chosen as the message and the transmitter sends a signal over a medium to indicate

that choice. The receiver receives a corrupted version of that signal and makes the

best decision it can about whether a 0 or 1 was intended. Suppose that the message

is a 1 with probability p. Also suppose that no matter what the transmitted message

was, the receiver makes a random decision error about the transmitted message with

a probability . Let A be the event that the intended message was a 1, and B be the

event that the receiver decision was a 1.

(a) There are four possible outcomes for this experiment. List them along with their

associated probabilities.

(b) Find a value for for which the intended message and received message are

independent. Comment on the value of this as a practical communication system.