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Let Jr.\" and t\" be the input and output respectively, of a binaryr channel. The channel response changes randome based on the value of a random variable R that is independent of it and has the following pmf: Prelim =}=p, Preb(R=1}=p1, Prcb{H=2)=p2: {po+p1 +p2= 1] The channel between X and Y is a BBC with a variable error probability e. such that lit, if]? = I} e: = 1,14, are = 1 1,!2, if]? = 2 In otherwords. the channel is described by: . IfR=, menv=xmmprobability1 I If R = 1, then Prett' = 1|X = 1] = Prob' = [III = Iii) = 334 and Prcb{Y = 1|}: = ) = Prcb' = DIX = 1) = 1K4 . If R = a, then Proof!" = 1p: = 1] = Prcb' = cur = c) = 1:2 and Prot" = 1|Jt' = ) = Prob" = DIX = 1) = If: a} Find the capacity,r of this channel if neither the transmitter nor the receiver has access to the value of the random variable ll. b} Now suppose that the encoder still has no access to the value of the random variable ll, but the receiver knows it for each transmission. In this case the channel can be thought of as having two outputs, it and R. Find the capacity of the channel in this case by maximizing rut; v, R]