. Let X(t) and Y(t) be zero-mean independent wide sense stationary random processes with autocorrelation functions R_{x}(\tau)=100 e^{-|\tau|} \cos (4 \pi) R_{x}(\tau)=50 e^{-\tau^{2}} Define a new random process Z(t)=X(t-1)+Y(t-2). Find

the auto correlation function of Z(t). Is Z(t) a wide sense stationary random process? Find the correlation function between Z(t) and Y(t).