answer with detailed explanation

Consider a compound distribution with pdf fs(r) for a > 0 defined by 0-non-le-x/0 fs(x) = > cnen(x) = > on (n - 1)! , x > 0. n=1 n=1 The set of mixing weights { on : n = 1,2...} is a discrete probability distribution. Prove that fs(x +y) =0> > citk+lej+1(x)ex+1(y). j=0 k=0