Past exam of the mathematics course of the University of Cambridge / 2018 / iii / Paper 207 / 4 / a

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- Solution a

Solution

The survivor function of a nonnegative event time is

F (t) = P (T > t) = \int_{t}^{\infty} f_{T} (u) d u .

Here the paper uses

F

for the survival function, rather than for the cumulative distribution function; the latter is

1 - F (t)

for a continuous distribution. The survivor function is nonincreasing, starts at 1 when there is no atom at zero, and tends to zero for an almost surely finite event time.

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