Probabilistic type 2 Bernoulli and Euler polynomials

Assume that the moment-generating function of the random variable $Y$ exists in a neighborhood of the origin. The aim of this paper is to investigate the probabilistic type 2 Bernoulli polynomials associated with $Y$ and the probabilistic type 2 Euler polynomials associated with $Y$, along with the probabilistic type 2 cosine-Bernoulli polynomials associated with $Y$, the probabilistic type 2 sine-Bernoulli polynomials associated with $Y$, the probabilistic type 2 cosine-Euler polynomials associated with $Y$, and the probabilistic type 2 sine-Euler polynomials associated with $Y$. We deal with their properties, related identities and explicit expressions.