Let us consider a binary symmetric channel, as shown in Figure 1, where the probabilities of the input X are Pr[X=0] = m and Pr[X = 1] = 1-m, and the error probability during the transmission from X and Y is p. 1-p 0 0 X Y P 1 1-p Figure 1: A typical binary symmetric channel, where the input is X and the output is Y. a) Given that p = 1/3 and m = 3/4, find H(X), H(Y), H(Y|X), and I(X;Y). (8 marks) b) Still given p = 1/3. Does m = 3/4 achieve the capacity of this binary symmetric channel? If not, find the capacity of this binary symmetric channel and find the value of m achieving this channel capacity. (4 marks) c) Is the following statement TRUE or FALSE: The capacity of the binary symmetric channel is de- pendent on the value of m. (No need to provide the justification for your answer.) (2 marks)