Consider a binary communication system that transmits either a zero or a one with with probability pi and p2 respectively. Transmitting probabilities have a ratio of pi /p2 = 3/4. Because of channel noise, about 5 percent of the time a transmitted zero is received as a one, and 10 percent of time a transmitted one is received as a zero by error. 1) Compute the probability of receiving zero. p) Suppose a zero is received, what is the probability that a zero was transmitted? E) Determine the overall error rate of the system.

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Consider a binary communication system that transmits either a zero or a one with
with probability pı and p2 respectively. Transmitting probabilities have a ratio of
pi /p2 = 3/4. Because of channel noise, about 5 percent of the time a transmitted
zero is received as a one, and 10 percent of time a transmitted one is received as a
zero by error.
a) Compute the probability of receiving zero.
b) Suppose a zero is received, what is the probability that a zero was transmitted?
c) Determine the overall error rate of the system.
Transcribed Image Text:Consider a binary communication system that transmits either a zero or a one with with probability pı and p2 respectively. Transmitting probabilities have a ratio of pi /p2 = 3/4. Because of channel noise, about 5 percent of the time a transmitted zero is received as a one, and 10 percent of time a transmitted one is received as a zero by error. a) Compute the probability of receiving zero. b) Suppose a zero is received, what is the probability that a zero was transmitted? c) Determine the overall error rate of the system.
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