When someone presses "SEND" on a cellular phone, the phone attempts to set up a call by transmitting a "SETUP" message to a nearby base station. The phone waits for a response and if none arrives within 0.5 seconds it tries again. If it doesn't get a response after n = 6 tries the phone stops transmitting messages and generates a busy signal.
(a) Draw a tree diagram that describes the call setup procedure.
(b) If all transmissions are independent and the probability is p that a "SETUP" message will get through, what is the PMF of K, the number of messages transmitted in a call attempt?
(c) What is the probability that the phone will generate a busy signal?
(d) As manager of a cellular phone system, you want the probability of a busy signal to be less than 0.02 If p = 0.9, what is the minimum value of n necessary to achieve your goal?