Al. a. Tchouproff 
291 
(2) Putting 
j = 0 1 = 1 
we find 
E[^'\r, iv] - ^[,., iv]]-^- = 1.3.5... (2m - 1) (<p^,, ^j} 
+ 
1 
+ 
(11). 
E [^'V, A-] - Z^,, ^]]--+^ = 1.3.-5... (2m + 1) |^ im (.^f, .v])™"^ <i>v^, .v] 
1 
(^[2, iV])'" ' ^[5, iV] + tV"^' (0[2, A'])'" ' N] 0[4, A'] 
1 s 
' (12). 
1 i!^ , . \ / 1 
Hence 
+ ... 
/i = 2 
/-(ft (0 ^ ri-i ri"~-i I'' <' 
^2. ^. + 1 - .-. 
r(./ ('■) ('■) 
+ (m/ - /«[i,iv])'" 
+ (m -m[,,jv])' 
— 2u — Z t V u u. 
1+J 
/i=i 
When r = 2, we find 
^2r t^r~h- 2 C,. C_ /X, 
y u. a . . 
^ (13). 
(14). 
In the case for which all the variates are distributed according to the Gauss- 
Laplace law, 
'^V'c.^. ^] = I .5^ (/^•^"'' t'^^" + 2 - "Hi- ^])'])} (15)- 
