Question: When you push the SEND button on your cell phone, the phone attempts to set up a call by transmitting a SETUP message to a

When you push the SEND button on your cell phone, the phone attempts toset up a call by transmitting a SETUP message to a nearby base station. Thephone waits for a response and if none arrives within 0.5 seconds it tries again.If it doesnt get a response after N tries the phone stops transmitting andgenerates a busy symbol. Assume that all transmissions are independent andthat with probability p the SETUP message will get through. Also assume thatif the SETUP message gets through, the cell phone always correctly receivesthe response from the base station within 0.5 seconds.

a) What is the PMF of X, the number of times the SETUP message istransmitted in a call attempt?

b) What is the probability that the call will generate a busy signal?

c) Assuming that there is no limit on the number of tries, i.e., your phone willkeep transmitting the SETUP message indefinitely until it gets through,what is the PMF of X, the number of transmissions in a call attempt?

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