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Generalization and Probabilistic Proof of a Combinatorial Identity

Guisong Chang and Chen Xu
The American Mathematical Monthly
Vol. 118, No. 2 (February 2011), pp. 175-177
DOI: 10.4169/amer.math.monthly.118.02.175
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.118.02.175
Page Count: 3
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Generalization and Probabilistic Proof of a Combinatorial Identity
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Abstract

Abstract In this note, we give a probabilistic proof of a combinatorial identity which involves binomial coefficients. Our results consist of showing that the identity essentially computes the moment of order n of the chi-square random variable with m degrees of freedom.

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