Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 207 / 6 / a / vi

Table of contents
- Solution vi

Solution

Measure time in years after age 70. Residence in the care home begins at time 3, so inclusion is conditional on

T > 3

: this is left truncation, also called delayed entry. Exact death at time 13 contributes

P (T = 13 ∣ T > 3) = \frac{F ( 13 ) - F ( 1 3 ^{-} )}{S ( 3 )} = \frac{S ( 1 3 ^{-} ) - S ( 13 )}{S ( 3 )} .

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