BIRTH AND DEATH PROCESS

Aircraft request permission to land at a single-runway airport on an average of one every 5 min; the actual distribution appears to be Poisson. Planes are landed on a first-come, first-served basis, with those not able to land immediately due to traffic congestion put in a holding pattern. The time required by the traffic controller to land a plane varies with the experience of the pilot; it is exponentially distributed, with a mean of 3 min

a) Determine the probability that one plane is granted permission to land. Answer in 2 decimal places.

b) Determine the generating function F(z). Give the value or term of the numerator_________and the value or term of the denominator________

c) What is the probability of two planes were required permission to land. Answer in 3 decimal places.

d) What is the average number of planes that were required permission to land but are still in motion. Answer in 1 decimal place.

e) Determine the average number of planes in a holding pattern. Answer in 1 decimal place.