Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 207 / 5 / c / i

Table of contents
- Solution i

Solution

Since

T_{i}

has cumulative hazard function

ϕ_{i} H_{0} (t)

,

P {H_{0} (T_{i}) > u} = P {T_{i} > H_{0}^{- 1} (u)} = e^{- ϕ_{i} u} .

Thus the cumulative-hazard time change

U_{i} = H_{0} (T_{i})

has an exponential distribution of rate

ϕ_{i}

.

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