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Mean, Variance and Transforms

  • Kai Lai Chung
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

The mathematical expectation of a random variable, defined in §4.3, is one of the foremost notions in probability theory. It will be seen to play the same role as integration in calculus—and we know “integral calculus” is at least half of all calculus. Recall its meaning as a probabilistically weighted average [in a countable sample space] and rewrite (4.3.11) more simply as:
$$E(X) = \mathop \Sigma \limits_\omega X(\omega )P(\omega )$$
(6.1.1)
.

Keywords

Power Series Independent Random Variable Mathematical Expectation Expected Number Multinomial Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1974

Authors and Affiliations

  • Kai Lai Chung
    • 1
  1. 1.Department of MathematicsStanford UniversityStanfordUSA

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