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The binomial distribution maximises entropy among sums of negatively related indicators with fixed mean and support
We show that the binomial distribution supported on $\{0,1,\ldots,n\}$ and with mean $np$ for some $0<p<1$ maximises entropy within the class of sums of negatively related indicator random variables with this mean and support. Our results generalise the main result of Yu (2008), who showed that this
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