I have 100 computers on a network.
Using the Poisson Process, the network is expected to generate a message 6 times a minute.
With this information, if I were to take 50 computers off of the network, can I say the new Expected Value is 3 messages per minute?
Assuming the computers act all independently with the according to identical Poisson processes, then the average waiting time until the next event for each computer is $1000s$, so the combined waiting time for $100$ computers is $10s$. By the same reasoning the combined waiting time for $50$ computers is $20s$ or 3 events per minute.