 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ib/paper-1/18h/b/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

For

y \geq 0

and

X \sim U (0, 1)

Pr (- lo g X \leq y) = Pr (X \geq e^{- y}) = 1 - e^{- y} .

The distribution function is zero for

y < 0

, so this is exactly the distribution function of

Exp (1)

. Therefore

- lo g X \sim Exp (1) .

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