49. Consider a renewal process having the gamma (n,) interarrival distribution, and let Y(t) denote the time

49. Consider a renewal process having the gamma (n,λ) interarrival distribution, and let Y(t) denote the time from t until the next renewal. Use the theory of semi-Markov processes to show that lim t→∞ P{Y(t) < x} =

1 n

n i=1 Gi,λ(x)

where Gi,λ(x) is the gamma (i,λ) distribution function.