Let N(t) denote a renewal process with inter-renewal distribution F and consider the number of renewals N(T ) in an interval (0, T ] forsome random time T independent of N(t). For instance, N(T )...

Let N(t) denote a renewal process with inter-renewal distribution F and consider the number of renewals N(T ) in an interval (0, T ] forsome random time T independent of N(t). For instance, N(T ) might represent the number of customers that arrive at a service station during a servicetime T . Find general expressions for the mean and distribution of N(T ).Evaluate these expressions for the case in which T has an exponential distribution with rate μ and F = G2, where G is an exponential distributionwith rate λ.