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In this paper, we propose a classification scheme that differentiates Ethernet and WLAN TCP flows based on measurements collected passively at the edge of a network. This scheme computes two quantities, the fraction of wireless TCP flows and the degree of belief that a TCP flow traverses a WLAN inside the network, using an iterative Bayesian inference algorithm that we developed. We prove that this iterative Bayesian inference algorithm converges to the unique maximum likelihood estimate (MLE) of these two quantities. Furthermore, it has the advantage that it can handle any general K-classification problem given the marginal distributions of these classes. Numerical and experimental evaluations demonstrate that our classification scheme obtains accurate results. We apply this scheme to two sets of traces collected from two campus networks: one set collected from UMass in mid 2005 and the other collected from UConn in late 2010. Our technique infers that 4%-7% and 52%-55% of incoming TCP flows traverse an IEEE 802.11 wireless link in these two networks, respectively.