Compute expected arc length on a circle
Company: DRW
Role: Quantitative Trader
Category: Statistics & Math
Difficulty: easy
Interview Round: Online Assessment
On the unit circle (radius \(1\), centered at the origin), pick **three** points independently and uniformly at random on the circumference. These three points partition the circle into three circular arcs.
Let \(L\) be the **length of the arc (along the circumference)** that contains the fixed point \((1,0)\) (angle 0).
Compute \(\mathbb{E}[L]\).
Overview: This question evaluates understanding of geometric probability, order statistics on a circle, and expectation computation for continuous random variables.
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