4.10 "Output" of a M/M/1 system In this problem you are asked to prove the important theorem of Section 4.10 for the case of a M/M/1 queueing system. Let a queueing system with a single server have Poisson arrivals at a rate lambda.gif (179
bytes), infinite queue capacity, and negative exponential service time with mean 1/mu.gif (189 bytes) (mu.gif (189 bytes) > lambda.gif (179 bytes)). Show that in the steady state the "output" stream leaving this queueing system is also Poisson at a rate lambda.gif (179

Hint: What is the pdf for the time between service completions when the server is continually busy?