(a) Draw a tree diagram that describes the call set up procedure. (b) If all transmissions are independent and the probability is “p” that a set-up 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 this goal ?
When someone presses SEND on a cellular phone, the phone attempts to set up a call by
transmitting a “set-up” message to a nearby base station. The phone waits for a response and if
none arrives with 0.5 second, it tried 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 set up procedure.
(b) If all transmissions are independent and the probability is “p” that a set-up 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 this goal ?
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