Maximizing the entropy of a sum of independent bounded random variables
Erik Ordentlich · IEEE Transactions on Information Theory · 2006
Let X1,...,Xnbe n independent, symmetric random variables supported on the interval [-1,1] and let Sn=sigmai=1nXibe their sum. We show that the differential entropy of Snis maximized when X1,...,Xn-1are Bernoulli taking on +1 or -1 with equal probability and Xnis uniformly distributed