Therefore, the response time probability is the life expectation conditioned on \(t_{in}\) when \(t=t_{in}\). Once having all the response pdf, for all the \(t_{in}\), They can reconstruct the overall life expectancy probability, applying the definitions. 
They remarks that the response time  pdf is actually more general that the life expectancy, because having it, it is possible to get all the conditional life expectancies, just properly normalizing, for any time \(t,\) the future age-ranked discharges. When in possess of all the response functions, for all \(t_{in}\), is finally possible to get the unrestricted life expectancy.