On Probabilistic Proofs of Certain Binomial Identities

P. Vellaisamy

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arXiv · 1405.2399

On Probabilistic Proofs of Certain Binomial Identities

P. Vellaisamy

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Abstract

We give 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 simple proof of an interesting result concerning the exponential distribution. The connections between a probabilistic approach and the statistical approach are discussed, which explains why certain binomial identities admit probabilistic interpretations. In the process, several new binomial identities are also obtained and discussed.

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P. Vellaisamy. 2014-05-10. On Probabilistic Proofs of Certain Binomial Identities. https://arxiv.org/abs/1405.2399

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