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This paper proposes a stochastic approach based on Monte Carlo simulation to derive the load demand of a fleet of domestic commuter plug-in electric vehicles. At first, appropriate non-Gaussian probability density functions are fitted to the employed datasets to generate random samples required in the Monte Carlo simulation. The datasets include home arrival time, daily travelled distance and home departure time of randomly selected private ICE vehicles. In each iteration, extraction of the charging profile is carried out for the individual PEVs in order to derive the hourly aggregated load profile of the fleet. Then, probability density function of the aggregated load of the PEVs within each hour is estimated. Eventually, the expected value of the hourly load demand can be calculated regarding the achieved power distributions. The PEVs are assumed to be charged through a distribution transformer. Thus, profile of the power delivered through the transformer to the PEVs is attained which can be useful for various distribution system applications such as network planning, load management and probabilistic load flow as well as sitting and sizing issues.