  In this paper, we present a probabilistic extension of the Fubini polynomials
and numbers associated with a random variable satisfying some appropriate
moment conditions. We obtain the exponential generating function and an
integral representation for it. The higher order Fubini polynomials and
recurrence relations are also derived. A probabilistic generalization of a
series transformation formula and some interesting examples are discussed. A
connection between the probabilistic Fubini polynomials and Bernoulli, Poisson,
and geometric random variables are also established. Finally, a determinant
expression formula is presented.
