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In this paper, we discussed an efficient statistical method with proof-of-work consensus approach for cloud and fog computing. With this method, solution with precise probability in minimal time is realized. We have used the expectation maximization algorithm and polynomial matrix factorization. The advantages of this statistical method are the less iteration to converge to the consensus solution and easiness to configure the complete mathematical model as per the requirement. Moreover, the energy and memory consumption are also less which make this approach appealing for cloud and fog computing. The experimental results also show that the proposed approach is significantly efficient in terms of time and memory consumption. This novel approach seems beneficial for Internet-of-Things (IoT), one of the most fast-growing technologies in network computing.