The output of a communication channel is Y = X + N where X and N are independent, zero mean, random variables. X represents signal and N is noise. (a) Find the correlation coefficient between the input X and the output Y. (b) Suppose we form an estimate of X (call it 'X') by multiplying Y times a constant a or 'X' = aY. Find the value of the constant a that minimizes the mean square error given by E[(X-'X')^2]. (c) Express the resulting (mean square error)/(standard deviation of X)^2.