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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2007/ii/paper-4/26j/a/solution

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Past exam of the mathematics course of the University of Cambridge / 2007 / ii / Paper 4 / 26J / a / Solution by

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

The nonzero off-diagonal rates are

(c, r, b) \to (c + 1, r, b) : λ, (c, r, b) \to (c - 1, r + 1, b) : μ c,

(1)

(c, r, b) \to (c, r - 1, b + 1) : μ r, (c, r, b) \to (c, r, b - 1) : μ b,

(2)

with a transition involving a negative coordinate omitted. These represent arrival, the two metamorphoses, and death. The diagonal generator entry is consequently $- (λ + μ (c + r + b))$ , so the holding rate is

λ + μ n

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