In decision-making problems under uncertainty, mean-variance analysis consistent with expected utility theory plays an important role in analysing preferences for different alternatives. In this paper, a new approach for mean-variance analysis based on cumulative distribution functions is proposed. Using simulation, a new algorithm is developed, which generates pairs of random variables to be representative for each pair of uncertain alternatives. The proposed model is concerned with financial investment for risk-averse investors with non-negative lotteries. Furthermore, the proposed technique in this paper can be applied to different distribution functions for lotteries or utility functions.