A study on the Poisson, geometric and Pascal distributions motivated by Chvátal's conjecture

Fu-Bo Li, Kun Xu, Ze-Chun Hu

Let $B(n,p)$ denote a binomial random variable with parameters $n$ and $p$. Vasěk Chvátal conjectured that for any fixed $n\ge 2$, as $m$ ranges over $\{0,\dots ,n\}$, the probabi…