2 problems

Let $X$ have a Poisson binomial distribution $Q$ generated by probabilities $p_i\in[0,1)$, let $\lambda=\sum_{i\geq 1}p_i<\infty$, and let $\pi_\lambda$ be the Poisson distribution…

Extension conjecture. The displayed inequality holds throughout $C'$, even though $g_{p_1,p_2}$ is not unimodal for $\langle p_1,p_2\rangle\in C'\setminus C$. The conjecture is bas…