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    Zero-Mean Gaussian Random Variable

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    Let X(t) be a random process defined as X(t)=Acos(Ω0t-θ), where A is a zero-mean Gaussian random variable with variance σ2A, θ is a random variable uniformly distributed on the interval [0,π], and θ and A are statistically independent. Is E[X(t)] constant? Is RXX(t1,t2) a function of t1 and t2 through the time difference τ = t1-t2?

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    Solution Preview

    See attached file.

    The statement of the problem lacks some details, so I have assumed what looks like the likely details possibly meant to be there, in the attached file with explanations.

    Let X(t) be a random process defined as X(t)=Acos(ω0t-θ), where A is a zero-mean Gaussian random variable with variance σ2A, θ is a random variable uniformly distributed on the interval [0,π], and ...

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    The solution discusses zero-mean Gaussian random variable.

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