Two points are chosen uniformly at random on a unit circle. What is the expected distance between them?

Two points are chosen uniformly at random on a unit circle. What is the expected distance between them?

Approach: Parameterize by angles and integrate over joint distribution.

4/π ≈ 1.273. The chord length is 2sin(θ/2) where θ is angular difference uniformly distributed on [0,π].

Follow-up: What is the distribution of the distance?

Key concepts: uniform distribution on circle, integration, trigonometry.