2014/05/10 by P. Vellaisamy, Vellaisamy, P.
Mathematics · Physics and Astronomy · #FOS: Mathematics #Primary 05A19 #Probability and Statistical Research #Secondary 60C99 #Statistical Distribution Estimation and Applications #Statistical Mechanics and Entropy #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1405.2399
openalex publication_date 2014/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.