 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ia/paper-2/12f/iv/solution

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

N = 0

, then

∣ N - E N ∣ = E N

P (N = 0) \leq P (∣ N - E N ∣ \geq E N) \leq \frac{var ( N )}{( E N ) ^{2}} .

The assumed limit therefore proves

P (N = 0) ⟶ 0 .

This is the second moment method in its simplest form.

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