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An assessment of the statistical errors occurring in the digital estimation of probability density function maybe required in a variety of applied disciplines; eg. engineering, management and maintenance planning. In special, for such purposes, this paper studies the statistical errors in the computer estimation of probability density functions, by simulation of correlated and uncorrelated data. The estimate error, being composed of a random portion and a bias term is analyzed and applied to the cases of uniform and standard Gaussian density functions. Then further investigation is undertaken by employing simulated data with various conditions.