Let {Z} be Gaussian white noise, i.e. {Zt} is a sequence of i.i.d. normal r.v.s each with mean zero and variance 1. Define Xt = J Zt, if t is even; (Z-1-1)/√2, if t is odd If {X} and {Y} are uncorrelated stationary sequences, i.e., if X, and Y, are uncorrelated for every r and s, show that {Xt + Yt} is stationary with autocovariance function equal to the sum of the autocovariance functions of {Xt} and {Y}.

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