Previously, DAG scheduling schemes used the mean (average) of computation or communication time in dealing with temporal heterogeneity. However, it is not optimal to consider only the means of computation and communication times in DAG scheduling on a temporally (and spatially) heterogeneous distributed computing system. In this paper, it is proposed that the second order moments of computation and communication times, such as the standard deviations, be taken into account in addition to their means, in scheduling "stochastic" DAGs. An effective scheduling approach which accurately estimates the earliest start time of each node and derives a schedule leading to a shorter average parallel execution time has been developed. Through an extensive computer simulation, it has been shown that a significant improvement (reduction) in the average parallel execution times of stochastic DAGs can be achieved by the proposed approach.