Consider a non- linear device such that the output is Y (t) = aX2 (t), where the input X (t) consists of a signal plus a noise component, X (t) = S (t) + N (t). Determine the mean and autocorrelation function for Y (t) when the signal S (t) and the noise N (t) are both Gaussian random processes and wide sense stationary (WSS) with zero- mean and S (t) is independent of N (t).