Birds arrive at a birdfeeder according to a Poisson process at a rate of six per hour.

a. Draw the state-transition diagram, and write the associated differential equations for P(t) and for (t).

b. What is the expected time you would have to wait to see ten birds arrive?

c. What is the probability that the elapsed time between the second and third bird exceeds fifteen minutes?

d. If you have already waited five minutes for the first bird to arrive, what is the probability that the bird will arrive within the next five minutes?