A modem transmits a signal, that is either a +1 voltage signal or a -1 voltage signal, into a channel. The channel adds to this signal a noise term that is drawn from the set {0, -1, -2, -3} with respective probabilities 4/10, 3/10, 2/10, 1/10.

(a) Find the pmf of the output Y of the channel.

(b) What is the probability that the output of the channel is equal to the input of the channel?