The Life Table   11 5. The probability that a life aged x will be living n years hence

is lx+n. This is written npx. It is also the probability that a life Ix

aged x will die sometime after attaining age x+n and hence is equal tot [dx+n+dx+n+1+dx+n+2 • • • to the end of the table].

The probability that a life aged x will be dead n years hence is

dx+dx+1+ .. +dx+n—1 _ lx—lx+n =1—npx•
   lx   lx

The probability that a life aged x will die in the nth year

from now is dx+n-1 = lx+n—1 —lx+n _ —n—lpx—npx•

lx   lx

f~1S0   ,/~   lx+n+m _ lx+n lx+n+m —   ,/,

   n+mpx =   —npx mPx+n

,/,   lx   lx   lx +n

And npx=px'px+1 Px+2    Px+n—1•

The probability that a life aged x will die in the (n+1)th year from now may be written as follows:

   dx+n   lx+n —lx+n+1 _

   qx—   =npx'gx+n=    —npx—n+1px•

lx   lx

The symbol qx which is the annual rate of mortality at age x refers to the one year of life from age x to age x+1. The expression nqx has no meaning.

nQx or Qx nl stands for the probability that a life aged x will die within the next n years and is equal to 1—npx.

n I`Cx or Qx stands for the probability that a period of at least n years will elapse before a life aged x will fail, or that a life aged x will not die within the next n years, i.e., will survive the next n years, and is therefore equal to npx.

1 mQx stands for the probability that a life aged x will live n years but will die before attaining age x+n+m.

lx+n —lx+n+m

n In x =npx ' mQx+n =   l   = npx —n+mpx•