A ternary confusion channel with input x and output y has transition probability matrix: X a b C 1 1/2 1/2 1 M N Y Px (a) Assume input has the following distribution, please find the mutual information between the input and output. 1 1) e = [ [1 1/2 01 lo 1/2 Transition matrix p(y|x) 3' 3' (b) Please find the channel capacity and the optimal input probability distribution that achieves the capacity.