The purpose of this problem is to illustrate that for an arrival process with independent but not identically distributed interarrival intervals, X 1 , X 2 , . . . , the number of arrivals N(t) in the...

The purpose of this problem is to illustrate that for an arrival process with independent but not identically distributed interarrival intervals, X₁, X₂, . . . , the number of arrivals N(t) in the interval (0,t] can be a defective rv. In other words, the ‘counting process’ is not a stochastic process according to our definitions. This illustrates that it is necessary to prove that the counting rv’s for a renewal process are actually rv’s.