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The basics of computer algebra and the language of Mathematica are described in this textbook, leading towards an understanding of Mathematica that allows the reader to solve problems in physics, mathematics, and chemistry.
The expectation for for a discrete distribution is the PDF-weighted sum :. The probability of for a discrete univariate distribution is given by the PDF:. Substitution of invalid values into symbolic outputs can give results that are not meaningful:. The PDF of a distribution whose measure is incompatible with the Lebesgue measure or counting measure on the integer lattice may not evaluate or may give an incorrect result:.
The result of the PDF is not normalized:. The distribution measure has an atom at the origin, and hence is incompatible with the Lebesgue measure:. The incompatibility manifests itself in a jump discontinuity of the CDF at the atom location:.
Mixed distributions are fully supported by Expectation , Probability , RandomVariate , etc.
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