Can a finite number of discrete delays approximate stochastic delay?

In stability analysis and control design for a system with stochastic delay, it is a question whether one can approximate the stochastic system, for instance in the sense of average, with a deterministic system that has a finite number of discrete delay terms with the same delays that appear in the stochastic system and the weight coefficients of these delayed terms are taken from the probability distribution function of the stochastic delay. In this note, we consider a linear system with stochastic delay and discuss conditions under which this approximation is valid and conditions where it is not. In particular, we assume that the delay has piece-wise constant realizations with constant dwelling time at each value and show that the above mentioned approximation loses its grounds when the delay dwelling time gets larger than the minimum delay in the system.