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Statistical Methods for Fuzzy Data by Reinhard Viertl

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22.4 Problems

a. Let π*(·) be a fuzzy density on r whose δ-level functions are all integrable functions with finite integral, i.e.

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Prove that all marginal densities

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are fuzzy densities.

b. Explain that the definition of the expectation of a fuzzy probability density f*(·) specializes to the classical expectation for classical densities f(·) with existing expectation.

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