# Question

A communication system sends binary data {0 or 1} which is then detected at the receiver. The receiver occasionally makes mistakes and sometimes a 0 is sent and is detected as a 1 or a 1 can be sent and detected as a 0. Suppose the communication system is described by the following set of conditional probabilities:

(a) Assuming 0s and 1s are equally likely to be transmitted (i. e.Pr (0 transmitted) = 1/2 and Pr (1 transmitted) = 1/2), find Pr (0 received and Pr (1 received).

(b) Suppose a 0 is detected at the receiver. What is the probability that the transmitted bit was actually a 1? Also, if a 1 was detected at the receiver, what is the probability that the transmitted bit was actually a 0?

(c) What is the probability that the detected bit is not equal to the transmitted bit. This is the overall probability of error of the receiver.

(a) Assuming 0s and 1s are equally likely to be transmitted (i. e.Pr (0 transmitted) = 1/2 and Pr (1 transmitted) = 1/2), find Pr (0 received and Pr (1 received).

(b) Suppose a 0 is detected at the receiver. What is the probability that the transmitted bit was actually a 1? Also, if a 1 was detected at the receiver, what is the probability that the transmitted bit was actually a 0?

(c) What is the probability that the detected bit is not equal to the transmitted bit. This is the overall probability of error of the receiver.

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