Problem 3. Let {X;, R;} be the interrenewal intervals and rewards for a renewal reward process. (a) Obtain a renewal equation for E RN(t)+1] by conditioning on the first renewal time. (b) Use the theorem proved in Problem 1 and the key renewal theorem to show that: E[RX] lim E RN(D)+1] = t-+00 LL (c) Assume that the reward process is defined as R; = X;. Show that this implies that lim E XN(D)+1] 2 E[X] with equality only when X is constant. Explain this t+00 relation