Let {Zt; t = 0, ± 1, ···} be a pure white noise process with γ = E{|Z1|δ}< ∞ for some δ > 0. Assume that the characteristic function (ch.f.) ϕ0 of Z1 is Lebesgue-integrable over (—∞, ∞). Let {gv;v = 0, 1, 2, ···, g0 = 1} be a sequence of real numbers such that where λ = δ(1 + δ)−1. Define , where the identity is to be understood in the sense of convergence in distribution. Then {Xt; t = 0, ± 1, ···} is a strongly mixing stationary process in the sense that if is the σ-fìeld generated by the random variables (r.v.) Xa, ···, Xb then for any where M is a finite positive constant which depends only on ϕ0 and

Sharp upper and lower bounds for the variance of a non-negative function of a non-negative random variable are obtained under rather weak hypotheses regarding the function. Comparisons between bounds are made and some specific examples are considered.

Necessary and sufficient conditions are found for a triangular array (finite or infinite) to be expected values of order statistics. The conditions are a wellknown recurrence relation, and a moment condition.

Bounds are obtained for the limiting distribution of the delay in queue for a GI/G/1 system via Martingale theory. These bounds are somewhat stronger than similar bounds recently obtained by Kingman. Simplifications of the bounds are obtained in the special cases where the service distribution is either IFR, DFR, NBU or NWU.