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In an IEEE 802.11 based mobile ad hoc network (MANET), a network node accesses a common wireless channel through the distributed coordinate function (DCF), which is provided at the medium access control (MAC) layer of the IEEE 802.11 standard. The binary exponential backoff (BEB) algorithm, which uses slotted contention windows, plays an important role in the DCF. This paper develops a mathematical model for analyzing the performance of the BEB algorithm, which takes into account the packet loss probability of a wireless link. Based on the developed mathematical model, we derive the backoff probability distribution of a node, the average number of backoffs of a node, the average size of a contention window, and the average packet delay. Moreover, we attempt to find the optimal value of the initial contention window size, to which a node resets its contention window size after a successful transmission, in order to avoid the oscillation of the contention window size and thus maximize the utilization of the wireless channel.