A modem transmits a +2 voltage signal into a channel. Thechannel adds to this si

Question

A modem transmits a +2 voltage signal into a channel. Thechannel 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 isequal to the input of the channel? c). What is the probability that the output of the channel ispositive? A modem transmits a +2 voltage signal into a channel. Thechannel 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 isequal to the input of the channel? c). What is the probability that the output of the channel ispositive?

Explanation / Answer

Let X be the value for noise a/ --> pmf for Y=f(x) = 2+x, (x=0,-1,-2,-3) Note that Y={+2,+1,0,-1}
b/ When x=0, output level = input level = +2
P(output=input) = P(X=0) = 4/10
c/P(output=positive) = P(X=0 or -1) = 4/10+3/10=7/10

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