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In this paper, we consider a multi-access coded caching system with decentralized prefetching, where a server hosts $N$ files, each of size $F$ bits, and is connected to $K$ users through a shared link. There are $c$ caches distributed across the network and each of the $K$ users connects to a random set of $r\leq c$ caches. Initially, we consider the model in which each of the cache subsets is accessed by exactly a specific number of users. For this model, a novel linear delivery scheme is introduced, using which the closed-form expression for the per-user delivery rate is computed. Furthermore, using techniques from index coding, the optimality of the proposed linear delivery scheme among all linear delivery schemes is proved. The results of the decentralized shared caching and conventional decentralized caching schemes are recovered as special cases of the proposed model. The model is further generalized by allowing each cache subset to serve any number of users. This enhances the flexibility of the system, enabling it to accommodate any arbitrary number of users. A delivery scheme is proposed for the generalized model and is shown to be optimal for certain user-to-cache associations.