To formulate the performance of a multiple-access network, we need a mathematical model. When the number of stations in a network is very large, the Poisson distribution, p[x] = (e^−λ × λ^x)/(x!), is used. In this formula, p[x] is the probability of generating x number of frames in a period of time and λ is the average number of generated frames during the same period of time. Using the Poisson distribution:

a. Find the probability that a pure Aloha network generates x number of frames during the vulnerable time. The vulnerable time for this network is two times the frame transmission time (T_fr).

b. Find the probability that a slotted Aloha network generates x number of frames during the vulnerable time. The vulnerable time for this network is equal to the frame transmission time (T_fr).