 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2010/ii/paper-3/26i/b/solution

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

T

with mean

m

m^{- 1} \int_{t}^{\infty} P (T > s) d s

. For C, and also the common long-run B/C renewal structure,

m = 2/ r

and the Erlang survivor give

P (D_{eq} > t) = e^{- r t} (1 + \frac{r t}{2}), f_{D_{eq}} (t) = \frac{r}{2} e^{- r t} (1 + r t) .

For A the exponential law is already its own equilibrium delay.

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