Consider a taxi depot where taxi and customers arrive independently in accordance with Possion processes with respective rates of three and seven per minute. A taxi will wait no matter how many other taxis are present. However, if an arriving customers does not find a taxi waiting, he leaves. (Assuming the sources of taxi and customers are unlimited)

(i) What is the probability that no customers and no taxis arrive in the next minute?

(ii) On average, how many taxi are waiting?

(iii) How long on average would a taxi need to wait for a customer?