200 ESSAY ON PROBABILITIES. 



both die in the same year; also |AB... denotes the 

 value of an annuity on the joint lives to be paid in 

 addition at the end of the year in which the joint 

 existence fails. 



8. When the condition is that a given status shall be 

 in existence at the moment in which another status 

 drops (whether the first last to the end of the year or 



not), single dots are placed over the two : thus A|l B 

 means the present value of II., to be received at the end 

 of the year in which A dies, provided B be alive at that 



moment; while A|lB means the same, provided B be 

 alive when the payment is to be made. 



9. When it is a condition that deaths are to happen 

 in a specified order, it must be represented by writing 

 small figures under the status. Thus, A : B|C means 



i 2 



an annuity on the life of C, to begin at the end 

 of the year in which B dies, provided A have died 



before B ; and A : (BC)|1 denotes the present value of 



I/, payable at the end of the year in which the longest 

 of the two status A and BC drops, provided that the 

 status BC is determined by the death of B. 



10. When the joint existence of one number of lives, 

 out of a larger number, is a condition, a figure may be 

 annexed as follows : ( A B C D) indicates a status which 

 exists as long as any two out of the four are alive. 



1 ] . The double sign || indicates the premium which 

 is to be paid during the continuance of the status on 

 the left, in consideration of the deferred benefit described 

 on the right ; premium being always interpreted as an 

 annuity due. And where a specific event, as distin- 

 guished from the duration of a status, is a condition, the 

 premium is to be held payable as long as any status exists 

 out of which that event may happen. Thus A : B||C 



1 2 



denotes the premium which should be paid as long as 

 A lives with B, or B after A, to secure an annuity to 

 C when both are dead, provided A die first. 



