Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-30T23:22:00.270Z Has data issue: false hasContentIssue false
  • English
  • Français

An extension of a lemma of Wald

Published online by Cambridge University Press:  14 July 2016

H. Robbins  and
E. Samuel
H. Robbins
Affiliation:
Columbia University, New York
E. Samuel
Affiliation:
Hebrew University, Jerusalem
Get access Rights & Permissions [Opens in a new window]

Extract

We define a natural extension of the concept of expectation of a random variable y as follows: M(y) = a if there exists a constant − ∞ ≦ a ≦ ∞ such that if y1, y2, … is a sequence of independent identically distributed (i.i.d.) random variables with the common distribution of y then

Type
Short Communications
Information
Journal of Applied Probability , Volume 3 , Issue 1 , June 1966 , pp. 272 - 273
Copyright
Copyright © Sheffield: Applied Probability Trust 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Blackwell, D. (1946) On an equation of Wald. Ann. Math. Statist. 17, 84–87.Google Scholar
[2] Derman, C. and Robbins, H. (1955) On the strong law of large numbers when the first moment does not exist. Proc. Nat. Acad. Sci. 41, 586–587.Google Scholar