There are N points which are randomly distributed (according to a uniform probability distribution) over the circumference of a circle.
Now consider the angular separation between two neighbouring points. The sum of all these angular separations wil always correspond to one full rotation, i.e.:
The expected value of can then be found as:
But the thing what I'm really dying to know is: how do I calculate the variance of ?
I've tried for several hours, but I just can't figure out where to start. Does anyone here have any idea? Thanks in advance!