Consider a version of the slotted ALOHA protocol, where the random delay before retransmission is mplemented as an independent probability p for retransmission in each subsequent slot after the collision, until successful. In other words, say if a node sends in slot 0 and immediately discovers that collision happens, t will retry in slot 1,2, each with independent probability p, until the transmission is successful. Now assume there are N active nodes, each looking to transmit one frame at the same time from time 0. A. (3 pts) If slotted ALOHA is used, what is the probability that at least 1 frame has been successfully transmitted in 2 slots? B. (3 pts) If slotted ALOHA is used, what is the probability that at least 1 frame has been successfully transmitted in 3 slots? C. We want to compute the efficiency of slotted ALOHA. The efficiency is defined as the expected fraction of slots where transmission is successful in the long run. For this computation, we make several simplification assumptions: 1) all nodes have infinite frames to send, and 2) we neglect the case where a node will immediately transmit a packet at the beginning or after a successful transmission. In other words, we only count in the slots where every node has a probability p of transmitting. What is the efficiency of slotted ALOHA? D. Suppose we know the number N. Find the probability p that will maximize the efficiency of slotted ALOHA. Show the process of computation. E. What is the maximum efficiency that we can get with arbitrary N