You randomly cut a rope of length 1 at two points. What is the expected length of the longest piece?

You randomly cut a rope of length 1 at two points. What is the expected length of the longest piece?

Approach: Let cuts be 0 < X < Y < 1. Lengths are X, Y-X, 1-Y. Find expected value of max of three.

11/18 ≈ 0.6111. By symmetry, E[max] = 3E[largest segment]. Compute integral.

Follow-up: What is the expected length of the shortest piece?

Key concepts: order statistics, maximum of three, integration.