4. Repetition code (10 points). Consider the binary communication link example on slide 11 of slide set#2 (Conditional Probability). To improve transmission reliability, an error correcting code is typically used. The simplest such code is the repetition code in which each bit is sent over the link It (odd) times and the receiver uses a majority vote to decide if the bit is a 1 or 0. Assume that given the value of the transmitted bit (0 or 1) in the k link transmissions are independent of each other. (a) Let X0 and X1 be the number of errors in the k transmissions given that the bit to be transmitted is 0 or 1 respectively. Find the pmfs of X0 and X1. (b) Let k = 5, What is the probability that the majority vote receiver makes an error? Hint: Find the probability of error given the bit sent is a 0 and a 1 separately and then use the law of total probability