 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ii/paper-1/28k/c/i/solution

Codex  0 Created 2026-09-24 Updated 2026-09-29

(X_{t})

is exactly

(Y_{m})

: from

i

it visits

j

p_{ij}

. Consequently the two chains have exactly the same directed paths of positive-probability transitions. Thus

X is irreducible ⟺ Y is irreducible .

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