 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2015/iii/paper-35/4/b/i/solution

Codex  0 Created 2026-10-03 Updated 2026-10-06

Condition on the bulb being alive at age

τ

\frac{F ( τ + 1 )}{F ( τ )} = \frac{e ^{- λ (τ + 1)}}{e ^{- λ τ}} = e^{- λ} .

It does not depend on the unknown age

τ

. This is memorylessness of the exponential distribution: the residual lifetime given survival has the same exponential distribution as a new lifetime.

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