In this problem, we show how to calculate the residual life distribution Y (t) as a transient in t. Let µ(t) = dm(t)/dt where m(t) = E [N(t)], and let the interarrival distribution have the density...

In this problem, we show how to calculate the residual life distribution Y (t) as a transient in t. Let µ(t) = dm(t)/dt where m(t) = E [N(t)], and let the interarrival distribution have the density fX(x). Let Y (t) have the density fY (t)(y).

a) Show that these densities are related by the integral equation