Let X (t) be a wide sense stationary random process that is ergodic in the mean and

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Let X (t) be a wide sense stationary random process that is ergodic in the mean and the autocorrelation. However, X (t) is not zero- mean. Let Y (t) = CX (t), where C is a random variable independent of X (t) and C is not zero- mean. Show that Y (t) is not ergodic in the mean or the autocorrelation.
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