We introduce FEDQ-Trust, an innovative data-driven trust prediction approach designed for mobile edge-based Internet of Things (IoT) environments. The decentralized nature of mobile edge environments introduces challenges due to variations in data distribution, impacting the accuracy and training efficiency of existing distributed data-driven trust prediction models. FEDQ-Trust effectively tackles the statistical heterogeneity challenges by integrating Federated Expectation-Maximization with Deep Q Networks. Federated Expectation-Maximization's robust handling of statistical heterogeneity significantly enhances trust prediction accuracy. Meanwhile, Deep Q Networks streamlines the model training process, efficiently reducing the number of training clients while maintaining model performance. We conducted a suite of experiments within simulated MEC-based IoT settings by leveraging two real-world IoT datasets. The experimental results demonstrate that our model achieved a significant convergence time reduction of 97% to 99% while ensuring a notable improvement of 8% to 14% in accuracy compared to state-of-the-art models.