Given the throughput of a Pure Aloha system to be T = Np(1 - p)^2(N-1) where N is the number of nodes and p is the retransmission probability, prove that the maximum possible throughput (a.k.a efficiency) is 1/2e. Follow the same steps as for Slotted Aloha: find the p which maximizes throughput, and then take the limit as N rightarrow infinity. Given the throughput of a Pure Aloha system to be T = Np(1 - p)^2(N-1) where N is the number of nodes and p is the retransmission probability, prove that the maximum possible throughput (a.k.a efficiency) is 1/2e. Follow the same steps as for Slotted Aloha: find the p which maximizes throughput, and then take the limit as N rightarrow infinity