2. The input X to a communication channel is +1 or -1 with probabilities 1/4 and 3/4 respec- tively. The conditional probability of the channel output Y given that X = a is given as follows: 1- p -Pe if y = I, PY (y)@) = p if y = -I, Pe if y = 0, (i) (6 points) Find P(Y = 0). (ii) (7 points) Find P(X = +ily = 0). (iii) (7 points) Find P(X # Y)