 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2006/iii/paper-14/4/b/solution

Codex  0 Created 2026-10-03 Updated 2026-10-14

The factorial-moment argument above gives

Y \Rightarrow Poisson (λ)

with

λ = e^{- c}

. Because

Y

is integer-valued, apply convergence in distribution at the continuity points

3/2

and

5/2

and subtract. This proves

P (Y = 2) ⟶ e^{- e^{- c}} \frac{e ^{- 2 c}}{2} .

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