1. Suppose that packets of size 8000 bytes are transmitted over a link which has
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Question
1. Suppose that packets of size 8000 bytes are transmitted over a link which has a bit error rate of 10-6 Assume that errors in different bits of a packet are independent. For each part below, first provide an expression for the probability and then compute its numeric value specified as a decimal number in scientific notation with at least 6 digits of precision. (a) What is the probability that a packet is received with no erors? (b) What is the probability that it is received with exactly one bit in eror? (c) What is the probability that it is received with at least one bit in error?Explanation / Answer
Given size of the packet is = 8000 bytes = 64000 bits
Given bit error rate is = 10-6 = 1 / 106 which means out of
106 bits 1 bit will be error.
Hence bit error probability is = 1 / 106
a)
Probability that a packet is received with no errors is = (1 - 10-6 )64000
Here 1 - 10-6 means a bit receieved without error.
Here we are expecting all the 64000 bits of packet without errors
hence Probability of packet is received with no errors is = (1 - 10-6 )64000
= (0.999999)64000
= 0.9380049695
Hence Probability of packet is received with no errors is = 0.9380049695.
b)
Probability that a packet is received with exactly one bit error is = (1/64000 * 10-6 )
Hence Probability that a packet is received with exactly one bit error is = 0.000000000015625
c)
Probability that a packet is received with atleast one bit error is =
1 - Probability that a packet is received with no errors
Here in a we calculated Probability that a packet is received with no errors = 1 - 0.9380049695
Hence Probability that a packet is received with atleast one bit error is = 0.0619950305
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