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Intrusion detection is one of the fundamental applications in wireless sensor networks (WSNs). Some applications require different detection capabilities at different areas in the deployment field. Gaussian distributed WSNs can fulfill such requirements and are widely deployed in practice. In addition, the presence of some high capability sensors leads to performance enhancement in term of intrusion detection probability. This makes it imperative to explore the intrusion detection problem in heterogeneous WSNs. This work is to examine the intrusion detection problem in a heterogeneous Gaussian distributed WSN theoretically and experimentally. A heterogeneous WSN model with distinct types of Gaussian distributed sensors is proposed, where both single-sensing detection and fe-sensing detection models are employed. Based on this network model, the intrusion detection probabilities under various application scenarios are theoretically derived and experimentally validated by extensive simulations. This work is to provide guidelines in designing heterogeneous WSNs for intrusion detection.