Consider a delayed renewal process {N(t), t 0} whose first interarrival has distribution G and the others have distribution F Let m(1): E[ND(t)]

(a) Prove that m(t) = G(t) + fm(1 x) dG(x), - where m(t) == Fn(t)

(b) Let A,(t) denote the age at time Show that if F is nonlattice with fx dF(x) and tG(t) 0 as t , then E[AD()] Sx dF(x) 2fxdF(x) ->

(c) Show that if G has a finite mean, then tG(t) 0 as o