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The focus of this paper is on energy-aware resource management in a cloud computing system. Much of the existing work assumes that the resource requirements for various applications are known and given as scalar values. However, it is very difficult to know the exact resource requirements, and thus, it is more appropriate to treat resource requirements for applications as random variables with known characteristics. For a desired quality of service, the required total resource amount can then be estimated as a function of the means and standard deviations of these random variables. Inspired by the modern portfolio theory, this paper presents algorithms that minimize the total amount of estimated resource in the system. A source of difficulty is that some of the aforesaid random variables may be correlated with each other. The proposed algorithms effectively deal with correlated applications. Experimental results show that, in spite of its simplicity and scalability, the proposed solution outperforms the well-known heuristics i.e., first fit decreasing (FFD) and best fit decreasing (BFD) by an average of 10% while having a low execution time.