16   Life Contingencies

Tx =J lx+tdt = the area under the curve and to the right of

0

PN, which represents the number living in a stationary population aged x and upwards, or the life-time in years to be enjoyed after age x by lx persons.

To=the total area under the curve, which represents the total number living in the stationary population, or the total life-time after birth of the lo persons born in any given year.

Therefore, Tx is the average future life time of a man aged x.

lx

12. Consider the curve, y=qx, where the unit of length along the x-axis represents one life year, but the length of on the Y axis represents unity, so that any shorter length must be a proper fraction and can represent the probability of death within one year.

Y'

AI

L

N

i

X

In this curve, yo=qo =0A x =ON qx =PN

and   px =P'P=1-qx.

13. Again, consider the curve y =dx =lxgx, where the unit of length along the x-axis represents a year and a smaller unit of length along the y-axis represents one death.