Abstract
The investigation of the role of independence in the classical SLLN leads to a natural generalization of the SLLN to the case where the random variables are 2-exchangeable; namely, let { X i : i ⩾ 1} be a sequence of random variables such that all ordered pairs ( X i , X j ), i ≠ j, are identically distributed. Then we show, among other things, that ▪ where X is in general a non-degenerate random variable. This provids a unified treatment of the SLLN for both exchangeable and pairwise independent random variables. We also show that, under 2-exchangeability, to preserve the Glivenko-Cantelli Theorem - sometimes refered to as the fundamental theorem of statistics - it is necessary that the random variables be pairwise independent.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
