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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
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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 

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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