All Questions

Can we find $\sum_i x_i$ given $\{\sum_i x_i^{2n}\}_{n\in \mathbb{N}}$, assuming $\{x_i\}_{i\in\mathbb{N}}$ is a set of positive real numbers? Perhaps an easier question is, can we find $\sum_i x_i$ ...

Let $G(t)$ be a probability generating function of some integer and non-negative r. v. $X$. Suppose that $$\lim_{t\to1}G'(t)=+\infty.$$ That is $$ \mathbb{E}X=+\infty. $$ Can you show that $$ \lim_{t\...

Recall that for a random variable $X$ with a moment generating function $M_X(t)$ the cumulant generating function is defined as \begin{align} K_X(t)=\log M_X(t) \end{align} The Taylor expansion of $...