In this paper, we consider a sub-optimal off-line stochastic scheduling of a single sensor that visits (measures) one site, modeled as a discrete-time linear time-invariant (DTLTI) dynamic system, at each time instant with the objective to minimize certain measure of the estimation error. The objective of this paper is to search the optimal probability distributions under two cost functions. We show that the optimal scheduling distribution is computable by solving a quasi-convex optimization problem in the case we focus on the minimization of maximal estimate error among sites. When the cost function is the average estimate error of all sites, the scheduling problem for a set of special DTLTI systems can be casted and efficiently solved as a convex optimization problem by exploiting the structure of the underlying Riccati-like equation. Furthermore, we propose a deterministic scheduling strategy based on the optimal stochastic one. Finally, we show some simulation results to verify our strategies.