= Solution
The graph of the positive-delay <probability density function> is a horizontal segment at height $1/R$ from $s=0$ to $r$, followed by zero from $r$ to $R$. Values at individual endpoints do not affect <probabilities>. The separate atom $1-r/R$ at zero is not a finite-height part of this density graph.
\Image[/past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2016/paper-1-delay-distribution.png]
{title=Positive-delay density and the full cumulative distribution, whose jump records the no-delay atom}
The companion <cumulative distribution function> in the figure is $F_S(s)=0$ for $s<0$, $F_S(s)=1-r/R+s/R$ for $0\leq s<r$, and $F_S(s)=1$ for $s\geq r$. Its jump at zero displays the discrete part without confusing density height with <probability mass>.
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