  The aim of this paper is to study probabilistic versions of the degenerate
Whitney numbers of the second kind and those of the degenerate Dowling
polynomials, namely the probabilistic degenerate Whitney numbers of the second
kind associated with Y and the probabilistic degenerate Dowling polynomials
associated with Y. Here Y is a random variable whose moment generating function
exists in some neighborhood of the origin. We derive some properties, explicit
expressions, certain identities, recurrence relations and generating functions
for those numbers and polynomials. In addition, we investigate their
generalizations, namely the probabilistic degenerate r-Whitney numbers of the
second kind associated with Y and the probabilistic degenerate r-Dowling
polynomials associated with Y, and get similar results to the aforementioned
numbers and polynomials.
