The Life Table   15 µ.x=861 x; Lx=k(85z—x); Tx=- (86—x)2.

.x(x—1)   x(x—1)

Under (ii) lx = kaxr z ; dx = kaxr   (1—arx) ;

2x -1

= —log a—   2    log r.

Under (iii) lx would take the form ksxg`Y, where

A = —log s and B= —log g . log c,

so that ,px =s`g`x(`t—1)

11. Consider the curve y=1.,, where the unit of length along the x-axis represents a year of life and a smaller unit of length along the y-axis represents one life, so that yo=lo.

Y

   Ni   iM

In this curve, PN represents lx QM represents 1x+1

so that   (PN—QM) represents dx.

Lx = f0td1 lx+= the area under the curve between PN and QM,

which represents the number living in a stationary population between the ages of x and x+l, or the life-time in years to be enjoyed between these ages by lx persons.