Pieces by position versus pieces by size
A stick of length is broken at two independent uniform points, giving a left piece, a center piece, and a right piece (by physical position).
What is the expected length of each piece by position (left, center, right)? Reconcile this with the fact that the ordered pieces (shortest, middle, longest) average .
Show a hint
The three positional pieces are the spacings of two uniform points. Are they exchangeable? What must each one average if they are exchangeable and sum to ?
Your answer
This one is open-ended. Work it through, then check your reasoning against the full solution.