Conditional Moments and Independence

Aureo de Paula

PIER Working Paper Archive from Penn Institute for Economic Research, Department of Economics, University of Pennsylvania

Abstract: Consider two random variables X and Y. In initial probability and statistics courses, a discussion of various concepts of dissociation between X and Y is customary. These concepts typically involve independence and uncorrelatedness. An example is shown where E(Y^n|X) = E(Y^n) and E(X^n|Y) = E(X^n) for n = 1, 2,… and yet X and Y are not stochastically independent. The bi-variate distribution is constructed using a well-known example in which the distribution of a random variable is not uniquely determined by its sequence of moments. Other similar families of distributions with identical moments can be used to display such a pair of random variables. It is interesting to note in class that even such a degree of dissociation between the moments of X and Y does not imply stochastic independence. and yet X and Y are not stochastically independent. The bi-variate distribution is constructed using a well-known example in which the distribution of a random variable is not uniquely determined by its sequence of moments. Other similar families of distributions with identical moments can be used to display such a pair of random variables. It is interesting to note in class that even such a degree of dissociation between the moments of X and Y does not imply stochastic independence.

Keywords: indeterminate distributions; moments; independence (search for similar items in EconPapers)
JEL-codes: A2 C00 (search for similar items in EconPapers)
Pages: 7 pages
Date: 2008-03-07
New Economics Papers: this item is included in nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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Journal Article: Conditional Moments and Independence (2008)
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