Slotted ALOHA There is a network with N nodes that share a medium based on slotted ALOHA. The probability that a node transmits in a time slot is denoted by p. We learned in class that the efficiency of a slotted ALOHA network can be expressed as /V) = Np(1-p)"-1 In this homework, we will find the "maximum" of this efficiency 1. Let us denote p. = argmaxp/(p). Prove that p. NL. (15 pts) Note: p6- 1 2. Prove that/(p") 1 as N oo. (15 pts) Hint: Substitute p. = NLthen you will have/(N) instead ofMp). Find lim-of(N)