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This letter reports a performance analysis of a dual-hop relay system composed of asymmetric radio-frequency and free-space optics (RF/FSO) links. This approach is based on the fact that FSO links can provide even wider bandwidths as compared to RF ones. In particular, an exact closed-form expression for the end-to-end outage probability of the RF/FSO relay links is derived. Overall, the RF/FSO links show a slightly worse performance than the RF/RF links, but the performance gap is gradually reduced as the signal-to-noise ratio (SNR) increases. Our mathematical analysis results were verified by exactly matching Monte Carlo simulation results.