Geodesic
Dependent Random Variables with Independent Subsets - II
Canadian mathematical bulletin, Tome 33 (1990) no. 1, pp. 24-28

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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.
DOI : 10.4153/CMB-1990-004-6
Mots-clés : 60E05, Random variables, pairwise independence, independence, joint distribution, marginal distributions 
Wang, Y. H. Dependent Random Variables with Independent Subsets - II. Canadian mathematical bulletin, Tome 33 (1990) no. 1, pp. 24-28. doi: 10.4153/CMB-1990-004-6
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     author = {Wang, Y. H.},
     title = {Dependent {Random} {Variables} with {Independent} {Subsets} - {II}},
     journal = {Canadian mathematical bulletin},
     pages = {24--28},
     year = {1990},
     volume = {33},
     number = {1},
     doi = {10.4153/CMB-1990-004-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1990-004-6/}
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