[solved] Let $N$ be a discrete random variable taking positive values and $X$ and $Y$ be random variables with sum $N$. Then $X$ and $Y$ are independent iff $N$ has a poisson distribution.
[solved] product of diagonals (from a given vertex) of regular $n$-gon inscribed in unit circle is equal to $n$
[Solved] If $$\sum_{j=1}^{\infty}\frac{a_j}{j}$$ is convergent then $$\lim_{n\to\infty}\frac{1}{n}\sum_{d=1}^{n}a_d=0$$
