Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2016 / Paper 1 / 16 / a / iii / 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.

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 $0\le s<r$, and $F_S(s)=1$ for $s\ge r$. Its jump at zero displays the discrete part without confusing density height with probability mass.