An orthogonal frequency division multiple access (OFDMA)-based primary user (PU) network is considered, which provides different spectral access/energy harvesting opportunities in RF-powered cognitive radio networks (CRNs). In this scenario, we propose an optimal spectrum sensing policy for opportunistic spectrum access/energy harvesting under both the PU collision and energy causality constraints. PU subchannels can have different traffic patterns and exhibit distinct idle/busy frequencies, due to which the spectral access/energy harvesting opportunities are application specific. Secondary user (SU) collects traffic pattern information through observation of the PU subchannels and classifies the idle/busy period statistics for each subchannel. Based on the statistics, we invoke stochastic models for evaluating SU capacity by which the energy detection threshold for spectrum sensing can be adjusted with higher sensing accuracy. To this end, we employ the Markov decision process (MDP) model obtained by quantizing the amount of SU battery and the duty cycle model obtained by the ratio of average harvested energy and energy consumption rates. We demonstrate the effectiveness of the proposed stochastic models through comparison with the optimal one obtained from an exhaustive method.