A transmitter transmits a message (a string of symbols) through a noisy communication channel. Each transmitted symbol is 0 or 1 with probability 6 10 and 4 10 , respectively. A 0 or 1 symbol is received incorrectly with probability 2 10 and 1 10 , respectively. Errors in different symbol transmissions are independent. a. Find the probability that a symbol is received incorrectly.
b. Find the probability that the string of symbols 1001010 is received correctly.
c. To increase the reliability of this communication system, each symbol is transmitted seven times and the received string is decoded by the majority rule. Find the probability that 1 is correctly decoded, i. e., that a 1 is decoded when a 1 is transmitted. You may leave your answer as a mathematical expression if you can't evaluate it.
d. Suppose that the redundant scheme of part (c) is used. What is the probability of a symbol being received incorrectly in this redundant scheme? You may leave your answer as a mathematical expression if you can't evaluate it.
e. Suppose that the redundant scheme of part (c) is used. What is the probability that the symbol sent was 1 given that the received string was 1011001? Is a 0 or 1 more likely to have been sent when 1011001 is received?