For a renewal reward process show that lim E[RN+] E[RX] E[X] Assume the distribution of X, is nonlattice and that any relevant function is directly Riemann integrable. When the cycle reward is defined to equal the cycle length, the above yields lim E[XN+1] = 1++00 E[X2] E[X]' which is always greater than E[X] except when X is constant with probability 1 (Why?)