Journal Article10.2307/1292174
An Introduction to Probability Theory and its Applications, Volume I
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About: This article is published in AIBS Bulletin. The article was published on 01 Jan 1958. The article focuses on the topics: Law of the unconscious statistician & Convolution of probability distributions.
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Citations
Second order tail effects
Casper G. de Vries
- 01 Apr 2000
Abstract: • A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers.
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A graphical approach for verification of the central limit theorem
Suresh Kumar Veluchamy
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TL;DR: In this article, a graphical approach for verifying the Central Limit Theorem (CLT) is presented. But, the approach is limited to the case where the distribution of the sample mean is known to be normal.
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Hannu Sakari Lyyjynen
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References
Co-integration and Error Correction: Representation, Estimation and Testing
TL;DR: The relationship between co-integration and error correction models, first suggested in Granger (1981), is here extended and used to develop estimation procedures, tests, and empirical examples.
Quantum Computation and Quantum Information
Michael A. Nielsen,Isaac L. Chuang +1 more
- 01 Dec 2010
TL;DR: This chapter discusses quantum information theory, public-key cryptography and the RSA cryptosystem, and the proof of Lieb's theorem.
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Class-based n -gram models of natural language
Peter Fitzhugh Brown,Peter Vincent Desouza,Robert Leroy Mercer,Vincent J. Della Pietra,Jenifer C. Lai +4 more
TL;DR: This work addresses the problem of predicting a word from previous words in a sample of text and discusses n-gram models based on classes of words, finding that these models are able to extract classes that have the flavor of either syntactically based groupings or semanticallybased groupings, depending on the nature of the underlying statistics.
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•Book
Lectures on the Combinatorics of Free Probability
Alexandru Nica,Roland Speicher +1 more
- 11 Sep 2006
TL;DR: In this article, the authors present a case study of non-normal distribution and non-commutative joint distributions and define a set of basic combinatorics, such as non-crossing partitions, sum-of-free random variables, and products of free random variables.
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Random Graphs and Complex Networks
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TL;DR: This chapter explains why many real-world networks are small worlds and have large fluctuations in their degrees, and why Probability theory offers a highly effective way to deal with the complexity of networks, and leads us to consider random graphs.
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