Expected lengths of stick pieces
A stick of length is broken at two points chosen independently and uniformly at random, producing three pieces.
What are the expected lengths of the shortest, middle, and longest pieces?
Show a hint
For any , compute and , the survival-function route avoids messy densities. For the longest, use inclusion-exclusion over the three pieces.
Your answer
This one is open-ended. Work it through, then check your reasoning against the full solution.