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This paper presents a new method based on Bayesian networks (BNs) for computing the exact probability distribution of the delay of a circuit. The method is based on BNs, which allows an efficient means to factor the joint probability distributions over variables in a circuit graph. The space complexity of the method presented here is O(m|C|), where m is the number of distinct values taken by each delay variable and |C| is the number of variables in the largest clique. The maximum clique size present in a BN is shown to be much smaller than the circuit size. For large circuits, where it is not practically feasible to compute the exact distribution, methods to reduce the problem size and get a lower bound on the exact distribution are presented. Comparison of the results with Monte Carlo simulations shows that we can reduce the size of the circuit by as much as 89% while maintaining the maximum difference between the predicted and simulated 3σ values to be less than 3%.