Multi-taper detection method (MTM) is a powerful technique in spectrum sensing for Cognitive radio networks. In this paper, reliable and simple analytical expressions for the mean and variance of the Probability Density Function (PDF) of the MTM spectrum detector are derived. Then, closed-form expressions for detection and false alarm probabilities for the MTM spectrum detector have been obtained.  Intensive simulation based work is conducted under AWGN channel conditions using MATALB to confirm and evaluate the proposed theoretical study. The confirmation and the evaluation processes are designated to verify many perspectives such as:  the receiver operating characteristics (ROCs), the detection rate with respect to SNR, and minimum required sample points  to achieve a certain performance. All these perspectives are simulated under setting of multiple Slepian tapers (), sample points  and false-alarm probability (). Also, a comparison with energy detection method is presented. The simulation results confirm that the proposed model is reliable and robust under all settings of the simulation parameters.