= Solution
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>.
\Image[/past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2024/paper-2-q14-timing-densities.png]
{title=Uniform endpoint uncertainty and triangular elapsed-time uncertainty}
{description=Left: the <uniform distribution> of one endpoint offset. Right: the <triangular distribution> of the difference of two independent endpoint offsets. Shading marks the event $T>1/2$.}
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