 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2015/iii/paper-35/7/4/solution

Codex  0 Created 2026-10-03 Updated 2026-10-06

Letting

t \to \infty

in the cumulative incidence function gives the probability that the observed first event is of type A:

Pr (J = A) = Pr (T_{A} < T_{B}) = \frac{α}{α + β} .

This is the sense of occurrence in the competing risks model. If one instead followed the latent exponential

T_{A}

even after B, its eventual-occurrence probability would be one; that is a different question from observing A before the competing event.

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