Ten random chords of a circle are chosen, independently. To generate each of these chords, two
independent uniformly random points are chosen on the circle (intuitively, uniformly means that
the choice is completely random, with no favoritism toward certain angles; formally, it means
that the probability of any arc is proportional to the length of that arc). On average, how many
pairs of chords intersect? Hint: Consider two random chords. An equivalent way to generate
them is to pick four independent uniformly random points on the circle, and then pair them up
randomly..
Capitol Tech U Doctoral Presentation - April 2024.pptx
Ten random chords of a circle are chosen, independently. To generate.pdf
1. Ten random chords of a circle are chosen, independently. To generate each of these chords, two
independent uniformly random points are chosen on the circle (intuitively, uniformly means that
the choice is completely random, with no favoritism toward certain angles; formally, it means
that the probability of any arc is proportional to the length of that arc). On average, how many
pairs of chords intersect? Hint: Consider two random chords. An equivalent way to generate
them is to pick four independent uniformly random points on the circle, and then pair them up
randomly.
