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A modem transmits a +2 voltage signal into a channel.

A modem transmits a +2 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?
c). What is the probability that the output of the channel is positive?

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