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Dependent Random Variables with Independent Subsets - II

Published online by Cambridge University Press:  20 November 2018

Y. H. Wang
Y. H. Wang*
Affiliation:
Concordia University, Montreal, Québec, H3G 1M8
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Abstract

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In this paper, we consolidate into one two separate problems - dependent random variables with independent subsets and construction of a joint distribution with given marginals. Let N = {1,2,3,...} and X = {Xn; n ∊ N} be a sequence of random variables with nondegenerate one-dimensional marginal distributions {Fn; n ∊ N}. An example is constructed to show that there exists a sequence of random variables Y = {Yn; n ∊ N} such that the components of a subset of Y are independent if and only if its size is ≦ k, where k ≧ 2 is a prefixed integer. Furthermore, the one-dimensional marginal distributions of Y are those of X.

Keywords

60E05Random variablespairwise independenceindependencejoint distributionmarginal distributions
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 1 , 01 March 1990 , pp. 24 - 28
Copyright
Copyright © Canadian Mathematical Society 1990

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