(a)
Compute probability the wait time for a Bundle is at most 1 hr:
(b)
Erlang distribution:
Desired probability:
This integral requires iterated IBP.
(c)
The results disagree. Method 2 is the correct approach assuming individual calls arrive according to a Poisson process.
It turns out that if you have some Poisson process, bundles of arrivals do not themselves follow a Poisson process.
Think of a Poisson process as some dots scattered on a timeline. Place a heavy dot at the location of each