Al. a. Tchouproff 
When ?• = 1, we have the identities, 
'^'i,(Af) = 0 and i/^ (^r) = 0. 
1 ^ 
293 
Noting that 
and putting 
we find 
X/ - Z„v) = [X/ - ml'^] + [>n['\- m^,, ni]-~X [X/ - 
iV ^- = 1 
1 
1 r <-ir 
iV ( = 1 j, = o /t=0 ' " 
1 (0 1 ^ -■> 
41 
N-1 
(') 
L'«i - W[l,.V]rM,_^_;,/ii,,(^-l)/i 
r 1,— > r <'■) n 
0 = 2 
,— !i--2 
'N-1] 
r 
1 ^ 
Hence, noting that 
Z^!'^ + S (- 1 )f CV /A^.'! /i^, + (- !)'• ya,, (,v-l)// 
;--2 
V 0) ^ 1 (0 
2 - Tat- — TY2 /"'[a. ^1 ~ /"at — i T2 /^s , 
1 
we find* 
vr, (N) = ^ .2 [m/ - m^i, .V]]'- + CV 2^ .2 - 
1 
+ 2V/ (r-/i)i 2 [mf'- mLj.^]P 
• 1 0) (,■> 1) 
+ 
2 /^P.^]^>-2-A-^^_A 
(!)• 
Cf. Biometrika, Vol. xii, p. 186, equation (6). 
Biometrika xiii 
19 
