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This paper considers the primary user activity or the subchannel availability in optimally distributing the available resources for an orthogonal frequency-division multiple-access (OFDMA) cognitive radio multicast network. For this purpose, a risk-return model is presented, and a general rate-loss function, which gives a reduction in the attainable throughput whenever primary users reoccupy the temporarily accessible subchannels, is introduced. Taking the maximization of the expected sum rate of secondary multicast groups as the design objective, an efficient joint subcarrier and power-allocation scheme is proposed. Specifically, the design problem is solved via a dual optimization method under constraints on the tolerable interference thresholds at individual primary user's frequency bands. It is shown that as the number of subcarriers gets large (which is often the case in practice), the dual-domain solution becomes globally optimum with regard to the primal problem. More attractively, the ??practically optimal?? performance of this approach is achieved with a substantially lower complexity, which is only linear in the total number of subcarriers as opposed to exponential complexity typically required by a direct search method. Our proposed design is valid for unicast and multicast transmissions and is applicable for a wide range of rate-loss functions, among which, the linear function is a special case. The superiority of the dual scheme is thoroughly verified by numerical examples.