 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2005/paper-1/4/a/i/solution

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

For

t_{0} \geq 0

P (0 \leq T \leq t_{0}) = \int_{0}^{t_{0}} α e^{- α t} d t = 1 - e^{- α t_{0}} .

For

t_{0} < 0

the event is empty and its probability is zero.

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