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In this paper, we investigate stochastic multichannel load balancing in a distributed cognitive network coexisting with primary users. In particular, we propose a probabilistic technique for traffic distribution among a set of data channels by incorporating statistical information of primary users' activities in different channels into the selection process without centralized control. Moreover, the proposed scheme is enabled by a multi-channel binary exponential backoff mechanism to further facilitate contention resolution in a multi-channel environment. It is shown through simulations that the proposed MAC layer enhancement outperforms well-known multi-channel MAC protocols both in terms of aggregate end-to-end throughput and average frame end-to-end delay. Furthermore, its performance is also compared to two heuristic channel selection techniques in a multi-channel cognitive network, coexisting with incumbents.