Problem 4 Suppose three active nodes A, B, and C are competing for accessing a channel using slotted ALOHA. Assume each node has infinitely many packets to send. Each node transmits in each slot with probability p. The slots are numbered slot 1, slot 2, slot 3, etc. Give the probability for each of the following events a) node B succeeds in slot 4; b) node B succeeds for the first time in slot 4; c) any node succeeds in slot 4 d) the first success (over all nodes) is in slot 4, i.e., no success before slot 4. e) Give the efficiency of the system (containing all the three nodes). f Suppose that the average packet size sent by node A is L bits, and each slot lasts for S seconds. What is the long-term throughput of node A (unit: bps)