Every random variable satisfies a certain nontrivial integrability condition
We show that every random variable X fulfills a certain nontrivial integrability condition, in the sense that there always exists a nonnegative function g--depending on X--growing to [infinity] as x-->[infinity], and such that Eg(X)<[infinity]. Refinements of this universal property allow us to give some simple but striking statements in connection with Markov's inequality and the central limit theorem.
Year of publication: |
2006
|
---|---|
Authors: | Adell, José A. ; Lekuona, Alberto |
Published in: |
Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 76.2006, 15, p. 1603-1606
|
Publisher: |
Elsevier |
Keywords: | Integrability Markov's inequality Central limit theorem |
Saved in:
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