Compute expected arc length on a circle
DRWQuantitative Trader · Online Assessment
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This question evaluates understanding of geometric probability, order statistics on a circle, and expectation computation for continuous random variables.
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]).
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