Compute expected arc length on a circle

Q: Compute expected arc length on a circle

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Question

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 $\mathbb{E}[L]$ .

Compute expected arc length on a circle

Solution

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