 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ii/paper-1/28j/b/i/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Put

s = λ + μ

. Solving either Kolmogorov equation gives

P (t) = \frac{1}{s} (λ + μ e^{- s t} λ (1 - e^{- s t}) μ (1 - e^{- s t}) μ + λ e^{- s t}) .

These entries have the correct initial values and their rows sum to one.

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