 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/i/solution

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

An integrable nonnegative probability density of this form requires

k > 0

. Normalization gives

1 = A \int_{0}^{\infty} e^{- k t} d t = A / k

, so

A = k

. This is the exponential distribution with rate

k

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