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Probabilistic aspects of Bernstein polynomials. (English) Zbl 1131.60007

In this paper, we describe different approaches to construct the basic Bernstein polynomials family and establish relation between the polynomials and geometrical probability. We give conditions under which the Bernstein curves acquire properties of probability density function of random variables. This demonstrates the geometrical nature of the Bernstein polynomials computational efficiency in solving problems of function approximation. Finally, we obtain formulas for computing expectation, standard deviation, and the skewness coefficient.

MSC:

60D05 Geometric probability and stochastic geometry
41A10 Approximation by polynomials
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