 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ia/paper-2/12f/iv/solution

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

Here

F_{1} (s) = 1/ (2 - s)

and

μ = 1

, so extinction is certain. Iteration gives

F_{n} (s) = \frac{n - ( n - 1 ) s}{n + 1 - n s},

and

P (X_{n} = 0) = F_{n} (0) = n / (n + 1)

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