# Math Help - pdf

1. ## pdf

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.

2. Originally Posted by winganger
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 $L = E - S \Rightarrow l = e - s$ where $e \in [8,9]$ and $s \in [0,1]$ and hence $l \in [7,9]$

So the resulting pdf is uniform on [7,9]