@article{Hu2025, 
author = {Qiuxia Hu and Bilal Khan and Serkan Araci},
title = {Expectation formulas for    q-probability distributions: a new extension via Andrews-Askey integral},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {1},
pages = {1448-1462},
keywords = {q-Chu-Vandermonde formula, the probability distribution W(x, y; q), basic hypergeometric series, q-integral},
url = {https://www.sciopen.com/article/10.3934/math.2025067},
doi = {10.3934/math.2025067},
abstract = {In this paper, we utilize the    q-Chu-Vandermonde formula to derive a novel expectation formula for the    q-probability distribution    W  (  x  ,  y  ;  q  ), extending previously known results. Several applications are presented, including a broader generalization of the Andrews-Askey integral. Although fractional    q-calculus is not directly employed in this work, its potential for future extensions is discussed, as non-integer order derivatives and integrals could offer deeper insights into    q-series and probability distributions.}
}