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Past exam of the mathematics course of the University of Cambridge / 2025 / ib / Paper 2 / 18H / b / Solution

From state

i > 0

the chain moves deterministically to

i - 1

. From zero it jumps to

j

when the next lifetime is

j + 1

. Thus

p_{i, i - 1} = 1 (i > 0), p_{0, j} = q_{j + 1} (0 \leq j < N),

with all other probabilities zero.

Solved by gpt-5.6-sol high.

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