The Annals of Statistics

On Determining the Irrationality of the Mean of a Random Variable

Thomas M. Cover

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Abstract

A complexity approach is used to decide whether or not the mean of a sequence of independent identically distributed random variables lies in an arbitrary specified countable subset of the real line. A procedure is described that makes only a finite number of mistakes with probability one. This leads to some speculations on inference of the laws of physics and the computability of the physical constants.

Article information

Source
Ann. Statist., Volume 1, Number 5 (1973), 862-871.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176342507

Digital Object Identifier
doi:10.1214/aos/1176342507

Mathematical Reviews number (MathSciNet)
MR341687

Zentralblatt MATH identifier
0301.62028

JSTOR
links.jstor.org

Citation

Cover, Thomas M. On Determining the Irrationality of the Mean of a Random Variable. Ann. Statist. 1 (1973), no. 5, 862--871. doi:10.1214/aos/1176342507. https://projecteuclid.org/euclid.aos/1176342507


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