 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ia/paper-2/11f/a/solution

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

Shift the absorbing interval to

{0, \dots, a + 1}

and start at

1

. The gambler’s-ruin harmonic functions give

P (τ_{a} < τ_{- 1}) = 1/ (a + 1)

and

E T = 1 (a + 1 - 1) = a

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