 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ib/paper-2/18h/a/ii/solution

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

The renewal-reward form of Kac's lemma says that the expected number of visits to state

i

during one return cycle from

k

k

\frac{π _{i}}{π _{k}} .

Here time spent means the number of discrete time instants at which the chain occupies

i

between consecutive visits to

k

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