Answer to Question #30157 in Statistics and Probability for mahtab.ruhi

Question

5. In a taxi stand there is space for only five taxicabs. Taxis arrive in a Poisson
process with rate 12 per hour. If there is no waiting room, arriving taxis leave
without passengers. Customers arrive at the taxi stand in a Poisson process once
every 6 minutes on average.
(a) Determine the limiting distribution of the number of customers waiting
for taxis.
(b) What is the probability that there are taxis waiting for customers?
(c) Determine the mean waiting time for a customer.