*35. Satellites are launched according to a Poisson process with rate . Each satellite will, independently, orbit...

*35. Satellites are launched according to a Poisson process with rate

λ. Each satellite will, independently, orbit the earth for a random time having distribution F. Let denote the number of satellites orbiting at time t.

(a) Determine Image.
Hint: Relate this to the queue.

(b) If at least one satellite is orbiting, then messages can be transmitted and we say that the system is functional.
If the first satellite is orbited at time Image, determine the expected time that the system remains functional.
Hint: Make use of part

(a) whenI mage.