1 92 Expectation of Moments of Frequency I)istribntio)ts 
we find in consequence : 
- ■ - - n^^' AT ' - 
u 
(1, 4) 
2, {N) ' 
(3) Substituting the values we have found for U^^\^^ in (15) we obtain 
w 
(1) 
2,{N) 
Kim = ((^'- 1) + - 2i\r + 3) 
...(19), 
W 
N~ 1 
(3) X, — i , 
2,w=-~^ {(i^-l)>« + 3(^-l)(i\^-^-2iV^+5)/x4/i2 
- 2 (SN'^ -6N+5) fii + {N-2) (N' - SN'^ + 9N- 15) fi./} 
K20), 
- - 1 /^o - IO/Z32 + 30/./] 
* The value of ~ '^'a.lA^)'*^ ^" Student's paper "The Probable Error of a Mean" (Biometriha, 
Vol. VI, p. 3), but uufortunately misprints have crept into the formula. 
