**Question 1:**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?

Answered: Image /qna-images/answer/90f9667a-5240-44fc-bfc8-981e2b2b59b3.jpg

Answered: Q1) When someone presses SEND on a…

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...

See similar textbooks

Similar questions

Suppose that each time Bar-bie throws a dart, she has a 3/4 probability of getting a bullseye. If Barbie shoots three darts, what is the probability that she gets a bullseye on at least two of them?
The probability of an integrated circuit passing a quality test is F. In a batch of 10 integrated circuits find the probabilities thati. 2 will failii. 8 will passiii. at least 2 will failiv. fewer than 2 will fail.
In a specific type of electronic card, the probability of a transistor being defective is 0.01. Let's assume there are 200 transistors on the electronic card. If there are no defective transistors, the electronic card is considered to be functioning. What is the probability of any electronic card not functioning?
Assume that we have three coins: The first coin is fair. The second coin is unfair with probability of heads equal to 0.8. The third coin is also unfair with probability of heads equal to 0.3. Consider an experiment involving two successive coin tosses. The result of the first stage of the experiment is determined by the toss of the fair coin. The result of the second stage of the experiment is determined by the toss of a coin, but suppose that the coin that is used depends upon the result of the toss of the fair coin. Specifically, if the toss of the fair coin results in heads, then the second coin is tossed. Otherwise the third coin is tossed. Let Hi and Ti be the events that ith toss resulted in heads and tails, respectively. Answer the following questions. a) Give a sequential description of the experiment using a tree diagram. b) Calculate the probabilities of the possible outcomes of the experiment. c) Calculate P(H2) d) Are the events H1 and H2 independent? Justify…
Jack has just been given a ten-question multiple choice quiz in history class. Each question has five answers, of which only one is correct. Since Jack has not attended class recently, he does not know any of the answers. Assuming Jack guesses randomly on all ten questions, find the probability that he will answer six or more of the questions correctly and avoid an F.
(b) Test two independent circuits one after the other. On each test, the possible outcome is either overvoltage (0) or undervoltage (U). Assume that all circuits are overvoltage with probability 0.4. Let X be the number of overvoltage circuit in the first test and Y be the number of overvoltage circuit before you observed undervoltage. If both circuit is overvoltage or undervoltage, Y = 2. Find the joint PMF of X and Y.
Do question 2
Suppose that if person with tuberculosis is given a TB screening, the probability that his or her condition will be detected is 0.90. If a person without tuberculosis is given a TB screening , the probability that he or she will be diagnosed incorrectly as having tuberculosis is 0.3. Suppose, further, that 11% of the adult residents of a certain city have tuberculosis. If one of these adults is diagnosed as having tuberculosis based on the screening, what is the probability that he or she actually has tuberculosis?
A university computer laboratory installs one of three operating systems on each computer used in the lab. It is known from product testing that during an hour of web browsing the probability a computer with system 1 installed will crash is 0.15, the probability of a computer with operating system 2 crashing is 0.08 and the probability of a computer with system 3 crashing is 0.1. Operating systems 1 and 3 are installed on the same number of computers while system 2 is installed on twice as many computers as system 1 (or system 3).a) What is the probability that a randomly selected computer crashes during an hour of web browsing?b) If a computer selected at random crashed during an hour of browsing the web, what is the probability it has operating system 2 installed?c) If a computer selected at random does not crash during an hour of web browsing what is the probability it has operating system 1 or operating system 2 installed?
Suppose that on any given day, there is a 20% chance that Lebron has a bad day, a 50% day that Lebron has a so-so day, and a 30% chance that Lebron has a good day. On a bad day, the probability that Lebron makes any given 3-point shot is 0.5. On a so-so day, the probability that Lebron makes any given 3-point shot is 0.7. On a good day, the probability that Lebron makes any given 3-point shot is 0.9. Suppose that tomorrow, Lebron takes a 3-point shot, and we record whether he hits or misses and what kind of day he was having. What is the probability that Lebron hits? What is the probability that if Lebron is having a bad day given that he misses a shot that day?
Assume that we have three coins: The first coin is fair. The second coin is unfair with probability of heads equal to 0.8. The third coin is also unfair with probability of heads equal to 0.3. Consider an experiment involving two successive coin tosses. The result of the first stage of the experiment is determined by the toss of the fair coin. The result of the second stage of the experiment is determined by the toss of a coin, but suppose that the coin that is used depends upon the result of the toss of the fair coin. Specifically, if the toss of the fair coin results in heads, then the second coin is tossed. Otherwise the third coin is tossed. Let H, and T, be the events that ith toss resulted in heads and tails, respectively. Answer the following questions. Calculate P(H,). Are the events H, and H, independent? Justify your answer analytically.

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS