  Let Y be a random variable whose moment generating function exists in some
neighborhood of the origin. The aim of this paper is to study the probabilistic
Lah numbers associated with Y and the probabilistic Lah-Bell polynomials
associated with Y, as probabilistic versions of the Lah numbers and the
Lah-Bell polynomials, respectively. We derive some properties, explicit
expressions, recurrence relations and certain identities for those numbers and
polynomials. In addition, we treat the special cases that Y is the Poisson
random variable with parameter {\alpha} > 0 and the Bernoulli random variable
with probability of success p.
