Transforms

Allan Gut
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Allan Gut: Uppsala University, Department of Mathematics

Chapter Chapter III in An Intermediate Course in Probability, 1995, pp 60-101 from Springer

Abstract: Abstract In Chapter I 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. This result will be proved in the chapter on convergence; see Theorem VI.5.2.

Keywords: Characteristic Function; Independent Random Variable; Uniqueness Theorem; Moment Generate Function; Probability Generate Function (search for similar items in EconPapers)
Date: 1995
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4757-2431-8_4

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DOI: 10.1007/978-1-4757-2431-8_4

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