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Mean Values and Variances

  • Erling B. Andersen
  • Niels-Erik Jensen
  • Nils Kousgaard

Abstract

Let X be a discrete random variable with a finite or countable sample space 5 and with point probabilities f(x). The mean value or the mathematical expectation E[X] of X is defined as
$${\rm{E}}[{\rm{X}}] = \sum\limits_{{\rm{x}} \in {\rm{S}}} {{\rm{xf}}({\rm{x}}),}$$
(5.1)
i.e. as a weighted sum of the elements of the sample space with the corresponding probabilities as weights. The mean value of X can be interpreted as a long run average of the outcomes of an experiment with sample space S and probability f(x) of the outcome x. This is illustrated in the following example.

Keywords

Sample Space Central Moment Discrete Case Point Probability Dispersion Measure 
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-Verlag Berlin · Heidelberg 1987

Authors and Affiliations

  • Erling B. Andersen
    • 1
  • Niels-Erik Jensen
    • 1
  • Nils Kousgaard
    • 1
  1. 1.Institute of StatisticsUniversity of CopenhagenCopenhagen KDenmark

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