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

Income Stake 

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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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