In this paper, we obtain an expectation formula with respect to the $q$-probability distribution $W(x,y;q)$ based on a Maclaurin expansion. The formula has many applications in mathematics. Some of the applications are also given, which include a probability version of the Al-Salam and Verma $q$-integral.
"An Expectation Formula Based on a Maclaurin Expansion." Taiwanese J. Math. 23 (3) 563 - 574, June, 2019. https://doi.org/10.11650/tjm/180802