Motivated by control applications relying on shared resources (such as computation time or bandwidth), we analyze the stability and robustness of discrete-time switched linear systems driven by a stochastic process. The class of systems we study encompasses Markov Chain and independent and identically distributed switching processes. For these systems, we recall existing definitions of stability and robustness, by relying on the input-to-state (ISS) property. We show that, for the class of systems under concern, δ-moment stability is equivalent to its ISS counterpart and that they both imply almost sure ISS. Several sufficient conditions are provided to guarantee these properties. All the concepts are illustrated by the anytime control of a mechanical system.