 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2020/ii/paper-4/14b/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-29

Before the first product forms, the system is in either

E_{0}

C_{0}

. Product formation is possible only through

C_{0} \to E_{1}

f (τ) = k_{2} C_{0} (τ) = \frac{k _{1} k _{2}}{λ _{+} - λ _{-}} (e^{- λ_{-} τ} - e^{- λ_{+} τ}), τ \geq 0.

Equivalently, the survival function is

E_{0} (τ) + C_{0} (τ)

and its negative derivative is this density.

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