Let: $F_{j+1,y}(s)$ be the cumulative distribution function of a binomial distribution with mean $y$, $j+1$ independent trials considered for $s$ successes. Is it possible to show in any way that:

$\frac{1}{F_{j+1,y}(s+2)}-\frac{2}{F_{j+1,y}(s+1)}+\frac{1}{F_{j+1,y}(s)}>0, 0\leq s\leq j-1$

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This can be helpful when comparing the expected value of random processes governed by poisson-binomial distributions against ones governed by binomial distribution. And in infer statistical dominance of a process over the other, indeed is a frequent term in bandit algorithms problems Thank you for your kind attention