Maximizing the Entropy of a Sum of Independent Random Variables
نویسنده
چکیده
Let X1; : : : ;Xn be n independent, symmetric random variables supported on the interval [-1,1] and let Sn = Pn i=1Xi be their sum. We show that the di erential entropy of Sn is maximized when X1; : : : ;Xn 1 are Bernoulli taking on +1 or -1 with equal probability and Xn is uniformly distributed. This entropy maximization problem is due to Shlomo Shamai [1] who also conjectured the solution1.
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