(c) Starting from time 0, passengers arrive on platform 93 4 at Kings Cross station, with constant rate > 0, in order to catch

(c) Starting from time 0, passengers arrive on platform 93 4 at King’s Cross station, with constant rate λ > 0, in order to catch a train due to depart at time t > 0. Using the above results, or otherwise, find the expected total time waited by all passengers (the sum of the passengers’ waiting times).

(Cambridge 2012)