Entropy of the Sum of Two Independent, Non-Identically-Distributed   Exponential Random Variables
  In this letter, we give a concise, closed-form expression for the differential entropy of the sum of two independent, non-identically-distributed exponential random variables. The derivation is straightforward, but such a concise entropy has not been previously given in the literature. The usefulness of the expression is demonstrated with examples. 
Andrew W. Eckford and Peter J. Thomas
cs.IT math.IT