Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2011 / Paper 1 / 12 / f / Solution

Use the lower limit $s=t+r_0$ for the inner integral:HenceThe prefactor is the probability that interruption occurs; the remaining exponential is its conditional positive tail. This is the positive difference of independent exponential waiting times. The exponent is dimensionless because both $r_0$ and $\bar{s}$ are measured in minutes.