A RANDOM VARIABLE WITH ZETA FUNCTION CONNECTIONS
Keywords:
random variables, zeta function, moment generating function, combinatoricsDOI:
https://doi.org/10.17654/0973563125004Abstract
We present an example of a particularly simple discrete random variable with surprisingly rich connections with calculus ($p$-series, specifically zeta values, and recursive integral calculations) and combinatorics (the binomial coefficients which will appear alongside the zeta values in the expansion of the moment generating function). We believe that our example could be used in the undergraduate probability class, as a bridge-building experience between probability theory and the traditionally related areas of calculus and combinatorics.
Received: January 7, 2025
Accepted: February 22, 2025
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Kenneth H. Rosen, Discrete Mathematics and its Applications, 8th ed., McGraw Hill Education, 2019.
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