A delayed renewal process is similar to a renewal process, except that the c.d.f. \(G\) of the first renewal time \(T_{1}\) may be different from the common c.d.f. \(F\) of the inter-renewal times \(T_{n+1}-T_{n}, n=1,2, \ldots\). Show that for a delayed renewal process \(\left(N_{t}\right)\)

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E[N] GF(n-1)(t) E[N]==