Probabilities of Death and Survival   27

or lx. ex=J lx+t.dt

0

= the total area under the curve

=the rectangle OL' on the assumption of a uniform distribution of deaths.

10. The expectancy of life at age x is not the period to which (x) has an even chance of living. For example in the English Life Table No. 8 the number living at age 20 is 793,435, and the number living at age 67 is 396,543. Thus (20) has approximately an even chance of living 47 years, but the expectancy of life at age 20 is 44.21 years.

Nor does the expectancy of life indicate the most probable year of death. Because ego = 44.21, we cannot say that (20) is more likely to die between the ages of 64 and 65 than he is to die at any other age. In all life tables there is a maximum value of dx, excluding the infantile ages. For example in the English Life Table No. 8-Males, every life at any age between the age of 2 and the age of 73 is more likely to die between the ages of 73 and 74 than at any other age because dx+„ has its maximum value when x +n =73 for each value of x from x = 2 to x = 73.