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 Nov8 comment Central Limit Theorem on the Circle @Sun: There actually is a convergence to WrappedNormal. Consider a circular random variable $Y:=X\ \text{mod}\ 2\pi$, where $X$ is a standard non-circular random variable with finite variance. Thus, a properly normalized sum of i.i.d. copies of $X$ converges (in distirbution) to a Gaussian random variable.Now, if you do the same with i.i.d. copies of $Y$ and append $\text{mod}\ 2\pi$ at the end of the summation scheme and you'll end up with a summation scheme converging to a wrapped normal distribution. Aug19 comment Central Limit Theorem on the Circle @D.Thomine: Not at all. In order to account for the fact, that $X_i$ is circular, we can simply use a real-valued random vector restricted to $[0, 2\pi)$. Thus, we use the classical division for real numbers. The summation scheme presented in my post obviously yields again a random vector restricted to $[0, 2\pi)$. Aug17 comment Central Limit Theorem on the Circle I mean a similar summation scheme as in the case of the classical CLT. Added it to the original post. Mar6 comment Strategy in an urn problem with two urns Thank you, @Henry. How would one proof analytically this strategy to be the best one and no other to be better in the above sense?