stem Down Time. Consider an alternating renewal process that represents the up and down states of a system. Suppose the up times have a distribution G with mean μ and variance σ 2 , and the down times...

stem Down Time. Consider an alternating renewal process that represents the up and down states of a system. Suppose the up times have a distribution G with mean μ and variance σ², and the down times have a distribution G0 with mean μ0 and variance σ2 0. Let D(t) denote the length of time the system is down in the time interval [0, t]. Find the average expected down time β = limt→∞ t −1E[D(t)]. Then show (D(t) − βt)/t^1/2 d → N(0, γ2) and specify γ.