We select randomly two points in the circumference (with length equal to 1) of a circle. Let $X,Y$ be those points (independent and uniformly distributed) and $D$ the arc distance between them. Since we move anti clock-wise, we select first $X$ then $Y$. Looking for $E[D]$.

My intuition says it might be $\frac{\pi}{4}$. Am I correct?

  • $\begingroup$ The points determine $2$ arcs. Is $D$ the length of the shortest arc? $\endgroup$ – drhab Apr 10 at 13:18
  • $\begingroup$ @drhab it is written as arc distance so I assume it is the smallest by definition $\endgroup$ – Μάρκος Καραμέρης Apr 10 at 13:21
  • $\begingroup$ D is the length of the arc from X to Y $\endgroup$ – EmKal Apr 10 at 22:28
  • $\begingroup$ dropbox.com/s/7n4c4e1e5k3qmkz/circle9.JPG?dl=0 $\endgroup$ – EmKal Apr 10 at 22:51
  • 1
    $\begingroup$ The correct answer is $\frac{1}{2}$. We can figure this also by using symmetry. $\endgroup$ – EmKal Apr 12 at 17:50

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.