We consider the problem of simultaneous user-scheduling, power-allocation, and rate-selection in an orthogonal frequency division multiple access (OFDMA) downlink, with the goal of maximizing expected sum-utility under a sum-power constraint. In doing so, we consider a family of generic goodput-based utilities that facilitate, e.g., throughput-based pricing, quality-of-service enforcement, and/or the treatment of practical modulation-and-coding schemes (MCS). Since perfect knowledge of channel state information (CSI) may be difficult to maintain at the base-station, especially when the number of users and/or subchannels is large, we consider scheduling and resource allocation under imperfect CSI, where the channel state is described by a generic probability distribution. First, we consider the “continuous” case where multiple users and/or code rates can time-share a single OFDMA subchannel and time slot. This yields a nonconvex optimization problem that we convert into a convex optimization problem and solve exactly using a dual optimization approach. Second, we consider the “discrete” case where only a single user and code rate is allowed per OFDMA subchannel per time slot. For the mixed-integer optimization problem that arises, we discuss the connections it has with the continuous case and show that it can solved exactly in some situations. For the other situations, we present a bound on the optimality gap. For both cases, we provide algorithmic implementations of the obtained solution. Finally, we study, numerically, the performance of the proposed algorithms under various degrees of CSI uncertainty, utilities, and OFDMA system configurations. In addition, we demonstrate advantages relative to existing state-of-the-art algorithms.