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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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| Published in: | Sankhya. Series A 1985-06, Vol.47 (2), p.215-221 |
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| Format: | Article |
| Language: | English |
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| container_end_page | 221 |
| container_issue | 2 |
| container_start_page | 215 |
| container_title | Sankhya. Series A |
| container_volume | 47 |
| creator | Etemadi, N. |
| description | 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. |
| format | article |
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| fulltext | fulltext |
| identifier | ISSN: 0581-572X |
| ispartof | Sankhya. Series A, 1985-06, Vol.47 (2), p.215-221 |
| issn | 0581-572X |
| language | eng |
| recordid | cdi_jstor_primary_25050536 |
| source | JSTOR Archival Journals and Primary Sources Collection |
| subjects | Law of large numbers Probability theory Random variables |
| title | On Some Classical Results in Probability Theory |
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