Maximizing the entropy of a sum of independent bounded random variables
Let X-1,..., X-n be n independent, symmetric random variables supported on the interval [-1,1] and let S-n = Sigma(n)(i=1) X-i be their sum. We show that the differential entropy of Sn is maximized when X-1,..., Xn-1 are Bernoulli taking on +1 or -1 with equal probability and X-n is uniformly distributed.
bounded random variables differential entropy majorization multiple-access channel schur convexity