a) Compute the probability of receiving “101" in terms of a . Consider, transmitted sequence could be any one of them above. b) Suppose a sequence “101" is received, what is the probability that “101" was actually transmitted, in terms of a ?

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Chapter1: Combinatorial Analysis
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2- Consider a binary 3-bit communication system that transmits either zeros or ones with with probability
pi and p2 respectively. Transmitting probabilities have a ratio of p1 /p2 = 3/4. Because of channel
noise, a transmitted zero is received as a one with probability a , with a similar random corruption
a transmitted one is received as a zero by error.
Note that all possible 3-bit sequences (2 = 8 different ones such that “000"...to... “111") can be
received at remote site due to random noise, regardless of whatever host sent or vice versa.
a) Compute the probability of receiving “101" in terms of a . Consider, transmitted sequence could be
any one of them above.
b) Suppose a sequence “101" is received, what is the probability that "101" was actually transmitted, in
terms of a ?
Transcribed Image Text:2- Consider a binary 3-bit communication system that transmits either zeros or ones with with probability pi and p2 respectively. Transmitting probabilities have a ratio of p1 /p2 = 3/4. Because of channel noise, a transmitted zero is received as a one with probability a , with a similar random corruption a transmitted one is received as a zero by error. Note that all possible 3-bit sequences (2 = 8 different ones such that “000"...to... “111") can be received at remote site due to random noise, regardless of whatever host sent or vice versa. a) Compute the probability of receiving “101" in terms of a . Consider, transmitted sequence could be any one of them above. b) Suppose a sequence “101" is received, what is the probability that "101" was actually transmitted, in terms of a ?
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