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. (1– 1/N)^N approaches l/e as N approaches infinity.