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

Take $s$ on the horizontal axis and $t$ on the vertical axis, both nonnegative. There is no interruption when the noise occurs after the scheduled ending, namely $t>s$. This is the part of the first quadrant above the diagonal $t=s$. Equality has probability zero, so assigning the boundary either way does not affect the calculation.

The same original diagram below also marks the region used in part (e); its lower boundary offset is an illustrative positive choice of $r_0$.