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In a heterogeneous wireless sensor network (WSN), relay nodes (RNs) are adopted to relay data packets from sensor nodes (SNs) to the base station (BS). The deployment of the RNs can have a significant impact on connectivity and lifetime of a WSN system. This paper studies the effects of random deployment strategies. We first discuss the biased energy consumption rate problem associated with uniform random deployment. This problem leads to insufficient energy utilization and shortened network lifetime. To overcome this problem, we propose two new random deployment strategies, namely, the lifetime-oriented deployment and hybrid deployment. The former solely aims at balancing the energy consumption rates of RNs across the network, thus extending the system lifetime. However, this deployment scheme may not provide sufficient connectivity to SNs when the given number of RNs is relatively small. The latter reconciles the concerns of connectivity and lifetime extension. Both single-hop and multihop communication models are considered in this paper. With a combination of theoretical analysis and simulated evaluation, this study explores the trade-off between connectivity and lifetime extension in the problem of RN deployment. It also provides a guideline for efficient deployment of RNs in a large-scale heterogeneous WSN.