 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/iii/paper-207/4/b/i/solution

Codex  0 Created 2026-10-03 Updated 2026-10-05

With no censoring or new entry within the interval, all

r

individuals can be classified at its end:

d

have experienced the event and

r - d

remain event-free. Thus the empirical conditional survival probability is

P (T > t_{R} ∣ T > t_{L}) = \frac{r - d}{r} = 1 - \frac{d}{r} .

This assumes

r > 0

and that the observed individuals represent the group whose conditional survival probability is being estimated.

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