Problem 2. 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 0.3 seconds, it tries again. If it doesn't get a response after n= 4 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 that a SETUP message will get through is p, what is the PMF of K, the number of messages transmitted in a call attempt? (c) As a manager of a cellular phone system, you want the probability of a busy signal to be less than 0.01. If p = 0.8, what is the minimum value of n necessary to achieve that goal? (d) Find and sketch the CDF of N, the number of attempts made by the cellular phone for p=1/3
Problem 2. 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 0.3 seconds, it tries again. If it doesn't get a response after n= 4 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 that a SETUP message will get through is p, what is the PMF of K, the number of messages transmitted in a call attempt? (c) As a manager of a cellular phone system, you want the probability of a busy signal to be less than 0.01. If p = 0.8, what is the minimum value of n necessary to achieve that goal? (d) Find and sketch the CDF of N, the number of attempts made by the cellular phone for p=1/3
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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