Q1) 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) 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? (b) What is the probability that the phone will generate a busy signal? (c) 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?
Q1) 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) 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? (b) What is the probability that the phone will generate a busy signal? (c) 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?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.CR: Chapter 12 Review
Problem 84CR
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Transcribed Image Text:Q1) 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) 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?
(b) What is the probability that the phone will generate a busy signal?
(c) 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?
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