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This work elevates coded caching networks from their purely information-theoretic framework to a stochastic setting, by exploring the effect of random user activity and by exploiting correlations in the activity patterns of different users. In particular, the work studies the $K$-user cache-aided broadcast channel with a limited number of cache states, and explores the effect of cache state association strategies in the presence of arbitrary user activity levels; a combination that strikes at the very core of the coded caching problem and its crippling subpacketization bottleneck. We first present a statistical analysis of the average worst-case delay performance of such subpacketization-constrained (state-constrained) coded caching networks, and provide computationally efficient performance bounds as well as scaling laws for any arbitrary probability distribution of the user-activity levels. The achieved performance is a result of a novel user-to-cache state association algorithm that leverages the knowledge of probabilistic user-activity levels. We then follow a data-driven approach that exploits the prior history on user-activity levels and correlations, in order to predict interference patterns, and thus better design the caching algorithm. This optimized strategy is based on the principle that users that overlap more, interfere more, and thus have higher priority to secure complementary cache states. This strategy is proven here to be within a small constant factor from the optimal. Finally, the above analysis is validated numerically using synthetic data following the Pareto principle. To the best of our understanding, this is the first work that seeks to exploit user-activity levels and correlations, in order to map future interference and design optimized coded caching algorithms that better handle this interference.