194 Expectation of MomeiUs of Frequency Distributions 
{N-iy SiN-lfiN-b) 
^ (24), 
1 
+ - 33/^4 /^s - 22/x,2 + 54^/] - [/x, - 15/,i, fi., - 10 fi,- + :JO/i./] 
- --^-^ [4^« - 40/^,; - 54^.r - 9Qfi, fi, + 336/., + 528/./ /., - 306/i,^] 
-iV ^ ( 25 ). 
+ ^ [6/X8 - 96/t„/..2 - 102/i/ - 176/., /., + 924/.4 /t^' + 1232/./ /., - 1044/.^^] 
- [4/,8 - 92/.,; /., - 95/.4= - 160/1, /.„ + IIIO/.4 /I./ + 1400/.;r /t^ - 1515/.,/] 
+ A_ [^^ _ 28/.6 /.., - 35/.4- - 56/.g /., + 42O/.4 /.0-- + 56O/.32 fx, - 630/62"] 
In the case when the law of distribution of values of X follows the Gauss- 
Laplace law : ' ■ 
■10 2(i\^-l) , 
-fi- L " 2, (AO - ^2, (N )]- = /"~2', 
8(i\r-l) 
E[v'2, (iV)~ ^2,(A')]" = 
j.r , 14 12(iV-l)(iV + 3) ^ 
E [V 2, - I'2,(A-)j' = ^y^^ H'-' , 
( CHAPTER IV 
I 
(1) We may also follow another road, to deduce the formulae obtained above, 
a road nearer to the one usual in English literature. 
Let us denote by nj the number of times in N experiments the variable X 
takes the value ^j, one of its k possible values (cf above. Chapter I, § I), and putting 
