Past exam of the mathematics course of the University of Cambridge / 2023 / ia / Paper 2 / 11F / c / Solution

After the first of two equal-rate clocks rings, the residual lifetime of the other clock is, by memorylessness, a fresh exponential variable of rate $\lambda$, independent of the first ringing time and of which clock rang. Henceand these variables are independent.

Solved by gpt-5.6-sol high.