10   Life Contingencies

For illustration we shall use the English Life Table No. 8—Males. In this table

to   = 1,000,000 and values of dx and lx follow,

do   =   120,441 =10 X (qo = .120441)

11   =   879,559=10—do=l0Xp0

dl   =   30,115 = 11 X (q1= .034239)

12   =   849,444=11—d1=11Xp1

d2   =   11,353=12X(g2=.013365)

13   =   838,091=12 —d2 =12 Xp2

etc.   etc.   etc.

16=1103—d103= 1103Xp103 11=1104 X (8104 = . 70399)

5 = 1104 — d104 = 1104 X p104

4 =1105 X (g1o5 = .78631) 1 =1105 —d105 =1105 X P105 1=11os X (g1o6 = .85859)

4. Thus l~Xpx=lx+1

lxXgx=dx, since qx is the annual death rate or annual rate of mortality at age x

lx -1x+1=dx

n-1

Ix —lx+n = E dx+r r=0

and   10=do+dl+d2+ . . . to the end of the table.

It—must be clearly understood that no figure in either the lx column or the dx column has any meaning when taken by itself. Each value of 1 is a number of survivors from among a number of persons lx who were alive at an earlier age x. Each value of dx represents the number of deaths between ages x and x+l out of a number 1 living at some previous age. If every value of lx and dx in any life table were to be multiplied by 100 or divided by 10, it would not alter the information given by~that table.

1104

d104 1105 d105 1106 d106