Uniformly distributed noise. Let the input random variable X to a channel be uniformly distributed over the interval -(1)/(2) ≤x ≤ (1)/(2). Let the output of the channel be Y=X Z, where the noise random variable is uniformly distributed over the interval -a / 2 ≤z ≤ a / 2. (a) Find I(X ; Y) as a function of a. (b) For a=1 find the capacity of the channel when the input X is peak-limited; that is, the range of X is limited to -(1)/(2) ≤x ≤ (1)/(2). What probability distribution on X maximizes the

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