3. (Total: 20 pts) Consider a stochastic system which scales its input by A(t), where A(t) is a stochastic process. Hence Y(t) = A(t)X(t). where X (t) is the system input, Y(t) is the output. We assume A(t) has mean MA(t) and autocorrelation RAA(t1, t2). (a) (6 pts) Suppose X(t) is a deterministic signal. i. Find the mean of Y (t). ii. Find the autocorrelation of Y (t). iii. If A(t) is WSS, is Y(t) also WSS? Explain. (b) (14 pts) Suppose X(t) is a stochastic process with mean px (t) and autocorrelation Rx x(1, t2). We assume X(t) and A(t) are independent. i. Find the mean of Y (t). ii. Find the autocorrelation of Y(t). iii. Find the cross correlation Rxy (1, t2) between the input and the output. iv. If both A(t) and X(t) are WSS, is Y (t) also WSS? Explain. v. If both A(t) and X(t) are WSS, are X (t) and Y(t) jointly WSS? Explain. vi. Suppose both A(t) and X(t) were Gaussian processes. Would Y(t) be also Gaussian? Explain. vii. Suppose X(t) is a white noise process. Would Y'(t) be also white noise? Explain