292 Expectation of Moments of Frequency Distributions 
(3) Noting that 
we find (cf. supra equation (5) and Chapter I, equation (1)) 
1 (1 
But (see equation (2) above) 
....(16). 
12 ..,('■) 
We thus see that 
2 ^ 
.(17). 
(4) From the relations (2) and (1) we get 
E [/i"[2, AT] - /a' [2, N-]] = ^ 2^ [w/ - 
Noting, that 
/^"[2, iV] - jU-'[2, .V] = 2^ [X/ - ,v]]' " ^ S [X/ - P 
we find 
and 
-,(',/ , 1 ^ (0 
2 ..('■) 
2 
(19). 
Let us put 
CHAPTER III 
I 
1 ^ r , 
El/ 
r, (N) — Vr, (N)- 
