Part of the Springer Texts in Statistics book series (STS)


In Chapter 1 we learned how to handle transformations in order to find the distribution of new (constructed) random variables. Since the arithmetic mean or average of a set of (independent) random variables is a very important object in probability theory as well as in statistics, we focus in this chapter on sums of independent random variables (from which one easily finds corresponding results for the average). We know from earlier work that the convolution formula may be used but also that the sums or integrals involved may be difficult or even impossible to compute. In particular, this is the case if the number of summands is “large.” In that case, however, the central limit theorem is (frequently) applicable.


Characteristic Function Independent Random Variable Uniqueness Theorem Moment Generate Function Probability Generate Function 
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Copyright information

© Springer-Verlag New York 2009

Authors and Affiliations

  1. 1.Department of MathematicsUppsala UniversityUppsalaSweden

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