This thesis investigates computational aspects and optimization techniques for the convolution operator over random variables in the Bend programming language, with a focus on parallel computing approaches. Convolution, a fundamental operation in fields as diverse as signal processing, image processing, and probability theory, can be computationally intensive, especially in the context of large data sets. This paper explores different methods for computational convolution, focusing on discrete convolution techniques, and evaluates their performance in a parallel computing environment. Two different approaches are implemented to compute the convolution: a naive sliding dot product algorithm and a parallel-oriented tree reduction approach. Both methods are implemented in the Bend programming language, which is a high-level functional language designed for parallel execution. The performance of these implementations was analyzed using Bend's Rust and C runtimes. The results show that the naive approach is simpler to implement and still outperforms the tree reduction technique even in parallel environments, since the algorithm is still not optimized and has a bottleneck. This thesis provides insight into the practical application of parallel computing in the optimization of mathematical operations and contributes to a broader understanding of parallel algorithm design.