Probabilistic Degenerate Fubini Polynomials Associated with Random Variables

Let Y be a random variable such that the moment generating function of Y exists in a neighborhood of the origin. The aim of this paper is to study probabilistic versions of the degenerate Fubini polynomials and the degenerate Fubini polynomials of order r , namely the probabilisitc degenerate Fubini polynomials associated with Y and the probabilistic degenerate Fubini polynomials of order r associated with Y . We derive some properties, explicit expressions, certain identities and recurrence relations for those polynomials. As special cases of Y , we treat the gamma random variable with parameters α ,β > 0 α , β > 0 , the Poisson random variable with parameter α > 0 α > 0 , and the Bernoulli random variable with probability of success p .