a. Explanation Given info: There were a total of 100 packets. The probability of losing a data packet is 1%. Packet losses are independent events. Calculation: The random variable X denotes that number of data packets that are re-sent. Criteria for binomial distribution: Each experiment has fixed number of trials Each trial is independent of the other There are two possible outcomes. They are success and failure. Probability of success is same for all trials. Here, the number of trials ( n = 100 ) is fixed. Hence, the first condition is satisfied. The trials are independent. Hence, the second condition is satisfied. There are two outcomes, losing a data packet (success) or not losing a data packet(failure). Hence, the third condition is satisfied. The probability of losing a data packet is 1%. Therefore P ( losing a data packet ) = 1 % = 0.01 . That is, P ( Success ) = 0.01 . There is a fixed probability of losing a data packet. Hence, the fourth condition is also satisfied. Thus, it is a binomial experiment. Therefore, X follow binomial distribution with parameters n = 100 and p = 0.01 . The probability of obtaining X successes in n independent trails of a binomial experiment is, f ( x ) = P ( X = x ) = ( n x ) p x ( b. To determine Compute the probability that at least one packet must be re-sent. c. To determine Compute the probability that two or more packets must be re-sent. d. To determine Compute the mean and standard deviation of the number of packets that must be re-sent. e. To determine Find the probability that at least one message requires that two or more packets be re-sent.

Applied Statistics and Probability for Engineers

6th Edition

ISBN: 9781118539712

Author: Douglas C. Montgomery

Publisher: WILEY

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Chapter 3, Problem 180SE

To determine

Find the distribution of data packets must be re-sent and include the parameter values.

To determine

Compute the probability that at least one packet must be re-sent.

To determine

Compute the probability that two or more packets must be re-sent.

To determine

Compute the mean and standard deviation of the number of packets that must be re-sent.

To determine

Find the probability that at least one message requires that two or more packets be re-sent.

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Chapter 3, Problem 179SE

Chapter 3, Problem 181SE

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Chapter 3 Solutions

Applied Statistics and Probability for Engineers

Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.2 - 3-16. The sample space of a random experiment is...Ch. 3.2 - For Exercises 3-17 to 3-21, verify that the...Ch. 3.2 - For Exercises 3-17 to 3-21, verify that the...Ch. 3.2 - For Exercises 3-17 to 3-21, verify that the...Ch. 3.2 - For Exercises 3-17 to 3-21, verify that the...Ch. 3.2 - For Exercises 3-17 to 3-21, verify that the...Ch. 3.2 - 3-22. Consider the hospital patients in Example...Ch. 3.2 - 3-23. An article in Knee Surgery, Sports...Ch. 3.2 - Prob. 24E Ch. 3.2 - Prob. 25E Ch. 3.2 - 3-26. The space shuttle flight control system...Ch. 3.2 - 3-27. A disk drive manufacturer sells storage...Ch. 3.2 - 3-28. 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