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 $\displaystyle \theta$ between two neighbouring points. The sum of all these angular separations wil always correspond to one full rotation, i.e.:

$\displaystyle \sum_{i=1}^{N}\theta_{i}=360^{\circ}$

The expected value of $\displaystyle \theta$ can then be found as:

$\displaystyle E(\theta)= \frac{360^{\circ}}{N} $

But the thing what I'm really dying to know is:

**how do I calculate the variance of** $\displaystyle \theta$

**? **
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!