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Compute the expected length of the arc

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Choose, at random, three points on the circle x 2 + y 2 = 1. Interpret them as cuts that divide the circle into three arcs. Compute the expected length of the arc that contains the point (1, 0). Remark. Here is a "solution." Let L1, L2, L3 be the lengths of the three arcs. Then L1 + L2 + L2 = 2π and by symmetry E(L1) = E(L2) = E(L3), so the answer is E(L1) = 2π/3. Explain why this is wrong.

Reference no: EM132855402

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