On Probabilistic Proofs of Certain Binomial Identities

This short note gives a simple statistical proof of a binomial identity, by evaluating the Laplace transform of the maximum of n independent exponential random variables in two different ways. As a by-product, we obtain a rigorous proof of an interesting result concerning the exponential distributio...

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Bibliographic Details
Published in:The American statistician 2015-07, Vol.69 (3), p.241-243
Main Author: Vellaisamy, P.
Format: Article
Language:English
Subjects:
Binomial identities
Binomial inversion
Exponential variates
Laplace transform
Laplace transforms
Probabilistic proofs
Probability
Random variables
Short Technical Note
Statistics
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Summary:This short note gives a simple statistical proof of a binomial identity, by evaluating the Laplace transform of the maximum of n independent exponential random variables in two different ways. As a by-product, we obtain a rigorous proof of an interesting result concerning the exponential distribution. The connections between a probabilistic approach and our approach are discussed. In the process, several new binomial identities are also obtained.
ISSN:0003-1305
1537-2731
DOI:10.1080/00031305.2015.1056381