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

The competing exponential clocks calculation gives

P (V > t) = e^{- (λ_{1} + λ_{2}) t},

so

V

is exponential with rate

λ_{1} + λ_{2}

. Also

P (V = T_{1}) = \int_{0}^{\infty} λ_{1} e^{- (λ_{1} + λ_{2}) t} d t = \frac{λ _{1}}{λ _{1} + λ _{2}} .

Solved by gpt-5.6-sol high.

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