On Some Classical Results in Probability Theory

Let$\{X_{i}\}$be a sequence of independent nondegenerate random variables. Let$S_{n}=\underset i=1\to{\overset n\to{\Sigma}}X_{i}$. In the following note we obtain an upper bound and a lower bound for$P\{\underset 1\leq i\leq n\to{{\rm max}}|S_{i}|>t\},t>0$. We then use these bounds to give si...

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Bibliographic Details
Published in:Sankhya. Series A 1985-06, Vol.47 (2), p.215-221
Main Author: Etemadi, N.
Format: Article
Language:English
Subjects:
Law of large numbers
Probability theory
Random variables
Online Access:Get full text
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Summary:Let$\{X_{i}\}$be a sequence of independent nondegenerate random variables. Let$S_{n}=\underset i=1\to{\overset n\to{\Sigma}}X_{i}$. In the following note we obtain an upper bound and a lower bound for$P\{\underset 1\leq i\leq n\to{{\rm max}}|S_{i}|>t\},t>0$. We then use these bounds to give simple proofs of some of the classical results including Kolmogorov-Feller theorem on the weak law of large numbers.
ISSN:0581-572X