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

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- Solution 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

λ

, independent of the first ringing time and of which clock rang. Hence

V \sim Exp (2 λ), W - V \sim Exp (λ),

and these variables are independent.

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