 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2007/ii/paper-3/25j/e/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

j

th component gives

p_{ij} (t) = \frac{r _{j}}{R} (1 - e^{- Rt}) + e^{- Rt} 1_{{i = j}} .

The chain has the interpretation of a rate-

R

Poisson clock which independently redraws a colour from

π

, allowing a redraw of the same colour. No redraw by time

t

e^{- Rt}

and retains the initial state; at least one redraw gives distribution

π

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