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for questions involving inequalities, upper and lower bounds.

4 votes
0 answers
408 views

Simmons' inequality on binomial random variables

Fix two positive integers $n,m$ such that $n>2m$ and $n\ge 3$, and let $X\sim \text{Bin}(n,\frac{m}{n})$ be a binomial random variable. For each $i\in \{1,\ldots,m\}$, set $\alpha_i = \mathbb{P}(X\le …
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