Suppose that a race is run along a linear track and that the starting point S and
ending point E are chosen randomly where S is uniform on [0, 1] and E is uniform
on [8, 9]. Let L be the length of the race. Find the pdf of L.

Suppose that a race is run along a linear track and that the starting point S and
ending point E are chosen randomly where S is uniform on [0, 1] and E is uniform
on [8, 9]. Let L be the length of the race. Find the pdf of L.

Well cant we just say the length $\displaystyle L = E - S \Rightarrow l = e - s$ where $\displaystyle e \in [8,9]$ and $\displaystyle s \in [0,1]$ and hence $\displaystyle l \in [7,9]$