6. Three points A, B, C are chosen independently at random on the circumference of a circle. Let b(x) be the probability that at least one of the angles of the triangle ABC exceeds xл. Show that - 1 − (3x − 1)² if ≤ x ≤ 1, if ≤ x ≤ 1. 3(1-x)² Hence find the density and expectation of the largest angle in the triangle. b(x) = {

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