CHAP. XIX.] OF STATISTICAL CONDITIONS. 319 



Let us, as another example, suppose 



= Or W = X l (1 - # 2 ) . . (1 - X n ) . . + X n (1 - X^ . . (1 - #n-i). 



This is equivalent to requiring the probability, that of the events 

 # 1} # 2 , . . x n one, and only one, will happen. The value of w will 

 obviously be 



W = S l (l-S 2 )..(l-S n )..+ S n (l-S l )..(l-S n _ l ) + -(l-S l )..(l-Sn), 



from which we should have 



Prob. [X, (1 - X,) . . (1 - X n } . . + X n (1 - X,) . . (1 - X^,)} 

 S l (1 - g 2 ) . . (1 - 8 n ) . . + S n (1 -*!)..(!- S n -i) 



This solution serves well to illustrate the remarks made in the 

 introductory chapter (I. 16) The essential difficulties of the 

 problem are founded in the nature of its data and not in that of 

 its qua3sita. The central equation by which A is determined, and 

 the peculiar discussions connected therewith, are equally perti- 

 nent to every form which that problem can be made to assume, 

 by varying the interpretation of the arbitrary elements in its 

 original statement. 



