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Cognitive Radio (CR) allows for usage of licensed frequency band by unlicensed Secondary Users (SU)s. However, these SUs need to monitor the spectrum continuously to avoid possible interference with the licensed Primary users (PU)s. In order to avoid causing harmful interference to a PU that is in operation, spectrum sensing is needed for the CRs. One of the great challenges of spectrum sensing is to detect the presence of the PU with little information about the channel and the signal transmitted from the PU. Cooperative spectrum sensing has been shown to greatly increase the probability of detecting the PU. Cooperative spectrum sensing refers to the spectrum sensing methods where local spectrum sensing information from multiple SUs are combined for PU detection. Distributed spectrum sensing methods have the potential to increase the spectral estimation reliability and decrease the probability of interference of CRs to primary communications. This paper considers the performance of a distributed Bayesian detection system consisting of N sensors and a fusion center, in which the decision rules of the sensors have been given and the decisions of different sensors are mutually independent conditioned on both hypotheses. Theoretical analysis on the performance of this fusion center is carried out. We obtain the conditions for the fusion center such that achieves the minimum average cost of making a decision for the overall system is smaller than the local risk of each sensor. The performance of our detector is compared to the traditional AND, OR and Majority decision fusion rules and numerical results show that AND, OR and Majority decision fusion rules are the special cases of the Bayesian fusion rule. In addition, we derive a lower bound for the risk of the fusion center for any given priori probability of hypothesis.