 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ia/paper-2/11f/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

P (V > t) = e^{- (λ_{1} + λ_{2}) t},

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}} .

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