Probability and Random Processes for Electrical and Computer Engineers, Second E

Question

Probability and Random Processes for Electrical and Computer Engineers, Second Edition

In the Internet, the TCP/IP protocol suite is used for transmitting packets of information. The receiving TCP entity checks the packets for errors. If an error is detected, it requests retransmission of the packet that is found to be in error. Suppose that the packet error probability is 10^-2. What is the probability that the third packet requires retransmission? What is the probability that the tenth packet requires retransmission? What is the probability that there is a packet retransmission within the first 5 packets? Following on the lines of (c), how many packets are required in order for the probability of retransmission to be equal to or greater than 0.1?

Explanation / Answer

Ans. a.
Third packet is retransmitted means it has failed three times. Therefore the probability is: 0.01 * 0.01 * 0.01 = 10^-6.

Ans. b.
Tenth packet is retransmitted means it has failed ten times. Therefore the probability is: 10^-20.

Ans. c.
Retransmission within within first 5 packets means there is at least one failed packet out of 5 packets i.e, = 1 - (0.99^5.)

Ans. d.
1-(0.99^x) = 0.1. Therefore, x = 2

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