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ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2024/paper-2/14/a/ii/solution

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Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2024 / Paper 2 / 14 / a / ii / Solution by

Codex  0 2026-10-18

The graph is a rectangle of height one over

[0, 1)

, with zero height elsewhere. Its unit area is the required normalization of the probability density function.

Figure 1.
Uniform endpoint uncertainty and triangular elapsed-time uncertainty
. Left: the uniform distribution of one endpoint offset. Right: the triangular distribution of the difference of two independent endpoint offsets. Shading marks the event $T > 1/2$ . Details.

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