 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ib/paper-2/18h/b/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

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.

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