Intersecting chords. Four points X 1 , X 2 , X 3 , X 4 are chosen independently and at random on…

Intersecting chords. Four points X 1 , X 2 , X 3 , X 4 are chosen independently and at random on…

Intersecting chords. Four points X1, X2, X3, X4 are chosen independently and at random on a circle (say of unit circumference for definiteness). Find the probability that the chords X1X2 and X3X4 intersect

2. Find the probability that the quadratic λ2 − 2Uλ + V has complex roots if the coefficients U and V are independent random variables with a common uniform density f(x) = 1/a for 0

 

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