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A probabilistic model for residential loads is proposed in this paper. The model differs from other similar models in that it uses a beta probability distribution function (beta PDF) to describe the load uncertainty. It further models the load parameter uncertainty as a bivariate distribution of load current means and standard deviations. By separating the probabilistic load uncertainty and the load parameter uncertainty, the model becomes very useful for the analysis of distribution systems where primarily residential consumers are connected, e.g., electrification projects. The model was tested using a Monte Carlo-type simulation and the results are sufficiently accurate for practical design purposes.