Spectrum sensing is one of the key issues in cognitive radio. Among the techniques for signal detection, the energy detector (ED) is widely used due to its simplicity. However, setting the threshold for the energy detector requires some knowledge of the noise power level, which can be provided by suitable estimation methods. In this paper, we derive analytical expressions relating the threshold, the received signal-to-noise ratio (SNR), the probability of detection (PD) and the probability of false alarm (PFA), assuming a practical noise power estimator. The analysis can be used to design EDs that fulfill spectrum sensing requirements in cognitive radio (CR) scenarios.