Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 1 / 28J / b / i

Table of contents
- Solution i

Solution

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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