2 problems

Let $X\in\{0,\ldots,n\}$ be a random variable with $p_0p_n>0$ and probability generating function $f_X$. Let $\delta>0$ and $R\geqslant1$. If every zero $\zeta$ of $f_X$ satisfies…

Let $X$ be a strongly Rayleigh random variable, and let $j,k\geq 1$. Write $\left\lfloor jX/k\right\rfloor$ for the integer-valued floor of $jX/k$. Poisson multinomial decompositio…