Problem:
On a network router, packets arrive at an average rate of 5 every microsecond. A packet just came in now, hot off the Internet.
Question- Determine the probability that the next packet will arrive in 0.3 microseconds.
What if it was 0.7 microseconds? How about two whole microseconds? When would we expect an 85% probability of an arrival (give answer in microseconds, 9 digits of precision).
Please show all the calculations step by step.