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A congested computer network has a 1% chance of losing a
Chapter 3, Problem 180SE(choose chapter or problem)
Problem 180SE
A congested computer network has a 1% chance of losing a data packet, and packet losses are independent events. An e-mail message requires 100 packets.
(a) What distribution of data packets must be re-sent? Include the parameter values.
(b) What is the probability that at least one packet must be re-sent?
(c) What is the probability that two or more packets must be re-sent?
(d) What are the mean and standard deviation of the number of packets that must be re-sent?
(e) If there are 10 messages and each contains 100 packets, what is the probability that at least one message requires that two or more packets be re-sent?
Questions & Answers
QUESTION:
Problem 180SE
A congested computer network has a 1% chance of losing a data packet, and packet losses are independent events. An e-mail message requires 100 packets.
(a) What distribution of data packets must be re-sent? Include the parameter values.
(b) What is the probability that at least one packet must be re-sent?
(c) What is the probability that two or more packets must be re-sent?
(d) What are the mean and standard deviation of the number of packets that must be re-sent?
(e) If there are 10 messages and each contains 100 packets, what is the probability that at least one message requires that two or more packets be re-sent?
ANSWER:
Solution
Step 1 of 5
a) We have to find the distribution of data packets must be resent
Given that there is a 1% probability of losing the data packet
E-mail message required 100 packets
Here n=100 and p=0.01
Let X be the no.of packets must be resent
Here
Hence the distribution of packets must be resent is binomial distribution with parameters n=100 and p=0.01