Consider a network node which receives packets according to a Poisson process at the rate of 60 packets/sec. Assume the packet lengths are exponentially distributed with an average of 1500 bytes, and that the output link data rate is 1 Mbps. Assume the packet processing time is negligible, so the only service time is the transmission (serialization) time of the packet. (a) What are the probabilities that the nodes input queue has 1 packet, 2 packets and 10 packets (excluding the packet that is being transmitted), respectively? (b) What is the mean number of packets in the system? What is the mean number in the queue? (c) What is the mean waiting time?