P8. In Section 6.3 , we provided an outline of the derivation of the efficiency of slotted ALOHA. In this problem we'll complete the derivation. a. Recall that when there are N active nodes, the efficiency of slotted ALOHA is Np(1-p)N-1. Find the value of p that maximizes this expression. b. Using the value of p found in (a), find the efficiency of slotted ALOHA by letting N approach infinity. Hint: (1-1/N)N approaches 1/e as N approaches infinity.

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