On the conditional expectation E(X X + W) in the case of independent random variables X, W

Ehrhard Behrends

Statistics & Probability Letters, 1999, vol. 41, issue 4, 397-400

Abstract: Let X, W be independent real-valued random variables with finite expectation and E(W) = 0. We prove that only in the case W=0 the conditional expectation E(XX+W) coincides with X+W. The result is a consequence of the following cancellation theorem: Let P, Q, R be Borel probability measures on the real line such that the support of Q resp. R is contained in {x[less-than-or-equals, slant]0} resp. {x[greater-or-equal, slanted]0}; then P * Q = P * R implies that Q = R(=[delta]0).

Keywords: Conditional; expectation; Cancellation; Convolution; equation (search for similar items in EconPapers)
Date: 1999
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167-7152(98)00192-8
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:41:y:1999:i:4:p:397-400

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().