Let $X_{1}, ldots , X_{n}$ be $n$ independent, symmetric, random variables on the interval $[-1,, 1]$. Ordentlich (2006) showed that the differential entropy of $S_{n}=sum _{i=1}^{n} X_{i}$ is maximized when $X_{i}$, $i=1,ldots ,n-1$ are symmetric Bernoulli random variables and $X_{n}$ is ${rm uniform}(-1,, 1)$. We give a short derivation of this result via an alternative proof of a key lemma of Ordentlich (2006).
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