 



we find 



7 (/3 1 '-/3 2 ' + l)-(&-/3 2 + l) 

 7(3A'-2/3 2 / + 6)-(3A-2/3 2 + 6) ? 



16-741074 



1-674106 



10. 



