A RANDOM VARIABLE WITH ZETA FUNCTION CONNECTIONS

We present an example of a particularly simple discrete random variable with surprisingly rich connections with calculus (-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.