Understanding the glass transition and glassy dynamics in random copolymers and miscible polymer blends is crucial for both fundamental and applied polymer science. While there are multiple models describing the dependence of the glass transition temperature on the copolymer or blend composition (Fox, Gordon-Taylor, Kwei, and others), it is still not easy to describe or predict the broader temperature dependence of relaxation times in these systems. Here, we expand our TS2 (two states, two (time)scales) mean-field model to random copolymers and formulate simple and intuitive mixing rules for the model parameters as a function of composition. We obtain a new equation for the characteristic transition temperature, T*, that can serve as an approximate predictor for the glass transition temperature, T-g. The model then allows us to refine the prediction and calculate Tg based on the standard criterion (tau(alpha)(T-g) = 10(2) s). We can also calculate the temperature-dependent alpha- and beta-relaxation times for different copolymer compositions. To test the theory, we computed the glass transition temperatures and relaxation times for random styrene-methylmethacrylate (PS-r-PMMA) and statistical styrene-butylmethacrylate (PS-stat-PnBMA) copolymers and found good qualitative and semi-quantitative agreement with published literature data. The described approach can be easily extended to blends and copolymers with multiple components.