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In this paper, normal factor graph (NFG) based probabilistic inference approach for the cooperative spectrum sensing in cognitive radio (CR) is presented. Spectrum sensing problem is modeled as binary hypothesis testing problem. We have formulated the joint probability function with all latent and manifest variables which describe the system. Then decompose the joint distribution function into simpler conditional probability functions and represent them through normal factor graph. The exact marginalization is computed by passing the messages (probability values) among the nodes and edges using Sum-product-algorithm (SPA) / Belief-propagation (BP) algorithm. We compute messages for null and alternate hypothesis and apply Neyman-Pearson (NP) theorem based Likelihood ratio test (LRT) for optimal decision at fusion center. We consider non-central chi-square distribution for alternate hypothesis (H1). It is assumed that secondary users (SUs) are independently sensing the primary user (PU), therefore the graph has no cycle. It is employing energy detector based local sensing with hard decision. We consider non-ideal channel conditions for both PU-SU and SU-FC channels. Initially flat-fading, time-invariant channels with AWGN between PU-SUs and binary symmetric channels (BSC) and AWGN channels between SUs and fusion center (FC) are considered. Simulation results show that proposed methods improves the performance of the cooperative spectrum sensing.