Consider a slotted ALOHA system with a large number of nodes. In a time slot, each backlogged packet (packet collided in previous transmission) is transmitted with probability p. And in each time slot, a new packet arrives to the system with probability . The new packet will attempt transmission in the next slot. All these transmissions are independent of one another. If there are N backlogged packets in the current time slot, find the probability distribution of the number of backlogged packets in the next time slot. (Hint: the number of backlogged packets in the next time slot can be N, N - 1, or N +1) Calculate the average increase of the number of the backlogged packets in a time slot. If backlogged packets accumulate with the time, then the buffer will overflow and the system will be unstable. Is the given ALOHA system always a stable system? If not, under what condition the system becomes unstable