Hello, Related to the central rate of mortality presented in chapter 7 of the ActEd course notes, I do not understand why its denominator (integral from 0 to 1 from tpx dt) is smaller or equal to 1. Can somebody help me with an answer? Many thanks.
tpx is a survival probability, so it must be <=1. Integrating a function over the interval 0 to 1 gives the average value of that function over the interval (0,1). (Integrating from 0 to n and then dividing by n gives the average value over the interval (0,n) and here we're setting n=1.) So the average value of tpx over the interval t=0 to t=1 must be <=1.
