 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2003/paper-2/5/b/ii/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

P (X \geq t) = e^{- k t}

for

t \geq 0

. Since

{X \geq 3} \subseteq {X \geq 1}

P (X \geq 3 ∣ X \geq 1) = \frac{e ^{- 3 k}}{e ^{- k}} = e^{- 2 k} .

This is the memoryless property: after surviving the first unit, surviving two additional units has the same probability as it did initially.

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