All Questions

Consider the random variable $$X=\frac{1}{d}\sum_{k=1}^d\cos X_k$$ where $X_k$ are each drawn uniformly i.i.d. from $[0,2\pi]$. What is the CDF of X? It seems that a relatively direct way could be to ...

Let $\alpha$ and $\beta$ be incommensurate real numbers. Consider the function $f(x)={\rm cos}(x)+{\rm cos}(\alpha x)+{\rm cos}(\beta x)$ and its positive zeros $x_k(\alpha,\beta)$. Fix $\alpha$ and ...