I believe these two statements are true:
If interarrival times follow an exponential distribution, then the number of arrivals in time period T can be described by the Poisson process.
Likewise, if the number of arrivals in time period T follows a Poisson process then the interarrival time is an exponential RV.
Are these two statements effectively 2 sides of the same coin? can someone explain why or why not?
