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In this paper, we address statistically robust transmit design problems that maximize the average mutual information of amplify-and-forward (AF) multiple-input multiple-output (MIMO) two-hop relay channels having perfect channel state information at the receiver (CSIR) and statistical channel state information at the transmitter (CSIT). In the selected scenario, the source, relay, and destination terminals are equipped with correlated antennas where a direct link between the source and the destination terminals can be found. Moreover, the statistical CSIT consists of the channel means and covariance matrices of various links. The design problem is taken into account for regimes in large systems because there are no closed-form expressions of the average mutual information in the MIMO relay channel. The contribution of this study includes the derivation of asymptotic mutual information expressions for the MIMO relay channel in the large system limit. Additionally, an efficient optimization algorithm based on the asymptotic mutual information is proposed in order to find the asymptotically optimal source covariance matrix and the relay amplifying matrix. Numerical simulation results show that the new approach achieves indistinguishable performance compared to those of the maximization approaches in finite-dimensional systems, even for a small number of antennas at each link. The impact of the CSI of various links on the throughput of the MIMO relay channel is studied using the new approach.